Research Article Designing a Channel Access Mechanism for Wireless Sensor Network

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1 Hindawi Wireless Commnications and Mobile Compting Volme 217, Article ID , 31 pages Research Article Designing a Channel Access Mechanism for Wireless Sensor Network Basma M. Mohammad El-Basioni, 1 Abdellatif I. Mostafa, 2 Sherine M. Abd El-Kader, 1 and Hssein A. Konber 2 1 Electronics Research Institte, Cairo, Egypt 2 Faclty of Engineering, Al-Azhar University, Cairo, Egypt Correspondence shold be addressed to Basma M. Mohammad El-Basioni; bbasioni@eri.sci.eg Received 29 Jly 216; Revised 6 November 216; Accepted 23 November 216; Pblished 17 Janary 217 Academic Editor: Stefano Savazzi Copyright 217 Basma M. Mohammad El-Basioni et al. This is an open access article distribted nder the Creative Commons Attribtion License, which permits nrestricted se, distribtion, and reprodction in any medim, provided the original work is properly cited. Althogh there are varios Medim Access Control (MAC) protocols proposed for Wireless Sensor Network (WSN), there is no protocol accepted as a standard specific to it. This paper deals with completing the design of or previosly proposed MAC for WSN by proposing a channel access mechanism (CAM). The CAM is based on developing a backoff mechanism which mainly differentiates nodes backoffs depending on their different identification nmbers, and it employs a performance tning parameter for reaching a reqired performance objective. The probability distribtion of the backoff period is constrcted and Markov chain modeling is sed to analyze and evalate the CAM against the IEEE slotted CSMA/CA based on single- and mltihop commnication with respect to the reliability, the average delay, the power consmption, and the throghpt. The analysis reveals that the reqired performance of CAM against the IEEE slotted CSMA/CA can be obtained by choosing the maximm backoff stages nmber and the tning parameter vale and that CAM performs better than the IEEE with larger nodes nmber. The mltihop scenario reslts in a good end-to-end performance of CAM with respect to the reliability and delay becomes better with lengthier paths at the expense of increasing the energy consmption. 1. Introdction MAC [1 3] is the rdiment for any wireless commnication system to fnction properly. It coordinates access to and transmission over the medim common to several nodes and pts rles to minimize interference and packet collisions among them nder imposed constraints and desired performance goals. It is not highly tre to say that the collision case is the concrrent transmissions, becase concrrent transmissions may not case collision even if the transmitters reside in the same radio range. It is better not to point to the sender in clarifying the case of the collision, bt referring it to the receiver where the collision occrs at a receiver de to its reception to more than one signal at the same time becase of its residence in the common transmission area of more than one transmitter whether it is the intended receiver of one or more of them. The MAC protocols can be divided into two main approaches, contention-based [4, 5] (random assignment protocols) and contention-free [6, 7] (schedle-based) of which indoors may be classified into fixed-assignment protocols and demand-assignment protocols. Far from the bad channel tilization of the fixed-assignment and its other cons and far from the additional overhead of the demandassignment throgh polling and reservation, the contentionbased MAC protocol is more logical for accessing the channel; however, it is more prone to fail in sccessfl medim allocation and collision prevention. This depends on the characteristics of the contention-based MAC protocol itself and another high importance factor which is the logical topology that determines the nmber of talkers, who can talk to who, when and where they can talk, at what range, and so forth. Basedonthat,itispreferredtoseacontention-based MAC with a good performance works on a logical topology

2 2 Wireless Commnications and Mobile Compting pavedforitespeciallywithrespecttopredictabilityand nmber of contending nodes, where the condition nder which these protocols may fail in preventing collisions is the sorces nmber increase or the sorces transmission rate increase. The MAC layer design intended by the work proposed in this paper is based on the physical layer of the IEEE standard [8 1] and composed of two techniqes, a timing strctre mechanism (TSM), proposed by or previos work [11], inclding the setp of the logical topology by dividing the network into sbnetworks (sb-nws) sing mltichannels and identifying the time strctre of the sb-nw members work and the contention-based CAM proposed in this paper. The main TSM idea was to constrct a receive schedle which makes, at a time, only one node from a grop of nodes (sb- NW)listentothechannel,andeachnodetakesitstrn sccessively to listen for a small period. At any time a node wants to transmit, it can trn its radio to the transmit state and transmit directly in its maximm range or in a range sitable to the crrently listening node sing the CAM. The backoff periods are aligned with a reference time common to the nodes. The CAM is designed to be sitable to the proposed TSM and benefits from it, and it is based on developing a backoff mechanism, resorting to the common manner of increasing the backoff stages (i.e., repeating the trials of accessing the channel if it is fond bsy rather than annoncing channel access failre and discarding the packet), and sing a nmber of transmission trials to cope with the transmission failre rather than discarding the packet. The rest of this paper is organized as follows. Section 2 incldes a brief literatre review for wireless MAC protocols. Section 3 begins with giving an overview of the beaconenabled IEEE slotted CSMA/CA; then it illstrates the proposed CAM idea and its modeling. The performance assessment of CAM is depicted in Section 4, where the CAM performance is evalated against the slotted CSMA/CA in terms of single- and mltihop commnication; also the effect of different parameters on CAM performance and its tning is considered. Finally, Section 5 concldes the paper and sggests open isses for ftre work. 2. Literatre Review The wireless medim access schemes sed in different types of wireless networks are based on carrier sensing, backoff algorithms and mechanisms for avoiding hidden and exposed terminal problems. The Carrier Sense Mltiple Access with Collision Avoidance (CSMA/CA) with its two versions, nonpersistent and p-persistent, represents the basic form of channel access control. In nonpersistent CSMA, if the device senses the channel bsy, it backs off before trying to transmit again. When the channel is idle, the device transmits immediately. In p-persistent CSMA, the device contines sensing the bsy channel ntil it becomes idle, and in case of idle channel, it transmits or defers transmission according to a probability p. Keeping devices in the receive state when not transmitting consmes a large amont of energy. Mltiple Access with Collision Avoidance (MACA) [12] ses two additional packets, Reqest-to-Send (RTS) and Clear-to-Send (CTS) before the transmission to redce the occrrence of the hidden and exposed terminal problems. The RTS is sent by the sender, and the receiver willing to accept data responds with CTS; the other devices hear the RTSortheCTSandavoidinterferingtheinvolveddevices ntil end of transmission. The RTS/CTS represents overload on the network and cases additional delay. Modifications to these schemes were then proposed, sch as sing acknowledgment, sing Reqest-for-Reqest-to- Send packet by a bsy RTS receiver after finishing its transaction, employing waiting intervals other than the backoff time providing priority levels for wireless channel access as sed in the IEEE82.11 [13] distribted coordination fnction, and sing variations in backoff time comptation method sch as binary exponential backoff, mltiplicative increase and linear decrease, balanced backoff algorithm, and waiting time based backoff. Wireless networks do not only se contentionbased schemes bt also se contention-free access sch as the point coordination fnction defined in IEEE82.11 in which a coordinator device polls other devices for data. De to the energy constraint in WSN, the design of WSN MAC considers other mechanisms, in addition to that sed in coordinating the shared medim allocation and controls nodes activation to allow them to sleep saving their energy wasted in idle listening and overhearing. The sed medim allocation scheme itself shold be energy-efficient; for example, it does not employ large overhead. The MAC protocolsproposedinliteratreforwsncanbebroadly classified according to the scheme depicted in Figre 1. The contention-based synchronos sleep-schedling [14] can be throgh having each node following a periodic active/sleep cycle; the nodes that are close to one another synchronize their active cycles together, and if the next hop of a transmission overhears it, it remains awake ntil receiving the forwarded data rather than sleeping and delaying data forwarding p to its next active cycle. Bt this is not always the case, the next-hop node may be ot of the hearing range of both the sender and the receiver making data forwarding interrption problem navoidable; the staggered wake-p schedling [15, 16] is sed to address this problem which creates a pipeline for data propagation based on the depthlevel of nodes in a data-gathering tree, where the active period of one level partially overlaps with that of the lower level. In the asynchronos sender-initiated MAC [17, 18], the sender transmits a preamble to indicate a pending transmission. The receiver wakes p occasionally to listen to sch a preamble for appropriately responding. In receiverinitiated schemes [19], instead of long preambles, the sender listens to the channel waiting for the receiver small beacons, transmitted in dty cycle fashion, to synchronize with the receiver. The asynchronos schemes are simpler to implement than the synchronos bt it may reslt in very long delay. WSN MAC can be contention-free sing Time Division Mltiple Access (TDMA) or Freqency Division Mltiple Access (FDMA) or hybrid. In mltichannel MAC [2, 21], some isses are raised sch as limited nmber of available channels, channel selection and assignment policy, and recrsive channel switching overhead. Radio-triggered

3 Wireless Commnications and Mobile Compting 3 MAC protocols Sleep-based MAC protocols Radio-triggered MAC protocols Trying to redce the energy a node consmes in idle listening by concerning and dealing with node HW itself Cross-layer MAC protocol efforts Integrating MAC design with other layers to improve the performance On-demand wake-p (two channel wakep radio) Adding a circit of passive radio sensor hardware or separate low power wake-p receiver to the nodes responsible for waking p the ordinary RF transceiver Intermediate power level-based Optimizing the radio sleep capabilities sing existing node HW Centralized Distribted More efficient than distribted, bt less sitable to WSN Contention-based More simple to implement, scalable, and robst than centralized Contention-free Synchronos Asynchronos TDMA The most sed for WSN FDMA CDMA Not sitable for WSN Active sleep dty cycling Staggered wake-p schedling Sender-initiated (preamble sampling-based) Receiver-initiated (wakep beacons-based) Figre 1: Different approaches for WSN MAC protocols. MAC [22, 23] and cross-layer MAC [24, 25] designs are otherapproachesproposedforwsnwhichcanbeemployed with different types of channel access mechanisms. If radiotriggeredid[26,27]issed,anadditionalwake-phardware corresponding to each sed freqency and a transmitter able to transmit at different freqencies simltaneosly will be reqired. IEEE is the de facto physical and MAC layers standard specification sed for WSNs. In IEEE MAC, the channel time is bonded sing a sperframe strctre bonded by periodic transmission of a beacon frame. The sperframe has active/inactive portions, a CSMA-based Contention Access Period (CAP), and an optional reservationbased Garanteed Time Slot (GTS) scheme intended to spport devices reqiring dedicated bandwidth or low latency transmission throgh a Contention-Free Period (CFP). In or previos work [11], the channel time bonding mechanismoftheproposedmacisimplementedandevalated against the IEEE MAC sperframe strctre in a complete network form sing the same contention-based channel access mechanism sed in the standard and illstrated in the next section. In this paper, a design for the proposed MAC contention-based channel access mechanism isimplementedandevalatedagainstthestandard. 3. CAM Idea Implementation, Evalation, and Modeling This section firstly gives an explanation and insight on the IEEE contention-based channel access mechanism, and then it proceeds to explain the new backoff method of the proposed CAM which represents the difference between it and the standard channel access mechanism. This section also incldes a simple simlation-based evalation of CAM as a proof of concept and it ends with introdcing the CAM modeling Overview of the Beacon-Enabled IEEE Slotted CSMA/CA. The IEEE standard specifies the physical layer and media access control layer for low-rate wireless personal area networks (LR-WPANs), and based on it, other standards which define the pper layers of the stack are developed, sch as ZigBee [28], ISA1.11a [29], WirelessHART [3], MiWi [31], and 6LoWPAN [32].

