Technical Report. i-game: An Implicit GTS Allocation Mechanism in IEEE for Time- Sensitive Wireless Sensor Networks

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1 Techncal Report -GAME: An Implct GTS Allocaton Mechansm n IEEE for Tme- Senstve Wreless Sensor etworks Ans Koubaa Máro Alves Eduardo Tovar TR Verson: 1.0 Date: Jul 2006

2 -GAME: An Implct GTS Allocaton Mechansm n IEEE for Tme- Senstve Wreless Sensor etworks Ans KOUBAA, Máro ALVES, Eduardo TOVAR IPP-HURRAY! Polytechnc Insttute of Porto (ISEP-IPP) Rua Dr. Antóno Bernardno de Almeda, Porto Portugal Tel.: , Fax: E-mal: { akoubaa@de,mjf@, emt@de }.sep.pp.pt Abstract The IEEE Medum Access Control (MAC) protocol s an enablng technology for tme senstve wreless sensor networks thanks to ts Guaranteed-Tme Slot (GTS) mechansm n the beacon-enabled mode. However, the protocol only supports explct GTS allocaton,.e. a node allocates a number of tme slots n each superframe for exclusve use. The lmtaton of ths explct GTS allocaton s that GTS resources may quckly dsappear, snce a maxmum of seven GTSs can be allocated n each superframe, preventng other nodes to beneft from guaranteed servce. Moreover, the GTSs may be only partally used, resultng n wasted bandwdth. To overcome these lmtatons, ths paper proposes -GAME, an mplct GTS Allocaton Mechansm n beacon-enabled IEEE networks. The allocaton s based on mplct GTS allocaton requests, takng nto account the traffc specfcatons and the delay requrements of the flows. The -GAME approach enables the use of a GTS by multple nodes, whle all ther (delay, bandwdth) requrements are stll satsfed. For that purpose, we propose an admsson control algorthm that enables to decde whether to accept a new GTS allocaton request or not, based not only on the remanng tme slots, but also on the traffc specfcatons of the flows, ther delay requrements and the avalable bandwdth resources. We show that our proposal mproves the bandwdth utlzaton compared to the explct allocaton used n the IEEE protocol standard. We also present some practcal consderatons for the mplementaton of - GAME, ensurng backward compatblty wth the IEEE standard wth only mnor add-ons.

3 -GAME: An Implct GTS Allocaton Mechansm n IEEE for Tme-Senstve Wreless Sensor etworks Ans KOUBAA, Máro ALVES, Eduardo TOVAR IPP-HURRAY! Research Group, Polytechnc Insttute of Porto Rua Dr. Antono Bernardno de Almeda, 431, Porto, PORTUGAL {akoubaa, emt}@de.sep.pp.pt, mjf@sep.pp.pt Abstract The IEEE Medum Access Control (MAC) protocol s an enablng technology for tme senstve wreless sensor networks thanks to ts Guaranteed-Tme Slot (GTS) mechansm n the beacon-enabled mode. However, the protocol only supports explct GTS allocaton,.e. a node allocates a number of tme slots n each superframe for exclusve use. The lmtaton of ths explct GTS allocaton s that GTS resources may quckly dsappear, snce a maxmum of seven GTSs can be allocated n each superframe, preventng other nodes to beneft from guaranteed servce. Moreover, the GTSs may be only partally used, resultng n wasted bandwdth. To overcome these lmtatons, ths paper proposes -GAME, an mplct GTS Allocaton Mechansm n beacon-enabled IEEE networks. The allocaton s based on mplct GTS allocaton requests, takng nto account the traffc specfcatons and the delay requrements of the flows. The -GAME approach enables the use of a GTS by multple nodes, whle all ther (delay, bandwdth) requrements are stll satsfed. For that purpose, we propose an admsson control algorthm that enables to decde whether to accept a new GTS allocaton request or not, based not only on the remanng tme slots, but also on the traffc specfcatons of the flows, ther delay requrements and the avalable bandwdth resources. We show that our proposal mproves the bandwdth utlzaton compared to the explct allocaton used n the IEEE protocol standard. We also present some practcal consderatons for the mplementaton of -GAME, ensurng backward compatblty wth the IEEE standard wth only mnor add-ons. nterestng for WS applcatons, where energy consumpton and network lfetme are man concerns. Addtonally, the IEEE protocol also provdes realtme guarantees by usng the Guaranteed-Tme Slot (GTS) mechansm. Ths feature s qute attractve for tme-senstve WSs. In fact, when operatng n beacon-enabled mode,.e. beacon frames are transmtted perodcally by a central node called PA coordnator for synchronzng the network, the IEEE protocol allows the allocaton/deallocaton of GTSs n a superframe for nodes that requre real-tme guarantees. Hence, the GTS mechansm provdes a mnmum servce guarantee for the correspondng nodes and enables the predcton of the worst-case performance for each node's applcaton. However, the GTS mechansm, as proposed n the standard [1], presents some lmtatons n terms of effcency and deployment n WSs wth a large number of nodes. In fact, durng each superframe (dvded nto sxteen tme slots) only up to seven GTSs (from 1 up to 15 tme slots per GTS) can be allocated, formng the Contenton-Free Perod (CFP) (see Fg. 1). The remanng tme slots n the superframe compose the Contenton Access Perod (CAP) usng Carrer Sense Multple Access wth Collson Avodance (CSMA/CA) as a MAC protocol. 1. Introducton 1 The IEEE protocol [1] has been recently adopted as a communcaton standard for Low-Rate Wreless Local Area etworks (LR-WPAs). It presents the advantage to be flexble enough for fttng dfferent requrements of potental applcatons by adequately tunng ts parameters. Even though the IEEE protocol was not specfcally desgned for Wreless Sensor etworks (WSs), t s ntended to be sutable for them. In fact, low data rate, low power consumpton and low cost wreless networkng are the key features of the IEEE protocol, whch typcally ft the requrements of WSs. More specfcally, the IEEE Medum Access Control (MAC) protocol has the ablty to provde very low duty cycles (up to 0.1 %). Ths feature s partcularly 1 Ths work was partally funded by FCT under CISTER research unt (UI608). Fg. 1. Beacon Interval and Superframe Structure Snce each GTS s exclusvely assgned to one node, the number of nodes nvolved n the CFP s lmted to seven or less. Ths s because the IEEE standard [1] assumes that a node performs an explct GTS allocaton request by askng the PA coordnator for a certan number of tme slots. A node s admtted to transmt durng the CFP, f the number of avalable tme slots n the superframe s hgher than requested, and the mnmum CAP length wll not be volated after the allocaton [1]. Two negatve mpacts may result from ths explct allocaton scheme.

