Multi-hop Fast Conflict Resolution Algorithm for Ad Hoc Networks

Transcription

1 Multi-hop Fast Conflit Resolution Algorithm for Ad Ho Networks Shengwei Wang 1, Jun Liu 2,*, Wei Cai 2, Minghao Yin 2, Lingyun Zhou 2, and Hui Hao 3 1 Power Emergeny Center, Sihuan Eletri Power Corporation, Chengdu, China 2 National Key Laboratory of Siene and Tehnology on Communiations, University of Eletroni Siene and Tehnology of China, Chengdu, China 3 Information Tehnology Center, Tsinghua University, Peking, China Abstrat. Media aess ontrol is an important tehnology in ad ho networks. Based on the multi-hop Pseudo Bayesian (PB) algorithm and the single-hop Fast Conflit Resolution algorithm (FCR), in this paper, we propose a Multi-hop Fast Conflit Resolution (MFCR) algorithm for ad ho networks. We make the detailed introdution of the theoretial model, the pseudo Bayesian analysis and the algorithm deign. MFCR employs a ompetition probability foreasting method, whih is similar to the bakoff ounter used in FCR, ombined with the handshake proess used in PB to solve the utilization and the fairness problems of the time slot alloation. Simulations show that the MFCR has evident improvement in the network performane. 1 Introdution The media aess ontrol is an important tehnology in Ad-Ho networks [1]. Beause of the limitation of frequeny, the wireless hannel resoure is relatively sare. Meanwhile, the hannel fading, the interferene and the transmission ollision will deteriorate the transmission apaity [2][3]. Hene, the hannel resoure alloation will play an important role. The hannel of Ad-Ho networks is a multi-hop broadast shared hannel, only the nodes are far away from eah other an reuse the same frequeny at the same time [4]. In Time Division Multiple Aess (TDMA) Media Aess Control (MAC) protool [5][6][7], the wireless hannel is divided into periodi frames in time dimension, and eah frame onsists of some time slots. The goal of hannel resoure alloation is making nodes rationally utilize limited slot resoure aording to the network situation. The stati TDMA protool an t adjust the slot alloation sheme to the network situation, whih will ause the waste of the hannel resoure. In ontrast, the dynami TDMA protool an adjust the slot alloation flexibly to adapt to the network situation [8], so it an effetively use the slot resoure. The Five-Phase Reservation Protool (FPRP) is a typial dynami TDMA protool based on ompetition [9]. The nodes in the network obtain their own delivery slot through ompetition mehanism, so the slot alloation of eah time frame is different. * Corresponding author: liu_jun@uest.edu.n The Authors, published by EDP Sienes. This is an open aess artile distributed under the terms of the Creative Commons Attribution Liense 4.0 (

2 Due to the distributed harateristi, the FPRP protool an be exeuted independently by eah node. That is to say, the nodes more than two hops an simultaneously use the same slot. For eah node, the slot reservation proess an be regarded as a loal reservation proedure, whih only involves the slot reservation within two hops. Through the loal reservation proess, it makes the network have a good salability. In FPRP protool, the single wireless hannel is logially divided into the reservation hannel and the information hannel. To TDMA frame, it is the reservation frame and the information frame. Eah reservation frame and information frame has the same number of time slots. In the reservation phase, the node reserves time slot by a five phase handshake mehanism. In this way, FPRP an realize a onflit-free slot alloation for paket delivery. The reservation frame is followed by a number of information frames, the nodes in the network an transmit data in the information slot until the next reservation frame. 2 System model We use graph G (V, E) to represent the network topology, where V is the node set and E is the link set in the network. If there is a link between node i and node j, we use an undireted edge e i,j, e i,j E, to represent the one-hop neighboring relationship. If there is no diret link between node i and node j, but they have a ommon neighbor k, we define node i and node j as two-hop neighbor. We use matrix C(G)=[ ij ] NⅹN and D(G)=[d ij ] NⅹN to represent the one-hop onnetion relationship and the two-hop onnetion relationship respetively 10. The ij and d ij are defined as ij = 1, e ij E,i j 0, else d ij = 1, e,e ik jk E,e ij E,i j 0, else (1) (2) Owing to the nodes in a half-duplex wireless network annot reeive multiple pakets simultaneous and annot transmit and reeive at the same time 11, the time slot of eah node must be different from the one-hop neighbors and the two-hop neighbors to avoid transmission ollision. The main goal of the slot assignment algorithm is to maximize the hannel utilization with the minimum number of time frames. Consider a time frame has M slots and eah node s slot number is at least one. We use a M N matrix T = [ t mi ] M N to represent the slot alloation sheme in network. If time slot m belongs to node i, we set t mi = 1, otherwise t = 0, and define the slot utilization of node i as mi M t m= 1 mi ρ i = (3) M The slot utilization of the whole network an be expressed as 1 1 ρ = = N MN (4) N M N ρ 1 i t i= m= 1 i= 1 mi As a result, the slot alloation an be summarized as the following mathematial model 2