4 4 Wireless Commnications and Mobile Compting The IEEE network can operate in two modes of operation beacon- or nonbeacon-enabled modes. In nonbeacon-enabled mode, the peer-to-peer data transfer model, in which the devices wishing to commnicate need to receive constantly and simply transmit its data sing nslotted CSMA/CA, is employed. Indeed, this consmes more nodes energy as ndesirable manner for battery-powered nodes.thebeacon-enabledmodeismoresitableforbatterypowered nodes, where in this mode, a star topology is formed between devices and a single central controller, called the coordinator; these devices are allowed to sleep most of their times, while the coordinator listens to the channel for a longer time bt also is allowed to sleep periodically. The coordinator bonds its channel time sing a sperframe strctre bonded by the transmission of a beacon frame. Inbeacon-enabledmode,theslottedCSMA/CAchannel access mechanism, in which nits of time called backoff periods (backoff slots) are aligned with the start of the beacon transmission and each time a device wishes to transmit data frames, it shall locate the bondary of the next backoff slot and then wait for a random nmber of backoff slots. If the channel is idle, the device can begin transmitting on the next available backoff slot bondary; otherwise, following this random backoff, the device shall wait for another random nmber of backoff slots before trying to access the channel again. Each device shall maintain three variables for each transmission attempt: NB, CW, and BE: NB holds the nmber of times the CSMA/CA algorithm attempts to access the channel to transmit the crrent packet and it is initialized to zero before every new transmission. The vale of the attribte macmaxcsmabackoffs determines the maximm vale for this variable; that is, it determines the nmber of allowed attempts for CSMA/CA algorithm to accessthechanneltosendapacketbeforereportingchannel access failre; if the vale of NB is greater than macmaxcs- MABackoffs, the CSMA/CA algorithm shall terminate with a CHANNEL ACCESS FAILURE stats. CW defines the fixed nmber of backoff periods that the channel has to be idle before a node can start to transmit and in the standard it is set to 2 backoff periods. According to that, it is initialized to 2 before each transmission attempt and reset to 2 each time the channel is assmed to be bsy. BE refers to the backoff exponent, a basis of two is raised to the BE power (2 BE )toindicatethecontofpossiblebackoff periods nmber, and the CSMA/CA can randomly choose onefromthemtowaitthischosenbackoffperiodsnmber before attempting to assess the channel. This cont (2 BE ) represents a range of consective nmbers of backoff periods beginning from backoff period and so ending with (2 BE 1) backoff period. Each channel access attempt failre for a transmission, BE, is incremented by one to doble the range of possible backoff periods nmbers bt p to a maximm vale eqal to the vale of the amaxbe constant beyond which its vale is frozen, and also it has a minimm vale, macminbe (referred in the paper as m ). The slotted CSMA/CA prposes making the performing of the Clear Channel Assessment (CCA) and starting of Node 1 Node 2 Node 3 CCA atrnarondtime (8 symbols) (12 symbols) Backoff period (2 symbols) The start of the transmission if the channel assessed idle Figre 2: Illstration of the backoff period. Time Figre 3: The effect of a backoff period smaller than 2 symbols. packet transmission operations of nodes be aligned, conseqently, overlap of CCA operations will not occr, and neither false idle channel assessment nor collisions may occr. Not only does the synchronization of backoff periods achieve that, bt also the choice of the nit backoff period valeaffectsthisaim.thevaleofthebackoffperiodis selected to be eqal to a CCA dration pls a trnarond time for changing the transceiver to the transmit state which is the time taken by the node to be ready for the transmission start. Sothebackoffperiodeqals2symbolasshowninFigre2. If it is said that small backoff period is better to decrease the delay, the reply will be that if the backoff period is smaller than 2 symbols there will be an overlap among the CCA and trnarond times of nodes as shown in Figre 3. Node 2 sensed the channel idle and started to trn its transmitter on; dring that Node 1 was assessing the channel and its assessment ended before or on or jst after the time Node 2 began to send, and it did not hear its transmission and proceeded to transmit. The same thing can happen between Node 1 and Node 3. Althogh the nodes started to assess the channel in different backoff periods, they collided. The backoff period shold not also be greater than 2 symbols. A greater period, as illstrated in Figre 4, increases the delay which reslted from the backoff time and from locating the next backoff slot bondary withot any additional beneficial effect on preventing the channel sensing overlap and collisions. The CW is selected to be 2 backoff periods; that is, the node shold be sre that two idle CCA operations were performed before the beginning to transmit for preventing potential collisions of acknowledgement frames. If the reception of a packet had been completed at a node before the backoff period bondary at which it began to perform its

5 Wireless Commnications and Mobile Compting 5 Node 1 Node 2 Figre 4: The effect of a backoff period greater than 2 symbols. CCA and accordingly its reception had been completed at its destination node before the same backoff bondary (this packet can be ndeliverable by this node which wants to transmit while its acknowledgement is deliverable; that is, thesorcenodeoftheacknowledgedpacketcanbeotof therangeofthenodewantstotransmit,btthenodewants to transmit and its intended receiver fall in the range of the destination node), an overlap wold occr between the delay consmed by the destination node compted starting from the time of packet reception completion and represented in the trnarond time and the backoff period bondary locating delay to start sending the reqired acknowledgement and the CCA of the node wants to transmit which sensed thechannelidlewhileanacknowledgementwasgoingtobe transmitted. If this node does not perform a second CCA, it will start to transmit its packet with the destination node acknowledgement transmission and a collision wold occr, as illstrated in the Figre Backoff Method Explanation. In the proposed backoff method, the node comptes the backoff time in each backoff stage from bf (s) = (ID + intniform (, RID mod (s+1))) mod (2 m s 1 b )+( mod (+1), j= (bf (j) + cca (j))) where bf(s) is the fnction sed by a node to compte its backoff time in a backoff stage s, s is the index of the backoff stage in range [, m], ID refers to the identification of the node comptes the backoff period, RID refers to the identification of a receiving node, and cca(s) is a fnction which gives the time spent in channel sensing in stage s. In (bf(j) + cca(j)) is referred to as the backoff sm and denoted by bfsm(s). The first term of the eqation aims to make the backoff time of each node different from the others by making it dependent on their different identification nmbers, so that ifmorethanonenodehavedatatosendatthesametime, they wait different time periods before starting to sense the channel. The integer niform random nmber, intniform(, RID mod(s + 1)), sed in the first term depends on the identification of the receiving node. The prpose of this is to differentiate the backoff time of a certain node with the analysis, the clase s 1 j= (1) the passage of time, taking advantage of the presence of different receiving nodes, so that no node always has to wait a bigger time than its competitors; and this prevents the error repeating by backing off the same period each backoff trial after an overlapped sensing is done. Bt this random nmber islimitedtoacertainrangebyconsideringthemodlsof RID and a certain vale made to be dependent on the index of the backoff stage also in order to differentiate the backoff withtimeandsothatthepossiblerangetoanodeisallowed to become greater each backoff trial. The second term of the eqation considers the fact that the nodes may have data to send already in different times bt their different compted backoff delays make them start sensing the channel at the same time. Therefore, this term makes the backoff times chosen by the nodes depends on their starting time of having the data which is different among them; in this case, this is achieved by taking the sm of the delays which reslted from the previosly encontered backoff stages for this data (if any). For limiting the backoff time to a certain maximm limit, regardless of the vales of nodes IDs, the modlar arithmetic is involved in the two terms of the eqation, and themaximmlimitisselectedtobeasthemaximmlimitof backoff in the IEEE standard which eqals (2 m b 1), where m b is the maximm backoff exponent. The modli of the modlar operations determine the range of each eqation s term resltant vales; therefore it is made to be dependent on a parameter which controls the maximm vale of each term. The increase in vale increases the maximm vale of the second term while decreasing that of the first term and vice versa; by the same logic, is sed as a tning parameter for performance metrics. The range of is [, 2 m b 1]; the vales of the two variables ID and RID fall in the range [1, N], where N is the nmber of nodes in the sb-nw, assmed to fall within range [2, ) Using R Langage to Simlate Nodes Backoff. Acode in R langage [33] was written to simlate the nodes backoffs pon (1) and qickly manifest their corresponding behavior and its impact on star topology data transmission specially with respect to the eventating of collisions and channel access overlap at different simple assmption-based scenarios. The code assmes that each node takes its trn as a star topology receiver pon a predetermined schedle for a period eqal to a complete transaction (13-backoff nit). The node does not start a transmission process ntil it finishes its receiving slot. Packet generation is exponentially distribted over nodes with rate eqal to 1 and limited to be 1 packet per node over the simlation time. The packet generation time for all nodes is limited to be within a certain period from the start time to garantee that all nodes will have data to send dring the test period. There is only one transmission trial bt a nmber of backoff stages are allowed. The considered parameters are compted by averaging the otpts of a nmber of code rns (in each rn the time of having data for each node is changed).

6 6 Wireless Commnications and Mobile Compting.192 Destination node Received data Pkt. Transmitted Ack Node wants to transmit Received data Pkt. Transmitted data Pkt. 1st CCA 2nd CCA Figre 5: Illstration of the importance of performing two CCAs. Avg nmber of collisions Nmber of nodes Figre 6: CAM average nmber of collisions verss nmber of nodes. Loss percentage de to collision (%) Nmber of nodes Figre 7: CAM loss percentage de to collision verss nmber of nodes. By setting m to 5, m b to 5, to 5, and the time within which each node will generate a packet to 124 backoff nit, Figre 6 shows that the average nmber of collisions increases polynomially with the increase of the nmber of contending nodes with instantaneos rate of change linearly increases with increasing nodes nmber. This increase of collisions nmber and the inherent increase of nodes nmber which case the collision s conflict reslt in the increase of the loss percentage de to collisions occrrence; as shown in Figre 7, the loss percentage reached approximately 13% when nodes nmber is 7. Figre 8 shows the percentages of both the total nmber of time slots which enconter overlap in transmission attempts starts and the nmber of time slots which case concrrent channel access and accordingly collisions with respecttothetotalnmberofchannelaccessattempts.while Figre 9 draws the nmber of collision-prone transmission attempts which enconter conflict at the start of backoff comptation and the nmber of collision-raiser time slots, this is compted with restricting the time of nodes start data generation to a small period to increase the chances of concrrent transmission and channel access attempts. Percentage from total channel access attempts (%) Nmber of nodes Collision-prone sitations Collisions Figre 8: CAM percentages of collision-prone and collision-raiser sitations.

7 Wireless Commnications and Mobile Compting 7 Nmber of occrrences Collision-prone sitations Collisions Nmber of nodes Figre 9: CAM nmber of collision-prone and collision-raiser sitations. It is apparent from Figre 9 that the nmber of collisions happened is smaller with a big percentage than the nmber of chances that wold case them if the conflicting nodes select similar backoff periods. It cold be said that the backoff method solves approximately, on average, 8.8% of the channel access conflict sitations encontered; actally some of these sitations are originally cased by the backoff method itself de to its incapability to perfectly prevent conflicts, bt it is able to mend from this if the channel is fond bsy and no collision occr by preventing the repeating of the conflict at the following concrrent starts of transmission attempts of the conflicting nodes which decreases the nmber of collisions. However, generally the percentage of the total nmber of eventated conflicts with respect to the total nmber of channel access attempts is not considered to be a big percentage, as shown in Figre 8. Figre 1 indicates the fairness of the backoff method with respect to the backoff delay compted as the standard deviation of the average backoff delay encontered by each node. As indicated by Figre 1, the vale has a noticeable impact on the backoff delay fairness among nodes as it controls modlating high vales compted for the backoff to lower vales specially the ID-dependent vales and the effect of the integer niform random nmber sed in the first termofthebackoffeqationwillbemoreapparentwhen is big or is small and N is big. When is small and N less than 2 m b, the backoff delay fairness is better at lower N vales, while when N exceeds 2 m b,aworsefairness obtained changes between fall and rise with increasing N bt with small amont. When is big the ID-dependent vale, which is main contribtor in differentiating backoff delays, ismodlatedtosmallrangeofvaleswhichcasesmore fairness at higher vales decreases when N increases de to the effect of the second term of the eqation. Standard deviation of the average backoff delay =25 = Nmber of nodes Figre 1: CAM fairness with respect to backoff delay. After clarifying and proving the idea sing simple assmption-based simlation scenarios, the sbseqent sections consider a precios general modeling and evalation of the CAM CAM Modeling. In this section, a Markov chain [34] model for the CAM will be implemented. Regarding the IEEE slotted CSMA/CA, the generalized model presented in [35] is sed for its implementation; also this modelissedasabasisforcammodeling;thiswork represents a generalized accrate model which can be sed foreffectiveanalysisintermsofreliability,delay,andenergy consmption. It takes into accont the fll fnctionality of the protocol, the core of IEEE which is the exponential backoff process which is modeled, backoff stages limit, retry limits, acknowledgements, and nsatrated traffic. The state transition model represents the proposed CAM which is depicted in Figre 11. As indicated in the model, the three-dimensional Markov chain is described sing three stochastic processes, g(t), c(t), andy(t) which represent the backoff stage at time t, the state of the backoff conter at time t, and the state of retransmission conter at time t, respectively. The states from (i, 1, j) to (i, 2 m b 1,j)are the backoff states, the states (Q,...,Q L 1) consider the idle state when the qee is empty and the node is waiting for a new packet arrival, states (i,, j) and (i, 1, j) represent the first and second CCA, respectively, and states ( 1, k, j) and ( 2, k, j) model the sccessfl transmission and packet collision, respectively. The MAC qee is assmed to be a first-in-first-ot M/M/1 qee for both CAM and slotted CSMA/CA. The generated packets arrive at the qee with rate of λ packets persecond(pps).themeanservicerateμ of the qee packets eqals the reciprocal of the mean packet service time. Some of the notations sed in the analysis throghot the paper are present in Notations Comptation of the Backoff Probability Distribtion. In this section we are going to constrct the probability

