A Negotiation-based TDMA MAC Scheme for Ad Hoc ...sciei.org/uploadfile/2013/0820/20130820100037761.doc · Web viewNegotiation-Based TDMA Scheme for Ad Hoc Networks from Game Theoretical

Negotiation-Based TDMA Scheme for Ad Hoc Networks from Game Theoretical PerspectiveHui Leifang, Li Jiandong*, Li Hongyan, Ma YinghongBroadband Wireless Communications Laboratory, Information Science Institute, State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, Shaanxi Province, P. R. China

Abstract: A negotiation-based TDMA scheme for ad hoc networks, which was modeled as an asynchronous myopic repeated game and self-adjusted to choose proper time slots is proposed. During the simulation, the game theory has been utilized to model the negotiation procedure as a potential game. Compared to the traditional centralized TDMA schemes, our scheme operates in a decentralized manner and is scalable to topology changes. Simulation results show that, with respect to the coloring quality, the performance of our scheme is close to that of the classical centralized algorithms with much lower complexity. Moreover, there is a fairness benefit on it compared to CSMA/CA.Key words: TDMA scheme; asynchronous myopic repeated game; coloring quality; classical centralized algorithms

I. INTRODUCTION

Due to the multi-hop nature of ad hoc networks, different users can reuse the common channel in appropriate manners as long as they do not interfere with each other. TDMA is one of the multiplexing methods. It is especially effective for networks with high load or deadline-sensitive traffic. Slot assignment is the core component of TDMA protocols. Assigning different time slots to conflicting users is the objective of the slot assignment issue and is the subject of this paper.

Since the optimal static time slot scheduling is NP-hard[1-4], various heuristic methods have been developed. Ramanathan[2] models this problem as a graph coloring problem and designs three efficient greedy algorithms RAND, MNF and PMNF. But the centralized characteristic is not suitable for ad hoc networks. The first proposed TDMA protocol for ad hoc networks is FPRP[1,3]. Nodes select slots randomly by using a five-phase algorithm. But a node may not be assigned a slot and requires many runs to increase the chance to get a slot. Ref.[4] proposes a distributed TDMA slot assignment algorithm based on a distance-2 coloring scheme. It requires each node to maintain state within its three-hop neighborhood, which could be quite difficult and resource intensive. In NB-TDMA[5], TDMA scheduling is done on demand. A node wishing to transmit data toward a sink dispatches a mobile agent. This creates a coupling between the routing and MAC operation.

Moscibroda[6] et al. proposes a graph coloring scheme, which performs distance-1 coloring, in which only adjacent nodes have different colors. This scheme does not prevent hidden terminal collisions. DRAND[7] is the latest proposed TDMA scheme for ad hoc networks, which is the distributed version of RAND[2]. It gives the same maximum slot number as RAND, but the exchange procedure is complicated.

Owing to these drawbacks, a negotiation-based TDMA scheme for ad hoc networks is proposed in this paper, which is executed in a distributed manner and is self-adjusted to choose proper time slots. With respect to the number of time slots required (It is the measure of coloring/scheduling quality[3].), our scheme has similar performance to the classical PMNF[2] with lower computational burden and is better than RAND [2]/DRAND[7].

The rest of this paper is organized as follows. Section II outlines system model and expressions, followed by the problem formulation in Section III. Section IV gives the detailed procedure of our scheme. The scalability is introduced in Section V and simulation results are provided in Section VI. Finally, Section VII concludes the paper.

II. SYSTEM MODEL AND EXPRESSION

We consider an ad hoc network with several homogeneous users randomly deployed in a square area. Similar to other literatures, users around one user are its one-hop neighbors or two-hop neighbors in terms of the hops. Time is split into frames which are subdivided into time slots with equal length. All users share a common channel. We assume that each user has a half-duplex transceiver. Capture effect is not considered and the interference occurs when one user is transmitting and receiving simultaneously or receiving packets from different flows at the same time. Signal propagation delay is ignored, thus packets can be received by destinations immediately. Furthermore, we assume that users always have packets to transmit all the time. As mentioned earlier, a decentralized scheme is preferred for ad hoc networks. Under this mode, even if the stable state has been achieved through negotiation, it is still hard to make all users to know the state within a short time. Therefore, the latest system state is necessary. Besides, in TDMA system,

all users should be synchronized. In a word, one user needs to act as a coordinator to implement these functions, and all users are synchronized with the coordinator. We assume that there are N users in the network. Each user has a unique ID, labeled as i, .

and denote the one-hop and two-hop neighbor set of user i respectively. In each frame, there are TS time slots. We use A to represent the available time slots matrix. Its element

indicates time slot j is available for user i. Similarly, O represents the time slot occupancy matrix. Its element indicates user i occupies

time slot j to transmit with rate .