3 min M and max ρ (5) M s.t. C1: t mi 1 (i N ) m=1 C2 : ij + t mi + t mj 2 (i, j N,i j,m M ) C3: ik t mi + jk t mj 1 (i, j,k N,i j k,m M ) (6) where C1 denotes that eah node takes at least one slot, C2 represents two one-hop neighbors an't be alloated with the same slots, C3 stands for that two-hop neighbors an't use the same slots. 3 Pseudo baysian algorthm In this paper, we use the Pseudo Bayesian algorithm 12 to alulate the probability of nodes partiipating in the slot reservation. Through the five phase handshake reservation mehanism in FPRP, the node in the network an sense the urrent slot reservation status, suh as suess, idle, and onflit. Beause the reservation proess is a loal proess within two-hop, the node needs to maintain two parameters: one is the number of ompetition nodes within its two-hop; the other is the number of nodes want to reserve the slot, but an't ompete for the urrent slot due to the slot being reserved by others. When a node is informed that the urrent slot is alloated to one of its neighbors, it stops the ompetition for the urrent slot, but an still partiipate in the ompetition for the next slot. The status of idle, onflit, and suess will affet the number of ompetition neighbors within two-hop, so the nodes an partiipate in the remaining reservation proess with a modified ompetition probability. Aording to Pseudo Bayesian algorithm, the ompetition probability of eah node is related to the number of ompeting nodes within two-hop. That is, the number of ompetitors in two-hop is inversely proportional to the ompetition probability. Consider two situations in the network, the one is in the dense area (suh as the network enter area), the other is in the sparse area (suh as the edge of the network). Beause there are more neighbors in the dense area, more reservation ativities will take plae, and there will be more onflits. As it is hard to find the idle state in the reservation proess, the possibility of dereasing the ompetition probability is high. On the other hand, beause there are fewer neighbors in the sparse area, there will be fewer onflits, and it is easier to sense the idle state in the reservation proess. Aording to the Pseudo Bayesian algorithm, one a node finds an idle state in the urrent sot reservation proess, the ompetition probability will be inreased. So the possibility of inreasing the ompetition probability in the sparse area is higher than that in the dense area. Thus, the differene of node density in two-hop will result in unfair slot alloation. 4 Multi-hop fast onflit resolution algorithm In order to solve the problem in multi-hop pseudo Bayesian algorithm, we propose a Multihop Fast Collision Resolution (MFCR) based on single-hop Fast Collision Resolution (FCR) [13]. In FCR, when the node senses the idle slot, the value of bak off ounter dereases by one. When a node heks ontinuously idle slots, one the slot been idle again, the value of bak off ounter dereases by half. On the other hand, when a node senses the ollision, it doubles the value of ontention window (CW). Set a random number between 0 - CW as the value of bak off ounter. In this way, when ollision emerges, the node defers its hannel aess to derease the ollision possibility. 3