8 8 Wireless Commnications and Mobile Compting 2,, n 2, L c 1, n q Q q Q 1 q 1, L s 1, 1 q Q L 1 1 q 1,, 1 q p K (k I = ) 1 P 1, 1, 1,, 1, 1,, 2 m 2, 1, 2 m 1, P p K (k I = 1) p K (k I = m) 1 P 1 1, 1, m,, 1 m, 1, m, 2 m 2, 1 m, 2 m 1, P 2,, 2, L c 1, p K (k I = ) 1, L s 1, 1 1,, 1 1, 1, 1,, 1 1, 1, 1 1 p K (k I = 1), 2 m 2, 1 1, 2 m 1, 1 1 P P 1, 1, 1 1 m,, 1 1 m, 1,1 p K (k I = m) m, 2 m 2, 1 1 m, 2 m 1, 1 1 P P 2,, 1 2, L c 1, 1 p K (k I = ). 1, L s 1, n 1,, n p K (k I = ) 1 P 1 1, 1, n,, n 1, 1,n, 2 m 2, n 1, 2 m 1, n P p K (k I = 1) p K (k I = m) 1 P 1, 1, n 1 m,, n 1 m, 1, n m, 2 m 2, n 1 m, 2 m 1, n P Figre 11: State transition model for CAM.

9 Wireless Commnications and Mobile Compting 9 distribtion of the backoff period generated by a node in different backoff stages p K (k I = i) in case the node commnicates with its sb-nw members and in case the node commnicates with the Base Station (BS). To achieve that, the following definitions are introdced which are derived from generating the set of all possible backoff period vales with experiments which consider all the possible combinations of the backoff eqation variables vales nder specifiedconditions.therlangageissedtogenerate these experiments otcome, and the relations which describe the probability distribtion are derived from observing the pattern of these otcomes. In CAM, the receiving node identification, RID vale, may vary throgh the sccessive backoff stages; especially, according to the previosly proposed TSM, the receiving node in each receiving slot of the time frame is different; ths, the possible RID vales in different backoff stages encontered by a node can be represented by a permtation (with repetition). The effect of the RID valeonthevaleof the backoff periods compted by a node in different stages appears in the integer niform random nmber clase in the first term of the backoff eqation as an added vale to the node ID. This added vale, referred to as ADV, falls within a range; its lower bond is and its pper bond depends on the RID vale in the considered backoff stage with a maximm possible vale eqal to the nmber of the backoff stage; based on that, the range of ADV is indicated in the following definitions by its variable pper bond (UB). The following definitions find the probability of a certain backoff period vale compted by a node in terms of the nmber of times this node comptes it and the total nmber of the backoff periods compted by the node. The mathematical formlation of the backoff period probability depends on exploiting the recrrence of the combinations of variables case a backoff vale throgh a calclable nmber of repeating times rather than iteratively comptes all the backoff vales and then extracts the reqired information from them. This treats the problem of the long time consmediniterativecomptationwhichmaybeconsidered as an almost infinite with the hge nmber of iterations corresponding to the hge nmber of variables combinations which increases inflation with increasing the nodes nmber and the backoff stages nmber. Simpler expressions to take smaller time for compting the nmber of occrrence times of a backoff vale nder certain conditions are depicted in Appendix A. Definition 1. Let r(ub, s) beafnctionsedtocomptethe nmber of RID vales which reslt in a specific range of the ADV in a backoff stage s. Thenr(UB, s) is a fnction of this range UB and it can be compted as follows: N s+1 r (UB, s) = N s+1 +1 N s+1 1 if condition1 and condition2 are both tre or false if condition1 is tre and condition2 is false if condition1 is false and condition2 is tre, (2) where condition1 is eqivalent to Nmod(s + 1) UB >, condition2 is eqivalent to UB=IDmod(s + 1),and is the floor fnction. Definition 2. Let rnm(ub, s) denote the nmber of occrrence times of a specific range UB in a backoff stage s. Then rnm(ub, s) eqals the nmber of RID vales which reslt in the UB in the backoff stage s mltiplied by the nmber of occrrence times of a RID valeinastage,anditiscompted as follows: rnm (UB, s) = r (UB, s)(n 1) S, (3) where S is the stage at which we want to compte the backoff period, S [, m],ands [,S]. Definition 3. Let C be a two-dimensional array which represents the combinations of ADV throgh all stages from to S. ThearrayC hasnmberofrowseqalto(s + 1)! indexed by ro, one row for each combination; accordingly the nmber of the colmns of C eqals S+1indexed by co. Let V be a set of S+1vectors, where V=V, V 1,...,V S }. Vector V s represents the maximm range of ADV in stage s which is [, s]. If we denote the nmber of occrrence times of one combination corresponding to a row ro in C by cnm(ro), then cnm(ro) eqals the maximm nmber of occrrence times of a combination corresponding to a row in C mltiplied by the probability of occrrence of the intended combination corresponding to a row ro: cnm (ro) S+1 = max (rnm) = (N 1) z=1 S+1 S+1 z=1 ( ( z e=1 c ro,z V z 1 e z e=1 c ro,z V z 1 e rnm (V z 1 e,z 1) (N 1) S+1 ) rnm (V z 1 e,z 1) (N 1) S+1 ), where c ro,z is the element of the array C at the row nmber ro andcolmnnmberz and V z 1 e is the element nmber e in the vector V which corresponds to stage nmber z 1. (4)

10 1 Wireless Commnications and Mobile Compting Definition 4. Letthetotalnmberofoccrrencetimesofthe set of all possible backoff period vales of an experiment otcome be denoted by the notation tknm(s). Then tknm(s) eqals the sm of the nmber of occrrence times of all the ADV combinations which constitte the rows of C mltiplied by the nmber of the combinations of the time nits sed to perform CCA throgh a nmber of S stages; namely, tknm (S) =2 (S+1)! S ro=1 cnm (ro), (5) for every ID [1, N], [,2 m b 1],andS [,m]. Definition 5. Let the nmber of occrrence times of a possible backoff period valek of an experiment otcome be denoted by the notation knm(k, S), andletthe2 S -by-s matrix A represent all the combinations of the nmber of the time nits sed to perform CCA in all stages; then for every ID [1, N], [,2 m b 1], S [,m],anda aro A, where knm (k, S) = (S+1)! ro=1 k=bf ro (S) bf ro (S) =(ID+c ro,s+1 ) mod (2 m b ) bfsm () =, bfsm (S) = + (bfsm (S)) mod (+1), S (ID + c ro,co ) mod (2 m b ) co=1 + (bfsm (co 1)) mod (+1) +a aro,co cnm (ro), (6) when S>. The previos definitions relate the commnication within the sb-nw; the following definitions, Definitions 6 and 7, consider the commnication with the BS distingished by the existence of only one possible receiver, which is the BS, identified by ; therefore in this case, RID always eqals. Definition 6. Let the total nmber of occrrence times of the set of all possible backoff period vales of an experiment otcome, de to the commnication with the BS, be denoted by the notation bstknm(s);then bstknm(s) is defined as (7) bstknm (S) =2 S, (8) for every ID [1, N], [,2 m b 1],andS [,m]. Definition 7. Let the nmber of occrrence times of a possible backoff period vale k of an experiment otcome, de to the commnication with the BS, be denoted by the notation bsknm(k, S), andletthe2 S -by-s matrix A represent all the combinations of the nmber of the time nits sed to perform CCA in all stages; then for every ID [1, N], [,2 m b 1], S [,m],anda aro A, where bsknm (k, S) = bf (S) =IDmod (2 m b ) bfsm () =, bfsm (S) = 1, k=bf(s) + (bfsm (S)) mod (+1), S ID mod (2 m b ) co=1 + (bfsm (co 1)) mod (+1) +a aro,co when S>. (9) (1) Definition 8. The probability distribtion of the backoff period generated by a node in different backoff stages p K (k I=i)is compted as follows: for every k [,2 m b 1]and i [,m], p K (k I=i) = 1 N p K (k I=i) = 1 N N knm (k, i) ID=1 tknm (i) for sb-nw commnication, N bsknm (k, i) ID=1 bstknm (i) for commnicating BS. (11) Deriving the Stationary Distribtion. The nonzero state transition probabilities associated with the CAM Markov chain of Figre 11 represent the state transition de to decrementing the backoff conter by one, the transition from one backoff stage to the next one de to sensing the channel bsy, the transition from one transmission trail to the next one de to collision occrrence, the transition after channel access failre to the qee idle state, the transition after transmission failre to the qee idle state, the transition to the qee idle state after the maximm backoff stage in the last transmission trial, and finally the transition from the idle state to the first backoff stage in the first transmission trial; these probabilities are described by (12) (18), P (i, k, j i, k + 1, j) = 1 for 2 m b 1 k, (12) P (i, k, j i 1,, j) = (α + (1 α) β) p K (k I=i) for i m, (13)

11 Wireless Commnications and Mobile Compting 11 P (,k,j i,,j 1) =P(1 α) (1 β) p K (k I=) for j n, (14) P (Q m,,j) =q (α+(1 α) β) for j<n, (15) P (Q i,,n)=q (1 α) (1 β) for i<m, (16) P (Q m,,n)=q, (17) P (,k, Q )=(1 q )p K (k I=) (18) for 2 m b 1 k. The following analysis is concerned with finding the closed form for the stationary distribtion of the CAM Markov chain (b i,k,j ), where b i,k,j = lim t P(g(t) = i, c(t) = k, y(t) = j), i ( 2, m), k ( 1, max(2 m b 1,L s 1,L c 1)),and j (, n). Using (12) (18) and de to the reglarity of the chain, from (13), for <i m, j n, 2 m b 1 k, we have 2 m b 1 b i,k,j =b i 1,,j (α + (1 α) β) r=k p K (r I=i), (19) b i,,j = (α+(1 α) β) b i 1,,j, (2) and then by recrsive application and sbstittion of (2) for sccessive backoff stages, we can conclde that b i,,j =(α+(1 α) β) i b,,j ; (21) let α + (1 α)β = x; from (19), (2), and (21) we have From (14) we have m b i,k,j =x i 2 b 1 b,,j r=k 2 m b 1 b,k,j =P(1 α) (1 β) m 2 b 1 =b,,j r=k r=k p K (r I=), p K (r I=i). (22) p K (r I=) m b i,,j 1 i= (23) and then from (22) and (23), for i m, j n, 2 m b 1 k, m b i,k,j =x i 2 b 1 b,,j From (14) and (21) we have b,,j = (1 x) P m i= r=k p K (r I=i). (24) x i b,,j 1 =(1 x m+1 )Pb,,j 1 ; (25) let (1 x m+1 )P = y, andbyrecrsiveapplicationand sbstittion of (25) for sccessive transmission trials, we can conclde that b,,j =y j b,, ; (26) then from (24) and (26), (24) can be rewritten as m b i,k,j =x i y j 2 b 1 b,, r=k p K (r I=i). (27) We next derive the expression of b,, by applying the normalization condition: n j= 2 m b 1 k= + m i= n j= m n b i, 1,j i= j= b i,k,j + L s 1 ( k= L c 1 b 1,k,j + k= L 1 b 2,k,j )+ l= Q l =1; (28) after deriving the expression of each term in (28) in terms of the probability b,, and sbstitting with them on it, we obtain b,, =[( 1 yn+1 1 y ) 2 m b 1 k= m i= 1 xm+1 1 x (x i 2 m b 1 r=k 1 y n+1 1 y p K (r I=i))+(1 α) +(1 xm+1 )((1 P) L s +PL c )( 1 yn+1 1 y )+L ( 1 yn+1 1 q +P(1 x m+1 )y n q 1 + (1 P)(1 x m+1 ) 1 yn+1 1 y )]. 1 y xm+1 (29) 3.5. Single-Hop Commnication Analysis. The single-hop commnication scenario considers a nmber of nodes N which are reachable from each other; when each node has data to transmit, it contends with the others in accessing the shared channel according to the behavior described by the employed Markov chain models for slotted CSMA/CA and CAM. This section concerns the derivation of the reqired performance metrics expressions, starting with finding expressions for some of the models related probabilities reqired in the performance analysis implementation Deriving Expressions for the Models Different Associated Probabilities. The derivations of τ, α, β, and P for both slotted CSMA/CA and CAM are the same as done in [35], where m n τ= i= j= P=1 (1 τ) N 1, b i,,j =( 1 xm+1 )(1 yn+1 1 x 1 y )b,,,