III. PROBLEM FOR MULATION

Our TDMA procedure is divided into two phases: the negotiation phase and the collision-free transmission phase. The latter one is also known as TDMA phase1. During the negotiation phase, each user continuously judges its time slot choice based on the information collected before, makes change if necessary and then broadcasts relevant information. Its choice will influence the upcoming decisions and vice versa. Game theory[8-12] is a natural modeling technique. From the game theoretic perspective, users are decision makers, i.e. players, and time slots set are the action space. After getting proper time slots in the negotiation phase, the collision-free transmission phase get started.

3.1 Game theoretical model for the negotiation phaseSince all users are synchronized, at the beginning of each time slot, all users try to access it with a certain probability (the selection of this probability will be discussed later). It means that there is always a random combination of users accessing the channel in each time slot, forming a subset of the user set. This process repeats until the collision-free phase has been achieved. This procedure is well matched with the repeated game[8-9]. Firstly, the problem is a repeated game with asynchronous timing. Besides, each user can only get its neighbor information by listening to the channel. Using the game theoretical term, it is myopic. Therefore, users’ actions in every time slot form a normal game, and the negotiation phase is an asynchronous myopic repeated game. For the normal game, the utility function of a user, say i, can be defined as

(1) It expresses the local throughput of user i with current choice . If it selects time slot j, then .

In the first term, denotes whether user k occupies

time slot j, thus the product of reflects the collision. It means that as long as the same decision has been made within i’s two-hop area, user i might get a throughput of 0. The second term denotes the estimated throughput of its one-hop and two-hop neighbors, which can be got by the recorded information. From (1), we know that user decisions within two-hop area are needed. In each time slot, users who catched channel successfully will broadcast its one-hop neighbors’ choices and its own decision. Their one-hop neighbors who receive the information will update the record.

Accordingly, we define a potential function as

(2)

It is the sum of each user's throughput, in which is the decision set for users except i.

Theorem 1. The stage game , with

defined as (1) and potential function defined as (2), is a finite exact potential game.

Proof. The proof of Theorem 1 follows similar lines of the proof in Ref. [13].

So far, the stage game has already been designed and proved to be an exact potential game. With this property, we will discuss the performance of the game model.

3.2 Model analysisThe utility function should be selected to have the particular meaning of the local throughput. But as mentioned in Ref.[8], it must also have appealing mathematical properties that guarantee the equilibrium convergence. Nash Equilibrium (NE)[8-10] is a commonly used stable solution. Then how is the performance of the modeled myopic repeated game? Will it converge to the expected steady state?3.2.1 ExistenceIntuitively speaking, the steady state here means that all the potential collided users transmit in different time slots. It is obvious that the steady states do exist. From the perspective of game theory, all the finite potential games have at least one NE (Theorem 4.24 mentioned in Ref.[9]). Therefore, there are multiple NEs for this model.3.2.2 Optimality

Optimality here means that the number of time slots is minimized. Ref.[2] has pointed out that the optimal solution of the NP-hard problem can only be got through exhaustive search. Our model can get efficient scheduling but not the optimal one.3.2.3 ConvergenceIt makes no sense to speak of convergence for a normal form game as it is defined as having only a single iteration. Convergence is much frequently discussed in the context of repeated games. Convergence has close relationship with the decision rules[9] and decision timings[9] in every stage game. Potential game is a special game model. It is guaranteed to converge to the NE with different combinations of decision timings and decision rules. It has been shown in Ref.[9] that finite potential games converge in round-robin, random and asynchronous decision timings, no matter which decision rule it is using.

These features shed lights on our algorithm design. As long as the learning procedure is designed based on the convergence condition, our myopic repeated game model must arrive to the corresponding steady state.