4 1. The GTSs can be quckly consumed by a few number of nodes, preventng the others from havng a guaranteed servce. 2. A node wth a low arrval rate that has allocated a GTS, may only partally use t (when the amount of guaranteed bandwdth s hgher than ts arrval rate). Ths leads to underutlzaton of the GTS bandwdth resources. Due to the pre-fxed tme slot duraton n a superframe, t s practcally mpossble to balance the arrval rate of a node and ts guaranteed GTS bandwdth. The amount of wasted bandwdth ncreases wth the varance between the guaranteed bandwdth and the arrval rate. Ths paper proposes a smple and effectve soluton to overcome the prevously descrbed lmtatons of the explct GTS allocaton n the IEEE protocol. Bascally, the dea conssts n sharng the same GTS between multple nodes, nstead of beng exclusvely dedcated to one node, f a certan schedule that satsfes the requrements of all requestng nodes exsts. Sharng a GTS by several nodes means that the tme slots of ths GTS are dynamcally allocated to dfferent nodes n each superframe, accordng to a gven schedule. In contrast, an explct allocaton statcally devotes a GTS to only one node n all subsequent superframes. Hence, the GTS allocaton mechansm proposed n ths paper s based on the traffc specfcaton of the requestng nodes, ther delay requrements, and the avalable GTS resources. Instead of askng for a fxed number a tme slots, a node that wants to have a guaranteed servce sends ts traffc specfcaton and delay requrement to the PA coordnator. The latter runs an admsson control algorthm based on ths nformaton and the amount of avalable GTS resources. The new allocaton request wll be accepted f there s a schedule that satsfes ts requrements and those of all other prevously accepted allocaton requests; otherwse, the new allocaton request s rejected. We refer to ths as the mplct GTS allocaton mechansm (-GAME). We show that -GAME has the advantage to accept multple flows sharng the same GTS whle stll meetng ther delay requrements. It also mproves the utlzaton of the CFP by reducng the amount of wasted bandwdth of GTSs and maxmzes the duraton of the CAP, snce the CFP length s reduced to a mnmum. Related Work. The performance of the explct GTS allocaton n IEEE has been recently evaluated n [2]. That work proposes a delay bound analyss of an explct GTS allocaton. It also analyzes the mpact of the beacon and superframe orders on the throughput, delay and power effcency of a GTS allocaton. In ths paper, we extend the work n [2] by consderng mplct GTS allocatons. We also prove the mprovement as compared to the explct GTS allocaton approach, n terms of bandwdth utlzaton. Bascally, the problem that we are addressng n ths paper can be regarded as analyzng the schedulablty of a gven number of flows sharng a certan number of tme slots. Ths problem has already been addressed by some works n the lterature, but wth completely dfferent contexts and assumptons, as brefly outlned next. In [3-4], the authors have addressed multcycle pollng schedulng n feldbus networks. These papers have contrbuted to the schedulablty analyss of a set of perodc tasks wth deadlnes equal to perods under Rate Monotonc (RM) and Earlest Deadlne Frst (EDF) schedulng polces, where the nodes polled are dfferent from one cycle to another. In both approaches, the dea conssts n fndng the mnmum cycle, called prmary cycle, whch corresponds to the greatest common dvsor of all task perods, and computng the number of tme slots needed to transmt perodc traffc nsde each cycle, f the task set s schedulable. The last step conssts n executng tasks accordng to ther prortes (usng RM or EDF) n each prmary cycle. Our work dffers from these approaches n two aspects. Frst, we don't consder perodc message arrvals, but we adopt a more general representaton of the traffc usng the (b,r)-curve model where b s the burst sze of the flow and r s the average rate. Ths traffc model also ncorporates the classcal representaton of the perodc arrval model wth or wthout jtter [5]. For that reason, our analyss s based on the etwork Calculus theory. Second, the duratons of the cycles n the pre-cted approaches are fxed and related to the perods of the flows. Ths does not match wth our case, snce n the IEEE protocol one cycle s represented by a Beacon Interval (BI) (see Fg. 1), whose duraton depends on the beacon order parameter as t wll be shown n Secton 2. Moreover, snce the IEEE protocol does not allow more than seven GTS allocatons, ths may restrct the number of tme slots n each cycle n contrast wth the approaches n [3-4], where the number of tme slots s only lmted by the duratons of the prmary cycle and the tme slot. Contrbutons of ths paper. The contrbutons of ths paper are the followng. Frst, we present the motvaton for an mplct GTS allocaton mechansm for the IEEE protocol, showng that the explct allocaton mechansm proposed by the standard lacks bandwdth effcency, partcularly for low rate WS applcatons (Secton 3). We also ntroduce the mplct allocaton mechansm, -GAME, through a practcal example. Second, we evaluate the schedulablty analyss of an mplct GTS allocaton of k tme slots shared by nodes, where k <, under round robn schedulng (Secton 4). For that purpose we derve the servce curve and the delay bound guaranteed by such an allocaton, defned by the tuple (b, r, D) where b s the burst sze, r s the arrval rate, and D s the delay requrement. Fnally, we present the -GAME admsson control mechansm, based on our analyss and we provde some gudelnes for ts mplementaton, wth mnor add-ons to the IEEE standard protocol defned n [1] (Secton 5).