12 12 Wireless Commnications and Mobile Compting α=p (1st CCA bsy de to data transmission) + P (1st CCA bsy de to ACK transmission) =L(1 (1 τ) N 1 ) (1 α) (1 β) + L ack Nτ (1 τ)n 1 1 (1 τ) N (1 (1 τ)n 1 ) (1 α) (1 β), β= 1 (1 τ)n 1 +Nτ(1 τ) N 1 2 (1 τ) N +Nτ(1 τ) N 1. (3) The mean packet service time E[S] takes into accont the probability that the serviced packet may be transmitted sccessflly or discarded de to reaching transmission retry limit or channel access failre, and the average time taken in each case from the instant the packet is at the head of the qee is different, E[S] =RE[D] +P cr (n+1) (L c +E[T h ]) n +P cf [ 1 y j= 1 y n+1 yj (j (L c +E[T h ]) [ + m i= 2 m b 1 r= m+1 2 rp K (r I=i) +T SC e=1 (N e α (m+1) +2Ne β (m+1))) ]. ] C e αβ (m+1) (31) The Matlab is sed for solving the nonlinear system of eqations represented by τ, α, β,andq expressions Reliability Analysis. The derivation of the reliability, which is the probability of sccessfl packet reception, for bothslottedcsma/caandcam,isthesameasdonein[35], where R=1 P cf P cr =1 xm+1 (1 y n+1 ) y n+1. (32) 1 y Delay Analysis. The average delay is defined as the time interval from the instant at which the data packet is at the head of the MAC qee ready to be transmitted ntil its acknowledgement is received. The derivation of the average delay expression is the same as done in [35] for both slotted CSMA/CA and CAM, except for the term in the eqation of E[T h ] which refers to the backoff time; in CAM case this term eqals (for complete derivation see [35]) 1 m i= C αβ (i) m i= 2 i ( C e i αβ (i) e=1 l= 2 m b 1 rp K (r I=l)). (33) r= Energy Consmption Analysis. The average energy consmption is compted from (34), where E i, E sc, E t, E r,ande sp are the average energy consmption in idle-listen, channel sensing, transmit, receive, and sleep states, respectively. E sp term is neglected: E=E i m 2 m b 1 n i= k=1 j= n L 1 n m b i,k,j +E sc (b i,,j +b i, 1,j ) i= j= +E t (b 1,k,j +b 2,k,j ) +E i + n j= j= k= n j= (b 1,L,j +b 2,L,j ) L+L ack +1 k=l+1 L 1 (E r b 1,k,j +E i b 2,k,j )+E sp Q l. l= (34) Throghpt Analysis. The throghpt, which is defined as the fraction of channel time sed to sccessflly transmit data payload bits in nit time, is compted from TH = P sccess P bsy L (1 P bsy )S b +P sccess P bsy L s +P bsy (1 P sccess )L c, (35) where P bsy is the probability that there is at least one transmission in the considered nit time and it eqals (1 (1 τ) N ); P sccess is the probability of sccessfl data transmission conditioned by the fact that the channel is bsy and it eqals (Nτ(1 τ) N 1 )/P bsy ; the denominator of TH considers that the channel time has different probabilities of being free or bsy with failed or sccessfl transmission Mltihop Commnication Analysis. The aim of this section is to analyze the end-to-end performance of the proposed CAM when the packet is forwarded throgh intermediate node(s) to reach the final destination for comparing the CAM performance against the slotted CSMA/CA in mltihop topology. The algorithmic techniqe of divide and conqer is sed for finding the end-to-end performance, where the mltihop path is partitioned into a nmber of single-hops solved sing the previos analysis with adjsting the model parameters and may be with some modifications according to the employed topology; then the soltions obtained for each single-hop are appropriately merged to obtain the end-to-end mltihop performance. Figre 12 presents examples for the employed topology for each protocol; the topology of the slotted CSMA/CA is the logical topology for it which is the clster-tree. The proposed CAM topology is constrcted by dividing the network into sbnetworks, each one works on a different freqencychannel,somemembersarebs-neighbors,and its members work on or previosly proposed TSM [11]. The time slot eqals the time of one transmission, and no interaction between the sb-nws is assmed. The nmber of the BS-neighbors in all the sb-nws is approximately eqal, and the nmber of the non-bs-neighbors in all the sb-nws

13 Wireless Commnications and Mobile Compting 13 5 R T C A S Q P I H B O J 2 K X N W 1 M D G E F L V U BS BS-neighbor Non-BS-neighbor Gelatinos shape encloses a sb-nw members (a) BS Coordinator Device Connection between coordinators Connection between devices and coordinators (b) Figre 12: Mltihop network topologies (a) for CAM network and (b) for slotted CSMA/CA clster-tree network. is also approximately eqal. In CAM, no attention is given to a specific roting techniqe, that is, no determinants of the next hop; also in CSMA/CA, no determinants imposed for selecting the parent coordinator from the discovered ones. In the two topologies, when a node has a packet at the head of the qee ready to be sent, it can immediately start its transmission process to the crrently listening receiver; that is, all the intended receivers in any time are available; no sleeping schedle cases deferring of a transmission process, sch that only the effect of the medim access method is considered. The nodes are deployed niformly; the nodes which have the capability of coordinator represent 25% of the total nodes nmber and are deployed independently niformly throghot the area. The starts of the first packet generation of all the sb- NW members are separated by an ignorable time; accordingly the generation repetitions will be separated by an ignorable time. The clster-tree formation and commnication as well as the commnication between sb-nws BS-neighbors and the BS are performed sing 15 dbm, while the commnication among sb-nws members is performed sing a greater transmission power level 1 dbm for assring the reachability of the receiving node at any time. The following sections concern deriving expressions for the mltihop performance metrics for both the slotted CSMA/CA network and the CAM network. The mltihop network topology imposes changes in each node variables and the commnication conditions from one network to the other or may be from one hop to another in the same network, sch as the existence of different degrees of neighborhood to a transmitting node which raises the existence of hidden nodes, different packet arrival rates, and different nmber of contended nodes. Section analyzes the effect of mltihop commnication on the two networks models associated probabilities. Sections to analyze the end-toend reliability, delay, energy consmption, and throghpt; the same definitions and comptation are sed for finding these slotted CSMA/CA and CAM end-to-end performance metrics except few indicated differences Deriving Expressions for the Models Different Associated Probabilities. In this section,the derivations of α, β, andp for bothslottedcsma/caandcamwillbeintrodced. (1) Slotted CSMA/CA End-to-End Analysis.Intheclster-tree slotted CSMA/CA network and by assming that the nmber of each clster end devices members I d is approximately eqal and the nmber of children coordinators I c varies fromtoaconstantmaximmlimitforeachcoordinator, thepacketarrivalrateatthemacqeediffersfromthe end device λ d to the coordinator λ c ;alsoifnoaggregationis assmed, it will differ for coordinators at different levels, bt it may differ in case of aggregation employed from coordinator to another one if their I c vales are different. The packet generation rate λ at each node is eqal, in each time nit the network will have the nmber of packets described by λ generatedfromeachnode,andincomptingtheapproximate vale of the packet arrival rate at a node, it is assmed that all the transmitted packets to this node will be delivered sccessflly. The packet arrival rates are compted as follows: λ d =λ, λ ci =λ(1+i d + I ci ) if aggregation is assmed,

14 14 Wireless Commnications and Mobile Compting λ ci =λ(1+i d + I total c i (1 + I d )) if no aggregation is assmed, (36) where I total c i represents the nmber of the coordinators below the coordinatori in its tree branch, its children coordinators, its grandchildren coordinators, the children of its grandchildren coordinators, and so on. According to the packet arrival rate and the different neighborhood of each node and its neighbors, the node will have its own probabilities of τ, α, β, andp. Theneighbor- hood of a transmitting node, its receiver s neighborhood, and the neighborhood of its receiver s neighbors are distingished by defining some sets of nodes, each one has an effect on the transmitting node packet; these sets are Φ t,φ tc,φ tr,φ htr,φ hctr,ψ c,c t,andc. The set Φ t defines the neighborhood of a node t, which are the nodes srronding this node that can hear its transmissions and likewise it can hear their transmissions (the neighbor coordinators are discriminated by Φ tc and incorporate the BS), the set Φ tr defines the common neighborhood of the nodes t and r (Φ tr = (Φ t Φ r )), the set Φ htr defines the hidden nodes from the node t with respect to the transmission to node r inclding the BS, the set Φ hctr defines the hidden coordinators from the node t with respect to the transmission to node r inclding the BS, the set ψ c defines the set of coordinator c children from devices and coordinators, the set C t is a set of one element corresponding to the coordinator of node t, andthesetc defines the set of all coordinators in the network. (a) The Collision Probability.Thecollisionprobabilityrelated to node t is the probability that node t enconters a collision on a transmitted packet to its coordinator, and it is denoted by P t.thecollisionprobabilityp t is given by P t =PC senset +(1 PC senset )PC hdatat +(1 PC senset )(1 PC hdatat )PC hackt, (37) where PC senset is the collision probability of a transmitted packet from t to r de to concrrent channel sensing, PC hdatat is the collision probability of a transmitted packet from t to r de to hidden data transmission starts before or after the beginning of the packet transmission, and PC hackt is the collision probability of a transmitted packet from t to r de to hidden acknowledgement transmission starts before or after the beginning of the packet transmission. The probability PC senset considers the probability that at least one node from the common neighborhood of the transmitter and the receiver (except the BS) transmits at the same time slot. If each node in the common neighborhood senses the channel with its own probability τ, PC senset is compted from PC senset =1 (1 τ j ). j Φ tr,j=bs (38) Hidden acknowledgements to the transmitter t reslted from sccessfl data reception at the hidden coordinators from t pon which they transmit acknowledgements received at its receiver r and collide with its data. The probability PC hackt is given by PC hackt = PSR ht 1 k h Φhctr ψ h (1 τ k ) h Φhctr ψ h h Φhctr ψ h Cq q=1 j h Φhctr ψ h \d m } (1 (1 τ j ) n d m d m =d m,1,d m,2,...,d m,q } ( τ i i d m d m =d m,1,d m,2,...,d m,q } (α n +(1 α n )β n ))), (39) where h Φhctr ψ h stands for the size of the set of nodes which represents the nion of all the sets which contain the children of the hidden coordinators from t, h Φ ψ hctr h C q represents the nmber of combinations of size q from the set h Φhctr ψ h, d m represents the combination nmber m of size q, and they are sed in (39) to calclate the probability of at least one node from the set h Φhctr ψ h which begins a transmission. The notation PSR ht represents the probability of sccessfl data reception at the hidden coordinators from t and it is defined in Appendix B. The probability PC hdatat is the probability of at least one from the hidden nodes to t which begins a transmission in anytimenitofatimedrationeqaltotheaveragechannel occpation of a data transmission before the beginning of t transmission and one after it. The probability PC hdatat is calclated from PC hdatat =2L Φ htr \BS} q=1 j Φ htr \(k m BS)} (1 Φ htr \BS} C q ( i k m k m =k m,1,k m,2,...,k m,q } τ i (1 τ j ) n k m k m =k m,1,k m,2,...,k m,q } (α n +(1 α n )β n ))), (4) where Φ htr\bs} C q represents the q-combinations from the hidden nodes to t exclding the BS and it eqals the nmber of rows of the matrix K where each row contains one different combination.