IV. THE NEGOTIATION-BASED TDMA MAC SCHEME

4.1 Frame formatA frame consists of three parts as shown in Figure 1.

Fig.1 Frame formatIn the frame head, SI (Synchronization Information)

contains timing information to provide accurate synchronization in each frame. CP (Current Phase) indicates either it is in negotiation phase or collision-free phase. All users determine their actions according to the CP value. During the negotiation phase, CP=0; otherwise, CP=1. TS (Time Slot) represents the number of time slots in this frame. All the information in the frame head is sent by the coordinator with proper power to notify all users the current system state.

Time slots section is used to compete and negotiate in the negotiation phase and transmit packets in TDMA phase.

It should be emphasized that we assume there is a user acting as a coordinator, but the selection of it is beyond the scope of this paper.

4.2 Packet typesSeveral types of packets are involved in the

negotiation phase.-- RTSP (RTS Packet): It is used for similar purpose as RTS in CSMA/CA; however, the required length is much shorter than that of RTS. It is used to reserve the channel;-- CTSP (CTS Packet): It is used for similar purposes as CTS in CSMA/CA; however, the required length is much shorter than that of CTS. It is used to reply to RTSP and also to silence its own one-hop neighbors (i.e. the two-hop neighbors of the user who sent RTSP);-- NOTIFP (Notification Packet): It is used to broadcast its one-hop neighbor occupancy information recorded and its current choice;-- FBP (Feed Back Packet): It is used to feedback the current occupancy information to the coordinator. It can only be sent in frame tail.

4.3 Backoff issueThe backoff scheme we discussed here is similar to that of IEEE 802.11.

In the negotiation phase, for users who try to access channel in the current time slot, backoff is executed first. The user with the shortest backoff in its neighborhood broadcasts RTSP after his backoff, while those who have longer backoffs will cancel their attempts once RTSPs are received. This strategy can effectively alleviate concurrent attempts among adjacent users.

In CSMA/CA, RTS and CTS exchanges between source and destination pair, and other users who hear one of them will keep silent in the designated time. Different from that, our CTSPs are replied by all the one-hop neighbors of the source, collisions may occur at common neighbors. Figure 2 is an example.

User B, C and D receive RTSP from User A. If they reply CTSP at the same time, collisions occur at both User A and E. For User E, the collided CTSP makes it unaware of the reservation from User A. In order to avoid this case, the random backoff is also adopted when users reply CTSP.

Fig.2 Topology exampleThe handshake and backoff procedure is depicted in

Figure 3.

Fig.3 Handshake and backoff procedureAt the beginning of time slot i, suppose User A and

C try to participate in the negotiation. They backoff first (User A has a shorter counter than C’s). Then User A sends RTSP after his backoff, while User C cancels backoff and gives up the attempt. For the one-hop neighbor of User A, User B, C, and D reply with CTSP to RTSP after a random backoff and also set NAV to keep silent. User E hears CTSP from User B and C and set NAV. Waiting for a maximum backoff time after RTSP, User A broadcasts NOTIFP containing its choice.

4.4 Scheme description1) Negotiation phase We assume that in the initial state, TS is set to N, which is the number of users in the system. In order to minimize the number of time slots needed, each user chooses TS1 as their initial choice. Each user maintains three variables , indicating the current

choice; , the set of current available time slots and

, the current access probability, which is defined as the reciprocal of the access index.

Details of the negotiation phase are described as follows:

- Initialization:TS is set to N by the coordinator. For each user,

.- Repeat of the frame:Frame Head: SI, CP=0 and TS=N is sent by the

coordinator;Time Slot s : in time slot j, each user decides whether

to access channel according to . The user, who tries to negotiate, backoffs a random time.

– If nothing has received during the backoff period, the user, say i, sends RTSP and then waits;

– If RTSP is received by the backoffing user, say k, it cancels the current backoff, starts a new backoff, sends CTSP after backoff and then keeps silent in this slot;

– If RTSP is received by the non-backoffing user, say m, it sends CTSP after a random backoff

and keeps silent in this slot;– If one user receives CTSP but it is not the user

sent RTSP in current slot, the user, say n, keeps silent in this slot;

– After a maximum waiting time is run out, user i selects the time slot with the least index inas its current choice and broadcasts NOTIFP;

– k and m update and respectively once NOTIFP is received.

– Users who participate in the current negotiation decrease their , while other users increase

. If exceeds the given range, set .