5 2. Background 2.1 Overvew of the IEEE MAC protocol The IEEE MAC protocol supports two operatonal modes that may be selected by a central node called PA coordnator: (1) the non beacon-enabled mode where the MAC s ruled by non-slotted CSMA/CA; (2) the beacon-enabled mode where beacons are perodcally sent by the PA coordnator to dentfy ts PA and synchronze nodes that are assocated wth t. The most relevant MAC features are outlned next. In ths paper, we only consder the beacon-enabled mode, snce t enables GTS allocatons. In beacon-enabled mode, the Beacon Interval (BI) defnes the tme between two consecutve beacons, and ncludes an actve perod and, optonally, an nactve perod. The actve perod, called superframe, s dvded nto 16 equally-szed tme slots, durng whch data frame transmssons are allowed. Durng the nactve perod (f t exsts), all nodes may enter nto a sleep mode, thus savng energy. Fg. 1 llustrates the beacon nterval and the superframe structure. The Beacon Interval and the Superframe Duraton (SD) are determned by two parameters, the Beacon Order (BO) and the Superframe Order (SO), respectvely. The Beacon Interval s defned as follows: BI = abasesuperframeduraton 2, (1) for 0 BO 14 The Superframe Duraton, whch determnes the length of the actve perod, s defned as follows: SD = abasesuperframeduraton 2, (2) for 0 SO BO 14 In Eqs.(1) and (2), abasesuperframeduraton denotes the mnmum duraton of the superframe, correspondng to SO = 0. Ths value corresponds to ms, assumng 250 kbps n the 2.4 GHz frequency band, whch wll be consdered throughout the rest of ths paper. By default, the nodes compete for medum access usng slotted CSMA/CA durng the Contenton Access Perod (CAP). More detals can be found n [1]. 2.2 Explct GTS allocaton n IEEE The IEEE protocol also offers the possblty of havng a Contenton-Free Perod (CFP) wthn the superframe (Fg. 1). The CFP, beng optonal, s actvated upon request from a node to the PA coordnator for allocatng a certan number of tme slots. Fg. 2 shows the GTS characterstcs feld format sent wthn an allocaton request command frame [1] by a node to the PA coordnator. Fg. 2. GTS characterstcs feld format n IEEE BO SO The node explctly expresses the number of tme slots that t wants to allocate n the GTS Length feld. ote that the GTS length can be up to 15 tme slots. The GTS Drecton feld specfes f the GTS s n receve-only mode (value = 1),.e. data s transmtted from the PA coordnator to the requestng node, or n transmt-only mode (value = 0),.e. data s transmtted from the requestng node to the PA coordnator. The Characterstcs Type feld refers to a GTS allocaton f t s set to one or a GTS deallocaton f t s set to zero. Upon recevng ths request, the PA coordnator checks whether there are suffcent tme slots avalable n the superframe for ths request. If the number of avalable tme slots n the superframe s smaller than the number requested, the GTS allocaton request s rejected, otherwse t s accepted. The PA coordnator must ensure that the CAP length remans always greater than amncaplength equal to 7.04 ms [1]. In the former case, the correspondng node may send ts data frames durng the CAP, but wth no guarantee. If the GTS allocaton request s accepted, the admtted node must keep track of beacon frames for checkng whch tme slots have been allocated n the current superframe. Ths nformaton s located n the GTS descrptor feld (Fg. 3), whch s embedded n each beacon frame. A beacon frame cannot have more than seven GTS descrptors, lmtng the number of GTSs to seven. Fg. 3. GTS Descrptor Feld Format n IEEE The explct GTS allocaton adopted by the standard has the advantage of beng smple. However, t may be not effcent enough n terms of bandwdth utlzaton for flows wth low arrval rates, whch s typcally the case n wreless sensor networks, snce the guaranteed bandwdth of a GTS can be much hgher than the arrval rates (see Secton 3.2). 2.3 Delay bound analyss usng etwork Calculus In etwork Calculus theory [7], the delay bound analyss for a gven data flow wth a cumulatve arrval functon R( t ) assumes the followng. 1. It exsts an arrval curve ( t ) R( t ) such that s, 0 s t, R( t) R( s) α ( t s) α that upper bounds. Ths nequalty means that the amount of traffc that arrves to receve servce n any nterval s, t never α t s. exceeds ( ) 2. It exsts a mnmum servce curve ( t ) R( t ). β guaranteed to Then, the delay bound, D max, for a data flow wth an α t that receves the servce β ( t ) s the t β t : arrval curve ( ) maxmum horzontal dstance between α ( ) and ( ) { { }} ( αβ, ) sup nf τ 0: α( ) β( τ) Dmax = h = s s + (3) s 0

6 Fg. 4 presents an example of the delay bound for a lnear arrval curve α ( t) = b + r t that receves a rate-latency servce curve β RT, ( t ) R ( t T + = ), where R r s the guaranteed bandwdth, T s the maxmum latency of the servce and ( x ) + = max ( 0, x ). Ths servce curve s typcally used for servers that provde a bandwdth guarantee wth a certan latency. The latency T refers to the devaton of the servce (e.g. blockng factor of non-preemptve transmssons). Fg. 4. Arrval Curve, Servce Curve and Delay Bound The delay bound D max (presented n Fg. 4) guaranteed for the data flow wth the arrval curve α ( t) = b + r t (also called (b, r) curve) by the servce curve β RT, ( t ) R ( t T + = ) s computed as follows [7]: D max b = + T (4) R 2.4 Delay bound of an explct GTS Allocaton In [2], the authors have derved the delay bound for flows wth an arrval curve α ( t) = b + r t usng etwork Calculus. It has been shown that the servce curve offered by