15 Wireless Commnications and Mobile Compting 15 (b) Probability of Finding the 1st CCA Bsy. The eqation of α t which is the probability of node t finds the 1st CCA bsy which comprises the probability to find it bsy de to data transmission (α1 t ) and the probability to find it bsy de to acknowledgement transmission α2 t, α t =α1 t +(1 α1 t )α2 t, α1 t =L α2 t = Φ t \BS} q=1 j Φ t \(k m BS)} (1 Φt\BS} C q ( i k m k m =k m,1,k m,2,...,k m,q } τ i (1 τ j ) n k m k m =k m,1,k m,2,...,k m,q } PSR t 1 k h Φ tc ψ h\t} (1 τ k) ψ h Φ h\t h Φ tc ψ h \t C tc q q=1 j h Φ tc ψ h\(d m t)} (1 (1 τ j ) n d m d m =d m,1,d m,2,...,d m,q } (α n +(1 α n )β n ))), ( τ i i d m d m =d m,1,d m,2,...,d m,q } (α n +(1 α n )β n ))), (41) Φ where \BS} t C q and h Φtc ψh\t C q represent the qcombinations from all the neighbors of t exclding the BS and all the children of the neighbor coordinators of t exclding t itself, respectively. The notation PSR t represents the probability of sccessfl data reception at the coordinators of node t neighborhood and it is defined in Appendix B. (c) Probability of Finding the 2nd CCA Bsy. The probability β t, which is the probability of node t finding the 2nd CCA slot (denoted as CCA2) bsy given that the 1st CCA slot (denoted as CCA1) was idle, is derived in the same fashion sed in [36] bt with considering the different neighborhood and other different vales the nodes have. The node can assess its 2nd CCA bsy in two cases, the first one occrs if some other nodes in the medim were sensing their 2nd CCA dring this node 1st CCA and started a new transmission in the node s 2nd CCA slot. This can only happen if the other node started sensing in the slot jst before the intended node 1st CCA slot (denoted as slot1) and the channel was then idle. The second case of assessing the 2nd CCA bsy occrs when the 1st CCA idle slot was the slot between data transmission and acknowledgement (the probability of the second case occrrence is denoted by P betaack ); then β t = P (I slot1 I CCA1 ) P (S slot1 )+P betaack, (42) where I slot1 and I CCA1 are the events of finding slot1 and CCA1 idle, respectively; the event S slot1 is the event of start sensing in slot1. The conditional probability P(I slot1 I CCA1 ) is the probability that a given idle slot is preceded by another idle slot, P (I slot1 I CCA1 )=1 P (B slot1 I CCA1 ) P (I CCA1 ) =1 P (B slot1 I CCA1 ) P (B slot1 I CCA1 )+P (I slot1 I CCA1 ), (43) where B slot1 it the event of finding slot1 bsy; then β t can be rewritten as β t =(1 P (B slot1 I CCA1 ) P (B slot1 I CCA1 )+P (I slot1 I CCA1 ) ) P (S slot1 )+P betaack. The event I CCA1 occrs in for cases. (44) Case 1. A bsy slot before the idle CCA1 becase of a failed packet transmission de to collision: this is represented by the probability P bsyft for node t. Case 2. AbsyslotbeforetheidleCCA1 becaseofan acknowledgement following a sccessfl data transmission: this is represented by the probability P bsyat for node t. Case 3. A bsy slot before the idle CCA1 becase of a sccessfl packet transmission where the idle slot is the interframe space in between data and acknowledgement: this is represented by the probability P bsyst for node t. Case 4. An idle slot before the idle CCA1 happenedafter an acknowledged sccessfl transmission or an nacknowledged nsccessfl transmission: this is represented by the probability P idlet for node t. Sbstitting with these probabilities in (44), we have β t =(1 (1 + P bsyft +P bsyat +P bsyst P bsyft +P bsyat +P bsyst +P idlet ) j Φ t,j=bs (1 τ j )) P bsyat P bsyft +P bsyat +P bsyst +P idlet, (45) and the expressions which define these probabilities are presented in Appendix B.

16 16 Wireless Commnications and Mobile Compting (2) CAM End-to-End Analysis. In CAM, the packet generation rate λ at each node is eqal, in each time nit the network will have the nmber of packets described by λ generated from each node, the time nit described by λ eqals mltiples of the TSM frame greater than λ mltiplied by maximm nmber of allowed hops throgh a sb-nw, and in compting the approximate vale of the packet arrival rate at a node it is assmedthatallthetransmittedpacketstothisnodewillbe delivered sccessflly. It is assmed that if the BS-neighbors nmber does not represent the larger share in a sb-nw, they transmit their packets directly to BS and are not allowed to semltihops.thetopologydoesnotimplyaspecificform of doing aggregation; the roting may determine that, so no aggregation is assmed. The nmber of the sb-nw non-bs-neighbor members is denoted by I o andthenmberofthebs-neighbormembers is denoted by I BS. The average packet arrival rate at the BSneighbors λ BS is greater than that of the non-bs-neighbors λ o as they represent the critical zone arond the BS and it depends on both I o and I BS. The whole path taken by a transmitted packet lies in a specific sb-nw, except the last hop where the last hop sorce, which is a BS-neighbor, switches its working channel to the working channel of the BS. Assme that a one hop of packets transmitted from each non-bs-neighbor node is completed approximately within a TSM frame time and when each node scceeds to send its packet, whether generated or forwarded, it sends it to a receiver different from whom its peers send to, whether this receiver is a BS-neighbor or not. According to that, at the completion of one packet transmission from each node, the non-bs-neighbor node will receive a nmber of packets ranges from to (l max 2),wherel max is the maximm path length. The final intermediate node is a BS-neighbor and the average nmber of packets received by a BS-neighbor in a completion of each non-bs-neighbor nodes one packet transmission is approximately eqal to the nmber of non- BS-neighbors divided by the nmber of BS-neighbors in the sb-nw. Based on the previos considerations, the average packet arrival rates λ o and λ BS are compted as follows: λ o =λ(1+ l max 2 x= x l max 1 ), λ BS =λ(1+ I o I BS ). (46) (a) Deriving Non-BS-Neighbor Different Associated Probabilities. The probability of collision of a non-bs-neighbor transmitted packet depends on the nmber of non-bsneighbors in its receiver neighborhood in its sb-nw and their vales of τ. For simplicity and to enconter the problem of hidden nodes to the transmitter, it is assmed that all the non-bs-neighbor members always transmit with its fll range (or a range enogh for covering the whole employed field), therefore no hidden nodes to the transmitter. In case the receiving node is a BS-neighbor, the nmber of competing nodes N cp with a node tries to transmit will be eqal to (I o 1), and in case of its being a non-bs-neighbor, N cp eqals (I o 2). Under the previos assmptions, the derivation of α, β, andp for a non-bs-neighbor is trned to be the same as followed in the single-hop commnication analysis with notations and vales of variables indicate a non-bs-neighbor in a sb-nw: P o =1 (1 τ o ) N cp, α o =(L+L ack ( I oτ o (1 τ o ) I o 1 )) 1 (1 τ o ) I o (1 (1 τ o ) I o 1 )(1 αo )(1 β o ), β o = 1 (1 τ o) I o 1 + Io τ o (1 τ o ) I o 1 2 (1 τ o ) I o + I o τ o (1 τ o ) I o 1. (47) (b) Deriving BS-Neighbor Different Associated Probabilities. The probability of collision of a BS-neighbor transmitted packet depends on the nmber of BS-neighbors in all the sb-nws and their vales of τ. If the nmber of sb-nws is denoted by N s, then the nmber of BS-neighbors eqals I BS N s ; some of them may be hidden to others, where Φ tbs represents the common neighbors between the BS-neighbor t and the BS and Φ htbs represents the hidden BS-neighbors to the BS-neighbor t. The probabilities α, β, and P are derived in the same fashion as they are derived in case of slotted CSMA/CA; except here there is no hidden acknowledgement; the set of all the children of the neighbor coordinators contains only the BS-neighbors and is defined by Φ tbs Φ htbs ; and sccessfl concrrent transmissions from even two nodes do not exist End-to-End Reliability Analysis. The end-to-end reliability R e-to-e is the ANDing and in other words, the prodct of the probabilities of sccessfl packet reception at each intermediate node in the considered path then to the BS, R e-to-e = l n=1 R n, (48) where l is the path length in terms of its incorporated nodes nmber exclding the final destination which is the BS, R n is the single-hop reliability of the transmitted packet by the node nmber n in the path, then R 1 is corresponding to the first node in the path which is the sorce node, and R l is corresponding to the last node in the path which is a BS child coordinator End-to-End Delay Analysis. By ignoring the processing delay, the average end-to-end delay D e-to-e is the smmation of the average delays for sccessflly delivering the packet (D) at each node in the path inclding the PAN coordinator (BS)andtheaverageqeingdelay(w = (λ/μ)/(μ λ)) at each intermediate node in the path, where λ here refers

17 Wireless Commnications and Mobile Compting 17 to the qee packet arrival rate and μ is the packet service rate. D e-to-e = l n=1 (w n +D n ). (49) The channel switching time is added to the end-to-end delay in CAM case to incorporate the effect of a BS-neighbor switching to the BS channel to send its data to it (channel switching time is approximately the transmission time of a 32 byte ( 1 ms) [37]) End-to-End Energy Consmption Analysis. The total energy consmed to relay the packet throgh the path towards the BS is assmed to be the smmation of the total energy consmed by each node in transmitting the packet to the next-hop node. For simplicity, the switching between freqency channels is assmed to consme ignorable energy: E e-to-e = l n=1 E n. (5) Network Throghpt Analysis. The normalized system throghpt is defined and calclated here in the same way sed for single-hop analysis; the difference is in the definition of P bsy and P sccess. If we denote the set of all nodes in the network (except BS and PAN coordinator) by Φ total,here P bsy =1 i Φ total (1 τ i ), P sccess = i Φ total PST i P bsy, (51) where PST k, as defined in Appendix B, is the probability of sccessfl transmission by a node. Anothermetricsedtomeasrethenetworkprodctivity is the goodpt defined as the data bits sccessflly received at thebsinonetimenit.thenetworkgoodptg(in bits/sec) is the smmation of all nodes goodpts; let O n be the set of allpossiblepathsfordeliveringdatafromnoden to the BS; then G=(L 2 4) n Φ total r O n 4. Performance Assessment R e-to-e (n, r) D e-to-e (n, r). (52) This section assesses the performance of the proposed CAM. First, it tests the effect of different parameters on its performance, then the performance of the proposed CAM is compared to the beacon-enabled IEEE slotted CSMA/CA based on single-hop commnication, and finally the mltihop commnication performance is considered. The tests reslts were analyzed for better nderstanding for different behaviors and getting observations and conclsions can be sed for modifications and optimizations. Reliability Avg. delay (ms) m =3 Figre 13: m,,andλ effect on CAM reliability m =4 = =3 =4 =5 Figre 14: m,,andλ effect on CAM avg. delay Effect of Parameters on the Proposed CAM Performance. The effect of the parameters m, traffic load represented by λ, and the tning parameter on the average delay, the reliability, and the power consmption of the proposed CAM is stdied in this section considering a sb-nw commnication example with nmber of nodes eqal to 5 node, m b =5, and m =3. Figres 13 and 14 show that both the average delay and the reliability increase with the increase in m vale, while tning to a higher vale decreases both of them. For example, when the vale of m is increased from 1 to 4 at λ=5and =5,the reliability increased by abot %; at the same time, the delay is increased by abot 17.7%; with adjsting the vale of, the delay increment percentage cold be redced to be 55.3% while the reliability still higher bt with a smaller percentage abot 2% when eqals 25. The change of vale affects the possible vales range of the backoff eqation first term and cases the inverse effect to the range of the second term. When is small, the first term range is bigger than the second term range which reslts in higher reliability becase the events of modlating the vale of this ID-dependent term of the 5 different nodes to thesamevalearesmallerinthiscaseandagreaterspace is left for different nodes IDs to differentiate their backoffs, the main principle that the backoff eqation sed to improve reliability, even thogh the sm of the delays encontered in backoff and channel sensing dring the previos stages