4 MFCR applies the Fast Conflit Resolution in the multi-hop ad ho networks. In MFCR, n is used to predit the number of neighbors within two-hop, the role of n is similar to the bak off ounter used in FCR. The larger n is, the smaller the ompetition probability of a slot ahieves. Considering the fairness of slot alloation, we limit n between n min and n max. Through the five-phase handshake proess taken in FPRP protool, eah node an sense the reservation status of the urrent slot. At the beginning of reservation proess, n is initially set to the minimal value n min. After the reservation proess finished in a round, the node updates n aording to the following algorithm. Algorithm 1 Competition probability adjustment Input: Reservation status Output: Competition probability Note: x denote the number of ontinuous idle and k is the threshold of ontinuous idle state, 0< β < α < 1. h denote the number of hops to the suessful reserving node, and 0< a3 < a2 < a1 < 1. P denote the ompetition probability. 1. swith ( reservation status) 2. ase idle: 3. if x< k, then 4. n = max( αn, nmin ) 5. else 6. n = max( βn, nmin ) 7. ase onflit: 8. if the node is the reservation initiator 9. n = n + random(0,min(2 n, nmax ) n) 10. ase suess: 11. if h == 0, n = nmax 12. if h == 1, n = max( an 1, nmin ) 13. if h == 2, n = max( an 2, nmin ) 14. if h 3, n = max( an 3, nmin ). 15. end of swith 16. P = 1/ n Then repeat the above steps In Idle state, MFCR takes α and β as the amplitude fators to multiply by n, the redution of β to n is greater than that of α to n. When the number of the ontinuous idle states deteted is less than k, MFCR uses α to redue n, and the ompetition probability of the node inrease slowly. If the number of ontinuous idle state is equal to or bigger than k, whih means that only a few ompetition nodes are within two-hop, and the ollision probability is low. When a node enounters a onflit, it will derease the ompetition probability rapidly b sharply inrease of n. In other words, in MFCR, while the reservation ollision ours within two-hop, the proposed onflit resolution algorithm an derease the reservation ollision rapidly. 4

5 After suessfully reserving a time slot, the node updates n with the maximum value n max to derease the ompetition probability of the next time slot, whih guarantees the fairness of slot alloation. If a node gets the information that a one-hop or two-hop neighbor reserves the urrent slot suessfully, the node dereases n with fator a 1 and a 2 to inrease the ompetition probability of the next slot, whih speeds up the onvergene of slot alloation algorithm. If a node reeives a suessful reservation message omes from three or more hops away, the node inrease its ompetition probability with fator a 3 due to the spatial reuse of the time slot Performane evaluation In this setion, the performane of the proposed MFCR is evaluated. We set the network sene in a 1500m 1500m retangle area, the ommuniation range is 300 meters. The detailed simulation parameters are listed in Table 1. Table 1. Simulation parameters. Network range 1500 m 1500 m Communiation range 300 m Send buffer length 64 pakets Paket size 1024 bits Paket transmission rate 1 Mbps α 0.9 β 0.5 n min 2 n maxn 24 a 1 1/1.1 a 2 1/1.2 a 3 1/1.3 In addition to the above simulation parameters, we also define the following performane parameters. Network throughput: The total number of pakets sent suessfully per seond. Paket delivery rate: The total number of pakets reeived divides by the total pakets that the network generates. Average aess delay: The sum of the paket delay of all the reeived pakets divides by the total number of the reeived pakets. Suess rate of ompetition: The number of nodes that suessfully reserve the slot divides by the total number of nodes in the network during a frame time. Fairness of slot alloation: The variane of slot number alloated to eah node in a frame time. Slot utilization: The total times of suessful slot reservation divides by the slot number in a frame time. 5.1 Average suessful ompetition rate and average time slot utilization rate The paket generation rate is set to 20 paket/seond/node and the other parameters are the same as table 1. The number of nodes in the network is gradually inreased from 20 to 60. The network topology is randomly generated aording to the node number. We simulate the suess rate and the average slot utilization of FPRP and MFCR for 20 independent simulations. 5