a GTS allocaton of n tme slots s approxmated by a rate-latency servce curve β R, ( ) ( ) n T t = R n n t Tn, where R n s the guaranteed bandwdth of a GTS defned as: T R data n = n C BI and T n s the latency of the servce expressed as: Tn = BI n TS (6) T data defnes the maxmum duraton used for data frame transmsson nsde a GTS, wthout takng the control overheads (nter-frame spacng (IFS) and acknowledgement) nto account [2]. C denotes the data rate equal to 250 kpbs. As a result, t s shown that the delay bound guaranteed by the servce curve β R, ( ) n T t for a data flow bounded by a n br, curve s: ( ) b Dn,max = + BI n Ts n T C BI (( data ) ) ( ) Another servce curve n the form of a star functon was also derved n [2]. However, the analyss presented n that paper consders the rate-latency servce curve β R, ( ) n T t of n one GTS. (5) (7) 3. -GAME: An Implct GTS Allocaton Mechansm 3.1 System model and assumptons We consder an IEEE cluster composed of a set of sensor nodes n the range of a partcular node consdered as the PA coordnator. ote that ths star topology may be partcularly nterestng for large-scale sensor networks when usng clusterng and/or two-tered archtectures [6]. Moreover, the IEEE supports cluster-tree topologes, whch extend the star network by means of chld coordnators [1] that synchronze the nodes out of the range of the PA coordnator. We assume that the PA coordnator sets up the network wth a superframe structure defned by the beacon order BO and the superframe order SO. The beacon nterval (BI) and the superframe duraton (SD) are computed usng Eqs. (1) and (2), respectvely. Each node generates a flow F bounded by the arrval curve α ( t) = b + r t, where b s the maxmum burst sze, r s the average arrval rate and D denotes the delay requrement of flow F. We represent flow F by the tuple Fspec, = ( b, r, D ). Let RTS denote the guaranteed bandwdth per one tme slot. Observe that R TS can be computed usng Eq. (5) for n = 1. For a GTS wth a length of k allocated tme slots (k<15), we denote as RkTS the bandwdth guaranteed by k tme slots expressed as: RkTS k RTS = (8) The man problem addressed n ths paper s how to farly share the allocaton of k tme slots n the CFP between requestng nodes, wth respect to ther Fspec, = ( b, r, D ). Intutvely, flows are allowed to share a GTS allocaton of k tme slots, f two necessary condtons (C1) and (C2) hold: (C1) r RkTS = 1 (C2),max, 1 D D (C1) states that the sum of all arrval rates does not exceed the entre bandwdth of k tme slots. (C2) states that the delay bound guaranteed by the allocaton does not exceed the delay requrement, for each flow F. 3.2 Bandwdth utlzaton of explct GTS allocatons Ths secton defnes the bandwdth utlzaton of a GTS allocaton. It also presents the lmtatons of an explct allocaton n terms of bandwdth utlzaton effcency. Consder a flow F ( b, r, D ) = that has an explct GTS allocaton of k tme slots. Then, the bandwdth utlzaton of ths GTS allocaton s defned as: ( ) UkTS r RkTS r k RTS (9) = = (10)

7 ow, for a CFP of a length k tme slots, k 15, contanng all allocated GTSs ( k = k ) and = 1 correspondng to allocatng nodes, the average bandwdth utlzaton of the CFP s defned as: (11) 1 1 r U = U = U = R k CFP kts k TS = 1 TS = 1 Observe that the mnmum bandwdth that can be allocated s R TS (t s not dvsble). It s logcal to assume that, wth an explct allocaton, a node that requests a GTS allocaton of k tme slots has an arrval rate r that satsfes: ( 1) k RTS < r k RTS (12) From Eqs. (8), (10) and (12), we obtan: ( k 1) k < U kts 1 (13) Then, the mnmum utlzaton lmt s defned as: k ( k 1) Umn = k,1 k 15 (14) k Fg. 5 presents the mnmum utlzaton lmts for dfferent GTS length values, for one node. Fg. 5. Mnmum Utlzaton Lmts of an Explct Allocaton From Fg. 5, t can be understood that the lowest utlzatons can be expermented for GTSs wth one tme slot allocaton. Ths s because the arrval rates of the flows can be low fractons of the ndvsble R TS, whch trggers the motvaton for sharng the tme slot wth other nodes, f the delay requrements of the flows can stll be satsfed. Ths case s most lkely to happen n sensor networks snce ther arrval rates may be partcularly low. 3.3 Improvng bandwdth utlzaton va mplct GTS allocatons: -GAME Accordng to condton (C1) n Eq. (9), flows may share one GTS f the sum of ther arrval rates s smaller or equal to the guaranteed bandwdth of the GTS. The man problem n ths case s to fnd the adequate tme slot allocaton schedule n each beacon nterval that respects a per-flow guaranteed bandwdth greater or equal to ts arrval rate. The complexty of fndng the adequate schedule depends on the number of GTS allocaton requests and on the per-flow utlzaton of the GTS. A partcular smple form of sharng the GTS s by usng round robn schedulng, thus provdng a far share. However, round robn offers the same amount of guaranteed bandwdth to all flows wthout any dfferentaton. Hence, round robn s adequate when the arrval rate of each flow sharng the GTS s smaller than the bandwdth guaranteed by a far share of the GTS. More formally, for a GTS allocaton of k tme slots farly shared by flows Fspec, = ( b, r, D ), = 1.., then: k R r Ts = 1.. (15) ote that the far sharng of a GTS s effectve when the arrval rates of the flows are smlar. For nstance, a flow wth an arrval rate of 20 kbps cannot farly share the same resource wth a flow wth an arrval rate of 1 kbps. Hence, we assume that Eq. (12) must hold for flows that are canddates for sharng the same GTS wth other flows. Ths assumpton s relevant for WS applcatons, snce flows generated by sensor nodes have smlar behavors. For the sake of smplcty and wthout loss of generalty, n ths paper we analyze flows wth (at most) one tme slot allocaton. We make ths assumpton for two reasons. 