18 18 Wireless Commnications and Mobile Compting.14 Power consmption (mw) = m =4 =3 Figre 15: m,,andλ effect on CAM power consmption. Reliability Nmber of nodes (the backoff sm) is modlated in the second term to a small range of possible vales reslting in a higher percentage of recrrence for this term vale. This is at the expense of increasing the delay. Changing to higher vales redces the range of the first term vale and increases the second term range which according to the previosly mentioned illstration decreases both reliability and delay by a percentage decreases with m increase.theredctionpercentageisdecreasedwithm increase de to the salience of the second term effect of improving reliability at higher m vales; also the delay is increased in this case becase the sm of the delays which reslted from the previosly encontered backoff stages is increased and the modls of the modlo operation determines its range becomes greater. Changing to higher vales increases the first term vale recrrence percentage and decreases the second term vale recrrence percentage. When the second term recrrence percentage approaches the first term recrrence percentage and then becomes less than it, the reliability changes its behavior from the decrease to the increase; this appears as a convex crvatre in the decayed reliability and delay crves. When the maximm backoff sm is decreased behind themodlsofthesecondtermandcontinestodecrease with increasing, at this point, the reliability contines to decrease. As shown in Figres 13 and 14, the increase of the trafficloadslightlydecreasesthereliabilityandveryslightly increases the delay (almost no effect on the delay appears in the figre). With regard to the energy consmption, the proposed CAM energy consmption takes the inverse behavior of the reliability with respect to, sch that, nder the conditions of higher probability of collisions, higher traffic load, and higher nmber of retransmissions, the main components which affect the total energy consmption are of the packet transmission stage which case its increase. The effect of the idle backoff state energy consmption appears when the time spent in backoff highly decreases when m is small (m eqals 1orless), is high, and the traffic load is low. Generally from Figre 15, the energy consmption increases when m increases from 1 to 2 de to the considerable increase of the backoff time (as m = 3 and Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 16: Slotted CSMA/CA and CAM reliability verss nmber of nodes. m b = 5, the third backoff stage reslts in doble the rangeofpossiblebackoffperiodsofthesecondstage,while the backoff periods are maintained on that range in the sbseqent backoff stages) and the increase in the nmber of transmissions/retransmissions especially when the traffic load is low. The increase of the m vale from the vale 2 increases the reliability and decreases the power consmed in the transaction states while increasing the backoff power consmption (with lower rate) making the total energy consmption amont tend to have converged magnitdes and become approximately steady with increasing m regardless of the traffic load and Performance Assessment Based on Single-Hop Commnication. Figre 16 shows the reliability of the proposed CAM and the IEEE slotted CSMA/CA at different backoff stages drawn verss the nmber of nodes, N.AlsoFigres19, 2, and 21 represent the same comparison bt with respect to the average delay, the average energy consmption, and the throghpt of the two protocols. All vales are corresponding to = 5, m b = 5, m = 3, n = 3, L = 7S b,and L ack =1.7S b. As shown in Figre 16, the reliability of CAM which reslted from a certain vale of m is greater than the slotted CSMA/CA reliability which reslted from the same m vale with a big percentage, on average, 177%; this percentage increases when N increases. For example, at m eqal to 3, the reliability is increased by abot 68.3% when N is 3; this percentage increases ntil it becomes greater than 2% when N exceeds 6. Also, it cold be noticed that, lower m vales case in CAM network more reliability than that cased by higher m vales in slotted CSMA/CA, bt rather as thenmberofnodesincreasesthereliabilityofhighm vales in the slotted CSMA/CA is trned to be not only smaller than its lower m valescamreliabilitybtalsosmallerthanthe reliability of the two backoff stages CAM.

19 Wireless Commnications and Mobile Compting 19 Probability of discarding packets de to channel access failre Nmber of nodes Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 17: P cf of slotted CSMA/CA and CAM verss nmber of nodes. It is expectable to achieve more reliable commnication singtheproposedcamastheimplementedbackoffmechanism is designed to decrease the channel sensing overlap among contending nodes. The CAM actally redces the first carrier sensing probability in a randomly chosen time slot (τ); therefore the collision probability is redced and accordingly the probability of a packet being discarded de to reaching retry limits is redced. Regarding the probability of discarding packets de to channel access failre, as shown in Figre 17, at a certain m vale, it is also redced in CAM case with percentage decreases with N increase. The approaching of the CAM and slotted CSMA/CA collision probability and probability of nsccessfl channel access (x)inabackoffstageathigher N vales cases the approaching of the CAM and CSMA/CA probability of discarding packets de to channel access failre at higher N vales. As shown in Figre 18, x in CAM trns to begreaterthanitscsma/capeerathighern vales. This is referred to the approaching of both of them, α vale at higher N, while the β of CAM is greater than CSMA/CA de to higher occrrence of acknowledgement transmissions. Figres 19 and 2 reveal that, besides the increase of CAM reliability, with fixing m vale, the energy consmption which reslted from CAM network is smaller than CSMA/CA by on average 11%, except for m eqal to 1 where CSMA/CA consmes the less energy, bt this is at the expense of increase in the CAM average delay over CSMA/CA by, on average, 42.6%. The range of backoff vales the nodes pick from in CSMA/CA is dobled each backoff stage ntil its maximm limit reaches 2 m b 1andthenitstabilizesonthisrange.In CAM, the range of backoff vales possible for nodes has the pper limit 2 m b 1from the first stage (the same m b vale is reinvolved in both of them) which increases its average delay over CSMA/CA average delay corresponding to the same m vale.however,thedecreaseofcamlosspercentage appears in improving the throghpt of the CAM network even thogh its delay is greater as shown in Figre 21, with Probability of nsccessfl channel access attempt Nmber of nodes Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 18: Slotted CSMA/CA and CAM probability of nsccessfl channel access verss nmber of nodes. Avg. delay (ms) Nmber of nodes Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 19: Slotted CSMA/CA and CAM avg. delay verss nmber of nodes. fixing m vale, and the CAM network throghpt is greater than CSMA/CA by on average 117.4%, The increase percentage of the CAM average delay cold be redced by choosing the m and vales. For example, considering m eqal to 3 for slotted CSMA/CA in the previos comparison setp, as the reliability de to sing 4 backoff stages CAM is greater than the reliability of slotted CSMA/CA in the considered case by on average 195.8% as showninfigre16,alsothe3backoffstagescamreslts in reliability greater than it. Then from Figres 16, 19, and 2, setting m eqal to 2 in CAM reslts in greater reliability, greater average delay, and lower power consmption than m eqalto3slottedcsma/cabyonaverage136.3%,8.4%,and

20 2 Wireless Commnications and Mobile Compting Energy consmption (mw) Nmber of nodes Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 2: Slotted CSMA/CA and CAM energy consmption verss nmber of nodes. Avg. delay (ms) Nmber of nodes Slotted CSMA/CA (m =3) CAM (m =2, =5) CAM (m =2, =8) CAM (m =2, =11) CAM (m =2, =14) CAM (m =2, =17) Figre 22: Slotted CSMA/CA and CAM avg. delay at different vales verss nmber of nodes. Throghpt Reliability Nmber of nodes Nmber of nodes Slotted CSMA/CA (m =1) Slotted CSMA/CA (m =2) Slotted CSMA/CA (m =3) Slotted CSMA/CA (m =4) CAM (m =1) CAM (m =2) CAM (m =3) CAM (m =4) Figre 21: Slotted CSMA/CA and CAM throghpt verss nmber of nodes. Slotted CSMA/CA (m =3) CAM (m =2, =5) CAM (m =2, =8) CAM (m =2, =11) CAM (m =2, =14) CAM (m =2, =17) Figre 23: Slotted CSMA/CA and CAM reliability at different vales verss nmber of nodes. 14.5%, respectively; this means setting m eqal to 2 in the CAM reslts in small percentage of average delay increase while the reliability is high with a big percentage. Frthermore, tning the parameter via increasing its vale cold redce the delay more. Figres 22, 23, 24, and 25 compare the CSMA/CA performance and CAM performance compted for different higher vales of at m b =5, m =3, n = 3, L = 7S b,andl ack = 1.7S b.fromfigre22,it coldbenoticedthatwhen is set to 8, the CAM delay is, on average, greater by 4.9%, and this percentage is redced to be 2.25% when eqals 11, while the average reliability in this case is still greater by abot 98.4% and the average energy consmption is 13.17% lower. Setting to 14 reslts in redcing the average delay of the CAM by abot 2.12% while the CAM reliability is still greater by 72.5% and CAM energy consmption is less by 11.94%. Frther increasing more decreases CAM average delay as well as reliability; for example, at eqal to 17, we can obtain with CAM on average a 61.35% greater reliability, 4.5% less delay, 11.4% less power consmption, and 87.8% greater throghpt. Also the CAM delay which reslted from setting m eqal to 3 cold be tned to be close to CSMA/CA delay, bt the rest of CAM performance wold be worse than that reached from tning CAM two backoff stages performance becase the delay in this case is higher with a bigger percentage

21 Wireless Commnications and Mobile Compting 21 Energy consmption (mw) Nmber of nodes Slotted CSMA/CA (m =3) CAM (m =2, =5) CAM (m =2, =8) CAM (m =2, =11) CAM (m =2, =14) CAM (m =2, =17) Figre 24: Slotted CSMA/CA and CAM power consmption at different vales verss nmber of nodes. Throghpt Nmber of nodes Slotted CSMA/CA (m =3) CAM (m =2, =5) CAM (m =2, =8) CAM (m =2, =11) CAM (m =2, =14) CAM (m =2, =17) Figre 25: Slotted CSMA/CA and CAM throghpt at different vales verss nmber of nodes. abot 37.6%. When is set to 23, the delay reaches 4.9% increase percentage and the CAM reliability increase and energy consmption redction percentages are 21.2% and 2.12%, respectively. Setting to 26 decreases both the delay and the reliability and increases the energy consmption of the CAM over the CSMA/CA Tning the Vale. For finding the best vale to a given performance objective, the following analysis describes with more details the effect of the whole range of possible vales, which is [, 31] form b = 5,ontheperformance of CAM at different parameters vales, and compares it tothecsma/caperformancenderthesameconditions. Each sbfigre in Figre 26 sketches one performance metric for both CAM, indicated by solid lines, and the slotted CSMA/CA, indicated by dashed lines, compted for different vales of and m at certain vale of N. The variability of the backoff time vales has the biggest effect in determining the behavior of CAM reliability and accordingly the delay and energy consmption. For the commnication not to BS, there is no recrrence of the possible vales of the backoff eqation first term withot modlation de to the modlation sed in it p to a certain limit L eqal to (32 N m). After this limit, therangeofthepossiblevalesforthefirsttermdecreasesand the recrrence of backoff vales among nodes increases. Therecrrenceinthesecondtermoftheeqationis maximal at = ; then it takes to decrease as increases p to a certain limit L eqal to the minimm vale greater than the maximm backoff sm mins one, sbtracted from it one. Ths for N less than or eqal to 32 m, thegeneral tendency of the reliability crve is to increase with increasing at lower vales and decreases with increasing at higher vales. Between the start with increase and the ending with decrease, the reliability behavior at intermediate vales depends on L and L.If L is less than L,thereliability increases p to L, then over the vales of between the two limits, the reliability stabilizes on a constant vale becase in this case there is no recrrence neither in the first term vale nor in the second term vale, and the maximm backoff sm is constant; after L, the reliability decreases. This cold be noticed in the constant reliability between L and L for N less than or eqal to 15 at m eqal to 1 and N less than or eqal to 6 at m eqal to 2. When L is less than L, the interval between them enconters an increase in first term vale recrrence and a decrease in the second term vale recrrence; this cases, with general decaying behavior, the previosly mentioned crvatres in the reliability crve, depending on the relative vales of the recrrence percentage in the two terms and the maximm backoff sm vales, or in better words, depending on the probability of being in the backoff state. The m = 1 backoff stage cases the existence of L ;its vale decreases by 1 for each N increment ntil it reaches at N eqal to 31. The vale of L in each sbseqent vale of m islessbyonethanitsvaleatthedirectpreviosm vale; that is, the L vale reaches at N eqal to 3 when m eqals 2, N eqal to 29 when m eqals 3, and so forth. L vale increases with N increase and p to a certain N, it stabilizes on its reached vale. When m eqals 1, L increases ntil N eqals15;thenittakesaconstantvaleof16.atm eqal to 2 and N eqal to 6, L stabilizes on the vale of 24. The limit L at m eqal to 3 and 4 is always constant on the vales 28 and 3, respectively. Exception to the previosly mentioned general behavior, it is noticed that, at high vales when m eqals 1 (also when m = 2 bt with feeble emergence), the reliability increases rather than its expected decrease. As stated before, the backoff state is the dominant factor which determines the reliability behavior; when it increases, the first carrier sensing probability in a randomly chosen time slot decreases; as a reslt the sensing overlap decreases and the reliability