6 (a) Suess rate of ompetition Fig. 1. Comparison of the suess rate and the utilization rate. (b) Slot utilization rate As shown in Fig. 1(a), the average suessful ompetition rate dereases with the inrease of the nodes. The reason is that with the inrease of nodes, more onflits will emerge, thus ausing the deline in the suess rate of ompetition. MFCR has a higher suess rate than PB, whih is beause MFCR signifiantly redues the ompetition probability when it enounters onflits, reduing the potential onflits in the future. As shown in Fig. 1(b), the slot utilization rate of MFCR is higher than PB. It reflets that MFCR has a better spatial reuse apability than PB. Moreover, with the inrease of the node density, the ompetitors between two-hop inreased, whih leads more onflits. So the slot utilization dereases with the inrease of nodes. 5.2 Fairness of the slot alloation algorithm The number of nodes is 25, paket generation rate is 20 paket/seond/node, and the other parameters are the same as table 1. The network topology is randomly generated aording to the node number. We simulate the fairness of slot alloation for MFCR and PB for 20 times. (a) Normalized fairness of slot alloation Fig. 2 Comparison of the fairness and the network throughput. (b) Network throughput vs paket generation rate As shown in Fig. 2(a), the variane of the slot number per frame of MFCR is less than PB. In MFCR, the node suessfully reserving a slot will set the ontention probability to the smallest value, and the possibility to partiipate in the next slot ompetition dereases fast. However, in PB algorithm, the node that suessfully reserves a slot will partiipate in the next slot ompetition with the unhanged probability, while the ompetition probability of those nodes suffering ontinuous onflit is redued, whih will result in unfairness of slot 6

7 alloation. Therefore, MFCR performs better than PB algorithm on the fairness of slot alloation. 5.3 Network ommuniation performane The number of nodes is 50. The network topology is randomly generated aording to the node number. The network throughput, the average aess delay and the paket delivery rate are ahieved respetively under onditions of different paket generation rate. Fig. 2(b) is the network throughput omparison, the differene between the MFCR and the PB algorithms isn t obvious when the paket generation rate is low due to the light load. With the inrease of the paket generation rate, beause of the higher slot utilization and the fairness of slot alloation, the throughput of MFCR is higher than PB. With the inrease of the paket generation rate, the throughput of these two algorithms both tend to saturated due to the limited slot resoures. (a) Average aess delay vs paket generation rate Fig. 3 Comparison of the average aess delay and the paket delivery rate. (b) Paket delivery rate vs paket generation rate As shown in Fig. 3(a), with the inrease of paket generation rate, the number of the pakets that aumulated in the send buffer inrease rapidly, so the average aess delay in the network gradually inreases. However, owing to the higher time slot utilization and the higher suess reservation rate, the average aess delay of MFCR performs better than PB. Fig. 3(b) is the paket delivery rate omparison. When the paket transmission rate is lower than the paket arrival rate, the send buffer will overflow and the new arrival pakets will be disarded. Hene, the paket delivery rate will derease. Beause of the higher spatial reuse apability, more pakets are sent simultaneously at different node beyond two hops, the paket delivery rate of MFCR is higher than PB algorithm. 6 Conlusion In this paper, we propose a multi-hop fast onflit resolution algorithm, namely MFCR for ad ho networks. We make detailed introdutions of the theoretial model, the pseudo Bayesian analysis and the algorithm design. MFCR employs a ompetitive probability foreasting method, whih is similar to the bak-off ounter used in single-hop FCR, ombined with the handshake proess used in multi-hop pseudo Bayesian to solve the utilization and the fairness problems in distributed time slot alloation. We ompared the network throughput, the paket delivery rate, the average aess delay, et. between MFCR and PB. Simulations show that MFCR has evident improvement in the network performane. 7

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