1. It s common n WSs that flows are generated at low rates. It has been shown n [2] that the guaranteed bandwdth per one tme slot allocaton for a full duty cycle (BO = SO), s comprsed between 9.38 kbps and kbps, dependng on the superframe order (SO). The traffc pattern of most WS applcatons should have arrval rates much lower than these values, snce n WSs t s most lkely to have a large number of nodes wth low rates rather than a small number of nodes wth hgh rates. 2. Accordng to Fg. 5, the case of one tme slot allocaton s the most nterestng for the -GAME approach snce the utlzaton (wthout -GAME) can be very low (less than 50%), partcularly for flows wth low rates. ote that the methodology presented next can be easly extended based on the same prncples n order to merge flows requestng the same number of k tme slots (satsfyng Eq. (12), for k >1) nto one GTS wth reduced sze. Based on the defnton of mplct GTS allocaton, the utlzaton of the GTS of k tme slots shared by flows Fspec, = ( b, r, D ), = 1.., s defned as: U kts 1 = r k R (16) TS = 1

8 The bandwdth utlzaton of each flow n the GTS s defned as: U, kts r = k R TS (17) Fg. 6.a: One tme slot allocaton used by one node In summary, ths paper consders flows requestng an mplct GTS allocaton wth arrval rates r R Ts, whch corresponds to one tme slot allocaton n case of an explct allocaton. Our problem s then reduced to fnd a far share of mplct GTS allocatons nto a CFP wth a length of k tme slots for requestng nodes, where k. ote that n ths case, the CFP length (correspondng to mplct allocatons) does not exceed seven tme slots (k<7) snce only seven GTSs, each of one tme slot length, can be allocated n a gven superframe. 3.4 A practcal ntuton on the -GAME approach To gve a practcal ntuton on the mplct GTS allocaton approach, we present the followng llustratve example. Assume an IEEE cluster where the PA coordnator sets up the superframe structure wth BO = 0 and SO = 0. Ths confguraton corresponds to BI = SD =15.36 ms, Ts = 0.96 ms and R TS = 9.38 kbps [2]. A frst request. ow, let a node A generate a flow F A bounded by the arrval curve α A ( t ) = t kbts (a burst sze wth b A = 200 bts and an arrval rate of r A = 3 kbps) and wth a delay requrement D A = 150 ms. Then, F spec, A = ( 200 bts,3 kbps,150 ms). When node A requests a GTS allocaton, t must send F spec, A to the PA coordnator, whch has to decde whether to accept the flow or not. Based on the results n [2], wth BO = 0 and SO = 0 (Eqs. (5) and (6)), the servce curve offered by one tme slot allocaton s β 1 node,1ts ( t ) 9.38 ( t + = 14.40) kbts. Fgs. 6.a and 7.a present the allocaton of the GTS by node A and ts servce curve, respectvely. Usng Eq. (7), the PA coordnator can compute the delay bound guaranteed by one tme slot allocaton based on F spec, A. Ths delay bound s D A,max = ms. Observe also that the guaranteed bandwdth by one tme slot allocaton (9.39 kbps) s hgher than the arrval rate (3 kbps). As a result, both condtons (C1) and (C2) n Eq. (9) are satsfed; hence, the flow s accepted for one tme slot allocaton. The GTS wll be partally used by node A wth an utlzaton ra R TS = 32% (see Eq. (16)). A second request. Assume that a second node B generatng a flow F B wth a traffc specfcaton F spec, B = ( 400 bts, 2 kbps, 150 ms) wants to allocate a GTS. The tradtonal explct mechansm would requre the allocaton of a new tme slot exclusvely for node B. Ths would lead to an addtonal wasted bandwdth, as for node A, snce the arrval rate of r B s lower than R TS. We propose a dfferent approach that s to share the prevous GTS allocaton wth node A, f t would be possble to respect Fg. 6.b: One tme slot allocaton used by two nodes under round-robn schedulng Fg. 6.c: One tme slot allocaton used by two nodes under a schedulng dfferent from round robn Fg. 6.d: One tme slot allocaton used by three nodes under round robn schedulng Fg. 6.e: Two tme slot allocaton used by three nodes under round robn schedulng Fg. 6. Dfferent Implct GTS Allocatons Fg. 7.a: Servce curve of a one tme slot allocaton used by one node Fg. 7.b: Servce curve of a one tme slot allocaton used by two nodes under round robn schedulng Fg. 7.c: Servce curve of a two tme slot allocaton used by three nodes under round robn schedulng Fg. 7. Servce Curves of Implct GTS Allocatons

9 both Fspec, A and F spec, B. The problem s to determne the servce curve offered by the same tme slot for each flow. Assumng that the sharng of ths tme slot s based on round robn schedulng, the tme slot alternates between both flows n each beacon nterval (refer to Fgs. 6.b). Fg. 7.b shows the correspondng servce curve for each flow. Snce the tme slot s shared between two nodes, the bandwdth guaranteed for each flow s equal to R TS 2, and the latency s equal to 2 BI Ts (see Fgs. 6.b and 7.b). As a result, the servce curve granted for each flow usng round robn s β 2 nodes,1ts ( t ) 4.69 ( t + = 29.76). ow, applyng Eq. (7) to each flow F A and F B usng the per-flow servce curve β 2 node,1ts ( t ), we have: D A,max = ms and D B,max = ms, and thus condton (C2) s satsfed. Observe that the guaranteed rate of one tme slot s hgher than the sum of the arrval rates of both flows,.e. condton (C1) s satsfed. As a result, both flows can be accepted to share the same GTS allocaton under round robn