22 22 Wireless Commnications and Mobile Compting Reliability Reliability Reliability Reliability Reliability At N=5 =3pps transmission not to BS At N=6 =3pps transmission not to BS At N=1 =3pps transmission not to BS At N=15 =3pps transmission not to BS At N=32 =3pps transmission not to BS Avg. delay (ms) Avg. delay (ms) Avg. delay (ms) Avg. delay (ms) Avg. delay (ms) At N=5 =3pps transmission not to BS At N=6 =3pps transmission not to BS At N=1 =3pps transmission not to BS At N=15 =3pps transmission not to BS At N = 32 = 3 pps transmission not to BS Avg. energy consmption (mw) Avg. energy consmption (mw) Avg. energy consmption (mw) Avg. energy consmption (mw) Avg. energy consmption (mw) At N=5 =3pps transmission not to BS At N=6 =3pps transmission not to BS At N=1 =3pps transmission not to BS At N=15 =3pps transmission not to BS At N=32 =3pps transmission not to BS Figre 26: CAM and slotted CSMA/CA performance over the whole range of the vale. ofthetransmittingnodeincreasesandviceversa.thisis especially when m ishigher;thatis,thenodestaysmoretime in backoff states. The staying in the idle state at the qee, in contrary to the staying in the backoff state, increases with increasing as the mean packet service times of the nodes are decreased. At high vales, low m vales (m =1), and small λ (this exception is vanishing with increasing λ), the qee idle state dominates affecting the first carrier sensing probability in a randomly chosen time slot; therefore, this probability isdecreasedeventhoghthebackofftimesvariabilityis

23 Wireless Commnications and Mobile Compting 23 decreased; this illstrates the exceptional increase behavior of the reliability at high vales and m eqal to 1 which gives the possibility in some cases to have higher reliability while both thedelayandenergyconsmptionarehighlydecreasing. The CAM performance behavior can be described for the nodes to be sed as an indication for the expected performance nder certain conditions to help for dynamically changing performance settings, by sing lookp tables, crve fitting, approximation based on the determinable behavior mentioned before for the reliability with the backoff time vales, or by some other means. For example, let N eqal 1, and reliability, delay, and energy consmption crves can be fitted to constrct their representative mathematical fnctions; for best fit, each crve can be considered pon more than one interval of vales. For example, the whole range is divided into for intervals; each crve corresponding to an interval is fitted in a separate eqation with a low degree. From these eqations, the node comptes the performance indications corresponding to certain m and and optimizes the performance pon given reqirements sch as a reference performance vales, a specific metric to be optimized, and percentages for optimizing the specified metric and permitting for resltant degradation in the other metrics. Let the reference performance be the correspondent to the crrent vales of m = 2 and = 2, and for some reasons sch as freqent loss of acknowledgements, a need for increasing reliability becomes desirable with a specified percentage 5% on condition that the delay and energy consmption do not increase with more than the same percentage; other performance variations and tolerances can be employed to deal with the sitation where the mainly reqired performance specification cannot be achieved. In this case, the resltant vales of m and which achieve the reqired or the acceptable performance are 3 and 25, respectively. When the delay is the parameter to be optimized tilizing the same previos percentages, the resltant vales of m and in this case are 3 and 27, respectively. Also for some reasons sch as the falling of the battery level below a threshold or the occrrence of a deviation from a determined power consmption behavior, the optimization coldbedirected,forexample,toreachthelesserenergy consmption vale possible regardless of the other metrics vales, which in this case is corresponding to m = 1 and = Performance Assessment Based on Mltihop Commnication. The previos evalation reveals that the reqired singlehop performance of CAM against the slotted CSMA/CA can be obtained by choosing the m and vales and that CAM performs more better than slotted CSMA/CA in larger nmber of nodes. The comparisons performed in this section are based on the analysis presented in Section 3.6 for mltihop performance and on the small network examples of Figre 12. For example, Node 16 in the clster-tree network is corresponding to the following sets: Φ 16 = }, Φ 16c = }, Φ 16 4 = }, Φ h16 4 = 2 21}, Φ hc16 4 = 2}, C 16 = 4}, ψ =1 4}, ψ 1 = }, ψ 2 = }, ψ 3 = }, ψ 4 = }, ψ 5 = }. (53) The transmission level sed in the employed network example for the sb-nws BS-neighbors commnication with the BS reslts in the existence of no hidden nodes. No aggregation is assmed. The nodes were deployed randomly; therefore their IDs are randomly distribted throghot the area; ditto the aliases of a sb-nw s members are also randomly distribted throghot its area. The CAM backoff periods are compted within a sb-nw sing the aliases rather than the IDs while the IDs are sed in backoff comptation for the commnication with the BS to cope with the repetition of aliases in different sb-nws. It is worth noting that the commnication to the BS in the CAM has a different backoff probability distribtion as indicated in Section in Definitions 6 and 7. The following analysis compares the end-to-end performanceofcamandtheslottedcsma/ca.incsma/ca network, different samples of the whole network members (14, 15, 16, or 17 node) are considered in compting its performance for decreasing comptation time and coping with the limitation of the sed fnction, nchoosek, for compting neighbors different combinations, which is only practical for sitations where the inpt vector length is less than abot 15; then for each node, the performance corresponding to the lowest reliability is taken into accont. The vale of m in the CSMA/CA network is randomly selected to be 2; the CAM network needs identification of m and vales which achieve a reqired performance with respect to this setting of the CSMA/CA network. According to the network example, the vales of I o, I BS,andN s are 6, 2, and 3, respectively, l max waschosentobe4andλ was set to 3 pps. Other parameters were set like that m b =5, n=3, L = 7S b,andl ack = 1.7S b. By setting these parameters to thesevalesintheanalysis,compting,andcomparingthe performance of CSMA/CA and CAM over the whole range of possible valesbasedonone-hopcommnicationas done in Section 4.3, that is, the same nmber of competing

24 24 Wireless Commnications and Mobile Compting nodes sed in CAM is sed for CSMA/CA, the same λ is sed, and no hidden terminal is considered for both. The obtained reslts are sed as giding vales for determining the vales of m and for the employed example which incorporates variations on the commnication parameters not only between the two networks, bt also for different nodes in each network de to the natre of mltihop commnication. For the commnication between the BS-neighbors and the BS, two combinations of m and are chosen to achieve the acceptable CAM performance with respect to CSMA/CA regarding the reliability and delay, 4 and 31, respectively; this combination is fond to increase CAM reliability by abot 13% over CSMA/CA while its delay is greater by only abot 2.2%. The other combination is 6 and 31; this combination is fond to increase CAM reliability by abot 43.4% bt at thesametimeincreasescamdelaybyabot4.9%;this can be considered to be acceptable as the reliability metric at the BS is more important and this large delay can be dealt with decreasing the previos hops delay along the remaining mltihop path. For the commnication among the sb-nw members when the receiver is a BS-neighbor, six combinations for m and are chosen, 1 and 31, 4 and 31, 4 and 3, 3 and 29, 3 and 26, and 2 and 22. When the receiver is a non-bs-neighbor, for combinations for m and are chosen, 1 and 31, 4 and 31, 4 and 3, and 3 and 3. The effects of these combinations vary among redcing both CAM reliability with small percentage and delay with high percentage, increasing both with a relatively higher percentage for the reliability, very slightly increasing reliability while decreasing delay with a relatively higher percentage, and very slightly decreasing delay with increasing reliability by a relatively higher percentage. This optimization is only based on the reliability and delay, regardless of the power consmption. Mixtres of these m and combinations were sed in the considered example analysis and the following figres were obtained which represent the different variations of their behavior for one-hop path p to for-hop path. Each vale corresponding to n-hop path represents the average of vales of all the possible n-hop paths in the network. As mentioned before, the CAM offers commnication reliability greater than IEEE slotted CSMA/CA exposed to thesameconditions,whilethemltihopcommnication introdces additional loads on the IEEE network represented by a wider neighborhood; even thogh the sed transmission range is smaller than CAM and the collisions de to hidden terminals. These factors participate in decreasing the IEEE slotted CSMA/CA reliability more than the estimated when the vales of m and were being selected. The one-hop path delayofcamisgreaterthanitsvaleofslottedcsma/ca, as the concentration was on increase the reliability at the BS even at the expense of the delay; also the channel switching time at the BS-neighbor contribtes in increasing CAM delay. Asthelengthofthepathintermsofhopsnmberbecomes greater, the CAM end-to-end delay falls below the slotted CSMA/CA; the start and percentage of this falling depend on the m and combinations sed for sb-nw members commnication. End-to-end reliability Nmber of hops IEEE slotted CSMA/CA CAM 4,31-1,31-1,31 CAM 4,31-4,3-1,31 CAM 6,31-4,3-1,31 CAM 6,31-1,31-1,31 Figre 27: End-to-end reliability verss nmber of hops. As shown in Figre 27, CAM 6,31-4,3-1,31, where each pair represents m and for BS-neighbor, to BS-neighbor, and not BS-neighbor commnications, respectively, reslts in the higher reliability percentage over all path lengths, starting with a percentage greater than 1% for one-hop path increases for lengthier paths. Bt the CAM delay in this case is also greater by abot 54% for one-hop path; this percentage decreases ntil it reaches 2% less than IEEE slottedcsma/cadelay.fromfigres27and28,thecam 4,31-1,31-1,31 cold be chosen to be the combinations which achieve the most preferable CAM performance with respect to end-to-end reliability and delay, where the reliability of the one-hop path is greater by abot 46% and this percentage increases more than 1% for more lengthier paths; at the same time, the CAM end-to-end delay is greater only by 14.7% for the one-hop path; from the two-hop path, it starts to decrease with percentage which reaches 41% for the for-hop path. Also nder the selected m and vales for best performance, Figres 29 and 3 declare that CAM network tilizes, on average, 8% of the channel time in transmitting sefl data, while slotted CSMA/CA network tilizes abot 42% of the time; besides that the CAM mltihop network delivers data bits to the BS with rate eqal to mltiples of the CSMA/CA network data delivery rate. The sbnetworking natre of CAM network and its spport for mltipath commnication aid more in improving its performance with respect to throghpt and goodpt. The CAM exhasts more energy to achieve this performance in channel sensing, waiting acknowledgement, receiving acknowledgement, and longer backoff time at the BS-neighbors. The most important factor which increases CAM energy consmption over the IEEE slotted CSMA/CA as shown in Figre 31 is the energy consmed in transmission; in IEEE network the probability of sccessfl channel access is smaller which decreases transmission chances and

25 Wireless Commnications and Mobile Compting 25 End-to-end delay (ms) Average network throghpt 6.E E E E E E + 1.E + IEEE slotted CSMA/CA CAM 4,31-1,31-1,31 CAM 4,31-4,3-1, Nmber of hops CAM 6,31-4,3-1,31 CAM 6,31-1,31-1,31 Figre 28: Avg. end-to-end delay verss nmber of hops Slotted CSMA/CA network example CAM network example Figre 29: Mltihop network throghpt. accordingly the energy consmed in the transmit state. Also, the refge of the non-bs-neighbors in CAM to transmit with a greater transmission level contribtes in increasing its endto-end energy consmption. 5. Conclsion and Ftre Work This paper deals with completing the design of or previosly proposed MAC by designing a contention-based channel access mechanism (CAM) sitable to the previosly established logical topology and timing strctre mechanism. The CAM is based on developing a backoff mechanism which can be performed via mltiple stages and allowing mltiple transmission trials. The backoff eqation differentiates nodes backoff times depending on their different identification nmbers (IDs) bearing a consideration for achieving fairness among nodes and taking into accont the avoidance of error repeating after a sensing overlap, increasing the possible backoff vales range each backoff stage and the possible occrrence of sensing overlap de to the compted backoff vales themselves while the times of having data are different, Network goodpt (bit/ms) End-to-end power consmption (mw) E E E E +.E + Slotted CSMA/CA network example CAM network example Figre 3: Mltihop network goodpt. IEEE slotted CSMA/CA CAM 4,31-1,31-1,31 CAM 4,31-4,3-1, Nmber of hops CAM 6,31-4,3-1,31 CAM 6,31-1,31-1,31 Figre 31: Avg. end-to-end power consmption verss nmber of hops. and limiting the backoff time to a certain maximm limit regardless of the IDs and other incorporated variables vales. Aperformancetningparameter whichcontrolsthe maximm vale of each term of the backoff eqation is employed. This backoff idea is clarified sing simple assmptionbased simlation scenarios; then the probability distribtion of the backoff period generated by a node in different backoff stages is constrcted; and the Markov chain modeling is sed to analyze and evalate the CAM against the IEEE slottedcsma/cabasedonsingle-hopandmltihopcommnication with respect to the reliability, the average delay, thepowerconsmption,andthethroghpt. Changing the vale of the parameter is already fond to tne these mentioned performance metrics tradeoffs, making it possible to reach a reqired performance objective or set different modes of operation, for example, a direct transmission mode, a zero-backoff mode, and a highestreliability mode, by choosing variables vales sch as backoff stages nmber,, and CCAs nmber. Likewise, adaptability