schedulng. In ths case, the utlzaton of the GTS s equal to ( ra + rb ) RTS = 53% (see Eq. (16)), obvously hgher than that n the prevous case. Observe n Fg. 6.c that changng the schedulng polcy results n a change of the servce curve, even f the guaranteed bandwdth s the same. In Fg. 6.c, the maxmum latency s hgher than the one wth round robn schedulng. A thrd request. ow, assume that a thrd node C generatng a flow F C wth a traffc specfcaton F spec, C = ( 500 bts, 3 kbps, 150 ms) wants to allocate a GTS. Lke n the prevous requests, we compute the per-flow servce curve for each node whle sharng one tme slot usng round robn polcy β 3 nodes,1ts ( t ) 3.12 ( t + = 45.12) (see Fg. 6.d). The correspondng delay bounds for each of the three flows are: D A,max = ms 150 ms, D B,max = ms 150 ms, D C,max = ms 150 ms. As a consequence, node C cannot be admtted to share the same tme slot wth A and B, even though the sum of all arrval rates s stll lower than the guaranteed bandwdth ( < 9.38). Snce there are stll avalable resources n the superframe, t s possble to extend the CFP to two tme slots and apply the same admsson control algorthm to node C, but wth a servce curve β 3 nodes,2ts ( t ) 6.25 ( t + = 28.80) (see Fg. 6.e, Fg. 7.c). The correspondng delay bounds for each of the three flows are: D A,max = 60.8 ms 150 ms ; D B,max = 92.8 ms 150 ms ; D C,max = ms 150 ms. As a consequence, t s possble to meet the delay requrements of the three flows wth only two tme slots. Impact of the delay on the utlzaton. In ths latter case, the mplct allocaton mechansm saves one tme slot compared to an explct GTS allocaton. The bandwdth utlzaton of the CFP wth mplct GTS allocaton s then ( ra + rb + rc ) R2TS = 42% (Eq. (16)), whereas n case of an explct GTS allocaton the bandwdth utlzaton s ( ra + rb + rc ) 3RTS = 28% (Eq. (11)). The mprovement n terms of utlzaton depends on the delay requrement. For more relaxed delay requrements, the mprovement on utlzaton s more sgnfcant. For example, f the three flows had a delay requrement of 250 ms, t would be possble to allocate only one tme slot, resultng n an utlzaton of ( ra + rb + rc ) R1TS = 85%. What f the guaranteed bandwdth s lower than the arrval rate? Observe that n the prevous scenaros, the guaranteed bandwdths offered by a shared GTS usng round robn schedulng are hgher than the arrval rates of the three flows. ow, magne that node C has an arrval rate equal to 7 kbps. In ths case, round robn s not suffcent for flow C snce the guaranteed rate 6.25 kbps s lower than flow C's arrval rate. A frst opton s to extend the length of the CFP to have hgher bandwdth and compute the correspondng servce curve, whle stll applyng round robn. Ths technque s smple, but t tends to an explct allocaton. Another technque conssts n usng weghted round robn, by assgnng tme slots proportonally to the arrval rates, and thus provdng dfferentated servces nsde one shared GTS wth respect to the arrval rates. Each flow wll then have ts own servce curve wth respect to ts arrval rate, and the correspondng delay bound would be compared to the delay requrement of the flow, as made prevously. Ths technque s more effcent n terms of utlzaton, but ntroduces addtonal complexty to determne the weghts, the schedule and then the correspondng servce curves for each flow. For the sake of smplcty, we consder n ths paper the frst alternatve of extendng the CFP length. 4. Schedulablty analyss of an mplct GTS allocaton under round robn Ths secton presents a generalzaton of the practcal ntuton presented n Secton 3.4. Our purpose s to fnd a general expresson of the servce curve for flows that share k tme slots, where k usng round robn schedulng, assumng that flows F have arrval rates r RTs (the most relevant for WS applcatons). ote that n ths partcular case, k < 7, snce the maxmum number of GTSs per superframe s lmted to 7. Snce we are consderng a far share of a GTS usng round robn polcy, β (t) s equal to a rate-latency servce curve β RT, ( t ) common to all flows sharng the same GTS. Two dstnct cases need to be addressed. 1. Case of k =. Ths case s equvalent to an explct allocaton. Each node has ts own tme slot snce round robn s deployed. The delay bound s then computed based on Eq. (7) and compared to D. 2. Case of k <. ths case s more nterestng because the number of nodes s hgher than the allocated tme slots, as presented n the example (Secton 3.4). Obvously, t can be understood from the motvatng example that the guaranteed rate for each flow s:

10 RkTS k R = RTS = (18) The man problem s to compute the servce latency related to the servce curve. Observe, through the examples of Fg. 6, that the latency can be expressed as: T = p BI + q Ts (19) where p denotes the number of beacon ntervals that contrbutes to the servce latency, and q represents the number of tme slots to be subtracted from the latency. For k 7 and 1, we have: p = > 0 k and q = p k 1< 0 (20) Eq. (20) can be verfed wth the examples n Fg. 6 as well as wth all other combnatons of and k. As a result, the servce curve correspondng to a far share of k tme slots between nodes for k < under round robn schedulng s: k + βrt, ( t) = RTS ( t ( p BI + q Ts) ) (21) wth p and q are defned n Eq. (20). So, for a flow F wth r R, the correspondng delay bound guaranteed by the far share, based on Eq. (4), s: b D,max = + p BI + q Ts k R TS ( ) (22) Observe that Eqs. (21) and (22) are general expressons that are also vald n case of k = (n ths case, p = 1 and q = -1 and Eqs. (21) and (22) are equvalent to Eqs. (5-6) and (7) (wth n = 1), respectvely). In summary, a set of flows (F, = 1..) sharng a number of k tme slots where k are schedulable under round robn, f, for each flow wth Fspec, = ( b, r, D ) we have r k RTs (Eq. (15) mples condton (C1) n Eq. (9)), and D,max D (equvalent to condton (C2) n Eq. (9)) where D s obtaned from Eq. (22).,max 5. -GAME mplementaton approach 5.1 -GAME Admsson Control Algorthm Ths secton presents an admsson control algorthm for the mplct GTS allocaton mechansm (-GAME) presented n Sectons 3 and 4. We defne the admsson control algorthm n case of r RTs, = 1.. under round robn schedulng (results of Secton 4). We assume that flows wth r R Ts explctly request a number of tme slots based on ther arrval rates, usng Eq. (12). -GAME Management Algorthm 1 type Flow = (d, b, r, D) //traffc specfcaton and delay requrement 2 type FlowSetType = (F, where F requests a tme slot n the CFP) 3 nt = 0; // the number of flow sharng a GTS 4 nt k = 1; // the number of shared tme slot 5 FlowSetType FlowSet; Flow F; 6 On (arrval of a new flow F) do { 7 = + 1; 8 f (admsson_control (k,, FlowSet, F) == false) { 9 f (k == 7) { //the maxmum number of GTSs s reached 10 reject_request(f); 11 = - 1; break; 12 } 13 else { // k < 7 14 k = k + 1; //ncrease the length of the CFP 15 goto lne 8; 16 } 17 } 18 else { 19 accept_request(f); //accept the new flow to share the GTS 20 FlowSet_Add(FlowSet, F); //add the new flow to the GTSset 21 } Fg. 8. -GAME Management Algorthm Fg. 8 presents the -GAME management algorthm for mplct GTS allocatons under round robn schedulng. Fg. 9 presents the admsson control functon used to decde whether to accept or not a node requestng an mplct allocaton of a GTS based on ts Fspec = ( b, r, D). GTS Management Algorthm. When a new mplct GTS allocaton request ntated by a flow F = (b, r, D) s receved by the PA coordnator, the admsson control algorthm ncrements,.e. the number of flows sharng the same GTS. Then, the admsson control functon s called takng as nputs the number of allocated tme slots (k), the number of flows sharng ths GTS of k tme slots (), the set of flows sharng the GTS (FlowSet), and the new flow F requestng the GTS allocaton. If the admsson control functon returns false, then the PA coordnator tres to extend the CFP length by addng a new tme slot, f the maxmum length of seven tme slots has not been reached (snce, n ths case, each node allocates at most one tme slot n a superframe); otherwse the new request s rejected. If a new tme slot can be added to the CFP, then k s ncremented by one and the admsson control algorthm s called agan wth the new k value. If the admsson control returns true, the request of the new flow F wll be accepted and the latter s added to the FlowSet lst. The admsson control functon. Ths functon returns a Boolean value statng whether to accept or not the new flow requestng a GTS. As we have mentoned before, we assume that flows requestng mplct allocaton satsfes r RTs, = 1.. (for the valdty of Eqs. (16 ) to (22)). Ths decson s based on the shared GTS length (k), the number of flows sharng the GTS (), the specfcaton of the new flow F and the exstng flows n the FlowSet. The adm_crt flag s set to true at the start of the algorthm, and wll be set to false f the delay requrement cannot be met or

11 f the guaranteed bandwdth s hgher than the arrval rate. The delay requrement of each flow wll be compared to the guaranteed delay expressed n Eq. (22), whch s shown to be vald for both cases k < and k =. Actually, the case k > s not consdered n the -GAME admsson control functon, snce t s consdered as an explct GTS allocaton request, as we have prevously mentoned. -GAME Admsson Control Functon 1 R TS = guaranteed bandwdth by one tme slot 2 Ts = tme slot duraton 3 boolean admsson_control (nt k, nt, FlowSetType FlowSet,. Flow F) 4 { 5 boolean adm_crt = true; 6 f (k <= ) { 7 p = cel ( / k); 8 q = p * k 1; 9 for (nt = 1, ++; <=) 10 f (( D < (( b / (k * R TS / )) + ( p * B q * Ts))) or. (r>k*r TS /)) 11 adm_crt = false; 12 } else //the case (k>) s consdered as explct allocaton 13 adm_crt = false; 14 } Fg. 9. -GAME Admsson Control Functon 5.2 -GAME mplementaton gudelnes Ths secton presents some practcal consderatons for the mplementaton of the -GAME mechansm n IEEE An nterestng feature of -GAME s that ts mplementaton only requres mnor add-ons to the standard protocol,.e. t does not mpose any changes to the exstng protocol. The dea conssts n usng the reserved 6 th bt n the GTS characterstcs frame, embedded n a GTS allocaton request command feld (compare Fg. 10 and Fg. 2). Ths bt s referred to as Allocaton Type. The admsson control algorthm should be mplemented at a hgher layer (e.g. etwork Layer) and should return the decson to the MAC sublayer (Fg. 12). Fg. 12. Protocol Layer Archtecture for -GAME Hence, upon recepton of an mplct GTS allocaton request (Allocaton Type = 1), the MAC sublayer of the PA coordnator should forward the traffc specfcaton feld (shown n Fg. 11) to the hgher layer for processng by the admsson control module. The burst sze and the arrval rate felds should be expressed by four bts each (16 classes for each feld). The Delay Requrement feld s expressed by fve bts (32 classes). Usng ths frame format, the PA coordnator should defne a fxed range for each value (class) of the correspondng feld. These patterns should be known n advance by all nodes assocated to the PA before ntatng an mplct allocaton. The specfcaton of these classes and ranges s out of the scope of ths paper. When the flow specfcaton s