26 26 Wireless Commnications and Mobile Compting and dynamic performance adjstment cold be achieved by describing the compted CAM performance to nodes in some way. The CAM analysis reveals that the reqired performance ofcamagainsttheieeeslottedcsma/cacanbeobtained by choosing the backoff stages nmber and vales and that CAM performs richly better than the IEEE with larger nmber of nodes. In the single-hop commnication scenario, selecting the backoff stages nmber to be 3 for slotted CSMA/CA and selecting the CAM backoff stages nmber and to be 2 and 11, respectively, and with increasing nodes nmber achieve average of 98.4% higher reliability and 13.17% smaller energy consmption of CAM, while CAM delay is greater by 2.25%. Tning to higher vales frther redces the delay; when is 17, we can obtain with CAM a 61.35% greater reliability, 4.5% less delay, and 11.4% less power consmption. New analysis implementation is derived for the mltihop network considering the effect of different classes of neighborhood, the probability of collision de the hidden terminals data and acknowledgements, and different packet arrival rate for each node. The soltions obtained for each single-hop are appropriately merged to obtain the end-to-end mltihop performance. Mixtres of chosen backoff stages nmber and combinations are sed in the mltihop scenario for the commnication between the BS-neighbors and the BS and the commnication among sbnetwork members. One of these mixtres is chosen to be of the most preferable CAM performance where the reliability of one-hop path is greater by abot 46% and this percentage increases more than 1% for more lengthier paths; at the same time, the CAM endto-end delay is greater only by 14.7% for one-hop path; from two-hop path, it starts to decrease with percentage reaches 41% for for-hop path, bt this is achieved at the expense of consming more energy. Other optimizations on the proposed CAM can be directions for ftre work. The formlation of the backoff eqation itself can be optimized for offering better performance. The modeling and analysis of CAM can be enhanced to consider, for example, different vales for the m b variable. The tests conditions wold be varied. The devised model spports sing different vales only per single-hop; spporting different vales per node which wold be a possible ftre optimization enhances the dynamism of performance adjstment. Also, more accrate, comprehensive, and simple representation to the nodes of the derived performance tning schemes is an enhancement which needs to be researched. Appendix A. Simpler Representation of Backoff Periods Occrrence Nmber The backoff vales compted from the proposed backoff eqation nder certain conditions can take a simpler and reglar pattern facilitates finding a simple relation between the nmber of backoff vales occrrence times and the other variables, sch that this nmber can be compted from it directly withot experiencing looping comptation or with attenating the obligation for sing loops. Up on the observation on the pattern of the nmber of backoff vales occrrence times when the backoff stage nmber eqals for both the commnication to BS (bsknm(k, )) andwithinthesb-nw(knm(k, )), the following eqations are derived: range (N) = N if N<2 m b 2 m b otherwise. For every <2 m b Nwe have knm (k, ) = N 1 if k [1,range (N)] otherwise; for every =2 m b Nwe have knm (k, ) = N 1 if k range (N) 1 otherwise; for every >2 m b Nwe have knm (k, ) (A.1) (A.2) (A.3) = (N 1)(1 + N+ 2m b 2 m ) + f (k) if k 2 m b 1 (A.4) b otherwise, where f (k) = N 1 if <k (N+ 2 m b ) mod (2 m b ) (A.5) otherwise. The following eqations are derived for compting the nmber of backoff vales occrrence times in the second, third, and forth backoff stages, S [1,3],incasethe commnication is to BS (bsknm(k, S)):

27 Wireless Commnications and Mobile Compting 27 bsknm (k, S) = 2 S 1 iff k=idmod (2 m b ) + (smfn (S, CCAcomb, ID)) mod (+1), (A.6) CCAcomb=1 where smfn (S, CCAcomb, ID) MinBFsmTerm smfn (S, 2 S,ID 1) = TriggerBFsmTerm smfn (S, CCAcomb 1, ID) + even (CCAcomb) + h (CCAcomb, S) 2 if S==1 =2 m b 1 S 1 2S + f (n) if S =1 =2 m b 1 n=1 MinBFsmTerm = 1 if S==1 ==2 m b 1 S 1 S+ 1 f (n) if S =1 ==2 m b 1, 2 n=1 f (n) = (f (n 1) +2n) mod (+1), f () =, if CCAcomb == 1 ID mod (2 m b )==1 if CCAcomb == 1 ID mod (2 m b )>1 if CCAcomb == 1 ID mod (2 m b )== otherwise, 1 if S=1 TriggerBFsmTerm = S 1 S+ g (n) otherwise, n=1 g (n) =(g (n 1) +n)mod (+1), g () =, h (CCAcomb, S) = (S ==3) ((CCAcomb == 3) (o 1 (o 2 +o 3 )) + (CCAcomb == 5) ( (o 5 +o 6 +o 7 ) o 4 ) (CCAcomb == 7) (o 8 +o 9 )) (S ==2) (CCAcomb == 3) o 1 +(S ==3) ((CCAcomb == 3) (!(o 1 +o 2 +o 3 )) + (CCAcomb == 5) (!(o 4 +o 5 +o 6 +o 7 )) + (CCAcomb == 7) (!(o 8 +o 9 ))) + (S ==2) (CCAcomb == 3) (!o 1 ), o 1 = 1 if 3 ( 2) otherwise, o 2 = 1 if (+1) (IDmod (2 m b )+( 2 3 ) (+3)) 3 otherwise, o 3 = 1 if (+1) (IDmod (2 m b )+( 1 3 ) (+5)) 3 ( 1) otherwise,

28 28 Wireless Commnications and Mobile Compting o 4 = 1 if = otherwise, o 5 = 1 if (+1) (IDmod (2m b )+2) = otherwise, o 6 = 1 if (+1) (IDmod (2 m b )( 1 ) (2 + 7)) 3 ( 1) 3 otherwise, o 7 = 1 if (+1) (IDmod (2 m b )+( 1 3 ) (+6)) 3 ( 3) otherwise, o 8 = 1 if (+1) (IDmod (2m b )+2) 3 ( 2) otherwise, o 9 = 1 if ( (+1) ) (IDmod (2 m b )+2) 3 ( 2) 3 otherwise, o 1 = 1 if (+1) (IDmod (2m b )+2) otherwise. (A.7) The symbols,,, and! indicate logical and, divides, does not divide, and logical negation, respectively. B. Derivation and Representation of Some Terms First we define the notation PSR ht in the eqation of PC hackt which represents the probability of sccessfl data reception at the hidden coordinators from a transmitter t;theprobabil- ity PSR ht is given by (B.1), where PST k represents the probability that a node k transmits to its coordinator (or its receiver generally) sccessflly withot collision de to concrrent channel sensing, hidden data, or hidden acknowledgement. The PSR ht eqation considers the fact that there may be more than one sccessfl reception at the coordinators at the same time; that is, more than one child can send to their coordinators sccessflly at the same time if each one does not exist in the neighborhood of the other coordinators. Also the eqation considers the different degrees of nodes with respect to a transmitting node, some nodes will represent its neighborhood Φ t, some others are hidden from it Φ htr, and the others are neither neighbors ( Φ t )nor hidden ( Φ htr ); for each node degree, the event represents a transmission casing a hidden acknowledgement collision which occpies from the channel time different average periods; accordingly the combinations of sch events of different degrees occrring at the same time occpy different average periods determined by the smallest period occpied by an involved event. PSR ht =(L ack +L) n Φ hctr k ψ n k Φ t k Φ htr PST k +L ack n Φ hctr k (ψ n Φ htr ) PST k + n Φ hctr k (ψ n Φ t ) Φ hctr PST k (L ack +L) q=2 ( 1) q Φ hctr C q n h m h m =h m,1,h m,2,...,h m,q }, seqence of terms=q ( k ψ n,k Φ t,k Φ htr k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ n) Φ hctr PST k ) L ack ( 1) q q=2 Φ hctr C q n h m h m =h m,1,h m,2,...,h m,q }, smmation term=q prodct terms (( k (ψ n Φ htr ) k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ n) PST k ) z (h m \n) ( PST k )) k ψ z,k Φ t k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ z)

29 Wireless Commnications and Mobile Compting 29 Φ hctr q=2 ( 1) q Φ hctr C q n h m h m =h m,1,h m,2,...,h m,q }, smmation term=q prodct terms (( k (ψ n Φ t ) k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ n) PST k ) z (h m \n) ( PST k )), k ψ z k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ z) (B.1) PST k =τ k j Φ kn (1 τ j )(1 PC hdatak )(1 PC hackk ). (B.2) The PSR t in the eqation of α2 t represents the probability of sccessfl data reception at the coordinators in transmitter t neighborhood; that is, the probability of at least one of the nonmtally exclsive events of children sccessfl transmissions to the transmitter t neighborhood coordinators occrs. The probability PSR t is given by PSR t =L ack ( n Φ t c k ψ n k=t Φ t c PST k q=2 ( 1) q Φtc C q n h m h m =h m,1,h m,2,...,h m,q }, seqence of terms=q ( k ψ n,k=t k ((Φ hm,1 Φ hm,2 Φ h m,q )\Φ n) PST k )), (B.3) where Φ tc C q represent the q-combinations from neighbor coordinators of t. Last expressions presented in this appendix are related to the probabilities deriving β t,andtheyare a transmission and no node senses the channel from slot i ntil CCA1; then P idlet =(1 (1 τ j )) j Φ t,j=bs P bsyst C C q = k Φ t k=bs C PST k ( 1) q q=2 n h m h m =h m,1,h m,2,...,h m,q }, seqence of terms=q P bsyft =(1 (1 τ j )) j Φ t,j=bs (1 P bsyst, P bsyat P bsyst 1 j Φt,j = PSR t L ack. ( k (ψ n Φ t ) PST), k k ((Φ hm,1 Φ hm,2 Φ hm,q )\Φ n ) =BS (1 τ j) )=1 j Φ t,j=bs (1 τ j ) (B.4) The probability P idlet of an idle slot1 before the idle CCA1 happenedwhensloti, 1 i <, isprecededby Notations i=1 = ((1 τ t ) (1 τ j )) j Φ t,j=bs i 1 1 j Φt,j=BS (1 τ j) 1 (1 τ t ) j Φt,j=BS (1 τ j). α: The probability of finding the channel bsy in the 1st clear channel assessment (CCA1) β: Theprobabilityoffindingthechannel bsy in the 2nd clear channel assessment (CCA2) τ: Theprobabilitythatanodeattemptsafirst carrier sensing in a random time slot q : The probability of going back to state Q λ: Packet generation rate, sed with an appropriate sbscript to indicate the packet arrival rate at the MAC qee μ: Packetservicerate P: Theprobabilitythatatransmittedpacket enconters a collision (B.5)

30 3 Wireless Commnications and Mobile Compting R: Thereliability P cf : The probability that the packet is discarded detochannelaccessfailre P cr : The probability of a packet being discarded detoretrylimits D: Theaveragedelay E: The average energy consmption P(): Probabilityofanevent L s : The time period for sccessfl transmission L c : The time period for failed transmission L : The idle state length withot generating packets L: The length of data packet L ack : The length of acknowledgement S b : The time nit, aunitbackoffperiod m: The maximm backoff stages nmber E[T h ]: The expected total backoff delay E[S]: Meanpacketservicetime C αβ (i): All possibilities of choosing i elements from a set of bsy channel probabilities (1 α)β, α} C e αβ (i): One of the elements in the set C αβ(i) N e α (i), Ne β (i): Retrn the nmber of α and (1 α)β in C e αβ (i),respectively T sc : TheCCAtime I: Used to indicate the size of a specific sbset of nodes, sch as nmber of end devices in a clster and the nmber of the BS-neighbors inasb-nw,withasbscriptwhich identifiesthissbsetinformation Φ: Used to define sets of nodes distingish the different degrees and effects of neighborhood (neighbor, common neighbor, hidden, etc.), with a sbscript which identifies this set information ψ c : The set of coordinator c children C t, C: The coordinator of node t and the set of all coordinators, respectively. 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