receved by the admsson control module, t evaluates the acceptance of the new flow based on the algorthm defned n Secton 5.1. The decson should be notfed to the MAC sublayer through the servce access pont. In case of acceptance, the MAC sublayer allocates the tme slots n the CFP n round robn order to all accepted nodes. For that purpose, the MAC sublayer should establsh a certan order to allocate the tme slots accordng to round robn schedulng. Each beacon frame of a new beacon nterval should ndcate whch nodes are allowed to use the GTS n the current superframe, wth respect to the establshed order. Fg. 10. GTS Characterstcs Extenson Feld Format for Implct Request Allocaton If the Allocaton Type bt s set to 0 t refers to an explct GTS allocaton. In ths case, the allocaton process wll follow the standard recommendatons. If t s set to 1, t refers to the -GAME mplct allocaton mechansm proposed n ths paper. In ths case, to keep the IEEE wth no changes, the flow specfcaton nformaton Fspec = ( b, r, D) should be embedded n the hgher layer packets, as presented n Fg. 11. Fg. 11. Flow Specfcaton Feld Format for -GAME 6. Performance evaluaton The purpose of ths secton s to llustrate the advantage of -GAME n mprovng the bandwdth utlzaton effcency as compared to the explct GTS allocaton mechansm. Consder a set of 14 flows F, 1 14 wth the arrval rates as presented n Table 1. Table 1. Arrval rates of the flows F1 F 14 Flow Arrval rates r (kbts/sec) F1, F F2, F5, F6 1 F3, F4, F F7, F9, F F F F14 0.2

12 Snce the guaranteed delay bound typcally depends on the burst sze, we assume (wthout loss of generalty) that all flows have the same burst sze b = 200 bts, We consder a PA wth the same parameters as n Secton 3.4 ( BO = SO = 0 ). Consder also the followng three cases: 1. Explct GTS allocatons for 7 flows (F1 to F7) 2. Implct GTS allocatons for 7 flows (F1 to F7) 3. Implct GTS allocatons for 14 flows (F1 to F14) ote that condton (C1) s satsfed n all cases 7 14 ( r = kbps,. = 1 r = 9 1 kbps ). Fgs. 13 and 14 = 1 present the bandwdth utlzaton and the guaranteed delay bound, respectvely, as a functon of the number of allocated tme slots for the mplct GTS allocatons. The bandwdth utlzaton of the explct allocaton (9.5%) s obtaned from Eq. (11) and represented by a dotted lne for a comparson purpose. The bandwdth utlzaton of mplct allocatons s obtaned from Eq. (16). Fg. 13. Bandwdth Utlzaton Improvement wth -GAME It can be understood from Fg. 13 that the -GAME approach sgnfcantly mproves the bandwdth utlzaton compared to the explct allocaton. However, the degree of mprovement depends on the delay requrements of the flows as t s observed n Fg. 14. Fg. 14. Delay Bounds Guaranteed by the -GAME Approach For example, assume that all flows have a delay requrement D = 300 ms. It s possble to meet ths requrement for the seven flows (F1 to F7) wth only one allocated tme slot ( D,max = ms), snce r RTS / 7, 1 7. In ths case, the bandwdth utlzaton s 66.7%, whch s much hgher than 9.5% n case of the explct GTS allocaton. It s also possble to meet ths delay requrement for the fourteen flows wth only two allocated tme slots resultng n a utlzaton of 48.5%. In ths case, all the flows take advantage of a guaranteed servce wth only two allocated tme slots, whch s not possble usng the explct GTS allocaton mechansm. Moreover, by usng the mplct GTS allocaton, the length of the CFP s sgnfcantly reduced, thus ncreasng the CAP perod. 7. Conclusons Ths paper mproves on the state-of-the-art wth the defnton of -GAME, a new approach to allocate GTS n the IEEE protocol for WSs. Ths proposal s motvated by the bandwdth utlzaton neffcency of the explct GTS allocaton mechansm supported by the IEEE protocol for flows wth low rates. -GAME overcomes ths problem by allowng to share the same GTS between multple flows based on ther traffc specfcatons and delay requrements. The performance evaluaton study clearly showed the mprovement of -GAME compared wth the explct GTS allocaton mechansm n terms of bandwdth utlzaton effcency. Moreover, the mplementaton of -GAME only requres mnor add-ons to the IEEE protocol and ensures backward compatblty wth the standard, makng our approach easly mplementable n Commercal-Off-The- Shell (COTS) platforms. References [1] IEEE Standard-2003, "Part 15.4: Wreless Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons for Low-Rate Wreless Personal Area etworks (LR-WPAs)", IEEE-SA Standards Board, [2] A. Koubâa, M. Alves, E. Tovar, "GTS Allocaton Analyss n IEEE for Real-Tme Wreless Sensor etworks", submtted to WPDRTS 2006, avalable for download at [3] S. Cavaler, S. Monforte, A. Corsaro, G. Scapellato, "Multcycle Pollng Schedulng Algorthms for FeldBus etworks" Journal of Real-Tme Systems, V. 25 (2-3), pp , Sept.-Oct [4] P. Raja, G. oubr, "Statc and Dynamc Pollng Mechansms for FeldBus etworks", ACM SIGOPS Operatng Systems Revew, V.27 (3), pp , July [5] A. Koubâa, Y. Q. Song, "Evaluaton and Improvement of Response Tme Bounds for Real-Tme Applcatons under on-preemptve Fxed Prorty Schedulng", Internatonal Journal of Producton and Research (IJPR), (Taylor & Francs), V. 42 (14), pp , July [6] A. Koubaa, M. Alves, "A Two-Tered Archtecture for Real- Tme Communcatons n Large-Scale Wreless Sensor etworks: Research Challenges " In Proc. of 17th Euromcro Conference on Real-Tme Systems (ECRTS'05), WP Sesson, Mallorca (Span), July, [7] J-Y. Leboudec, P. Thran, A Theory of Determnstc Queung Systems for the Internet, LCS, Vol. 2050, 2001.

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