Frame Tail: each user returns FBP containing to the coordinator in a round-robin mode.

- Until: No one changes its decision in a frame.It should be pointed out that the adjustment of is

to make sure that all the users have chance to participate in the negotiation.2) Collision-free phase/TDMA phaseOnce there is no user changing their decisions in a frame, the negotiation phase is terminated and the collision-free phase is started, which is indicated by CP=1 in the frame head. The coordinator decides TS value based on the collected information in frame tail.

Till now, a TDMA MAC scheme for ad hoc network is designed. Its advantages are multiple folds. Firstly, the negotiation procedure is also a process of neighbor discovery. Compared to the traditional centralized TDMA schemes and the latest DRAND[7], a priori topology information is not required. Secondly, the decentralized negotiation process only collects local knowledge thus lightens the computational burden compared to the centralized solution. Finally, fairness is taken into consideration. During the negotiation phase, is changeable to ensure the competition chance. Once the collision-free phase is achieved, each user transmits once in a frame. While in CSMA/CA, the user who has already transmitted successfully is prone to transmit more, which causes unfairness.

V. SCALABILITY

The collision-free transmission under static topology has been achieved. But how to make it be scalable to changes? Now we give the basic mechanisms.

5.1 Coordinator alternationThe coordinator broadcasts the basic information in the whole procedure. In order to avoid one user consuming too much energy, an alternation is required among all users.

Current coordinator can include the alternation

expectation in SI to indicate that a new coordinator is wanted. The user who wants to be the coordinator contains the application in the FBP. Then current coordinator selects one by a predefined rule and conveys this information in SI of next frame. Thus, all users will be aware of the new coordinator.

The following time benchmark can barely follow the current one or be redefined by the new coordinator.

5.2 Topology changeIf one user is going to leave, it informs its neighbors in advance. Even though there is no advance notification, its one-hop neighbors will clear this record if the corresponding time slot has been idle for several frames.

For a new user joining in, if the system is in the negotiation phase, it just follows the time benchmark and participates in the negotiation. While in collision-free phase, since the time slots have already been negotiated, the new senses in each time slot. If there are still available time slots (due to the release of leaving users), it tries to capture the idle time slot by backoffing first. Backoff is used to avoid the collision of simultaneous attempts in that idle time slot. Therefore, the user with the fastest backoff will capture that time slot. Even if two users attempt at the same time after the same backoff time and then collision happens, this information can still be validated in the following time slots or frames.

If all the time slots have been occupied, new users send applications in the frame tail. Similarly, backoff is also performed before application to stagger multiple new users. Once several applications have been received by the coordinator, it simply increases the number of time slot to accommodate new users whereas the current users will not be influenced. It is quite straightforward, but may cause redundant time slots. Here is another method. The coordinator initiates the negotiation process again by setting CP=0. Due to the re-negotiation, the latter method will get an appropriate TS value but requires longer time to achieve steady states compared to the former one.

VI. SIMULATION RESULTS

We first consider a small ad hoc network with 10 users, i.e. N=10. Their locations are generated randomly within an 80-by-80 area, with a uniform distribution for its X and Y coordinates. The regular transmission range is set to 40 for each user, making every link bidirectional. The initial access index is set to 5, thus . And the index window is [2, 15]. If one user negotiates in a time slot, its access index will be increased by 2 for the next time slot, and those

users whose attempts have been terminated by RTSP/CTSP or those who do not access at all in the current time slot will have their indices decreased by 1, as long as they are still in the range of the index window; otherwise, the initial value is reset.

Fig.4 Topology example and the initial state Figure 4 is the initial state of a random generated topology. We can see that each user selects TS1 in the initial state. When the collision-free phase is reached, each user selects a time slot which is different from the choices of its one-hop and two-hop neighbors, as shown in Figure 5. Take User 1 as an example, since TS1 to TS6 have been occupied within its two-hop areas, it chooses TS7.

Fig.5 Negotiation result of our schemeFrom Figure 5 we know that the value of TS has

been reduced from 10 to 7 after negotiation. No user can choose another time slot with smaller index. The steady state has been achieved.

Since the randomness is introduced in our scheme, the steady state is not unique. There exist several steady states with the same number of time slots. Fig. 6 gives another result. As mentioned earlier, time slot assignment issue is usually solved by graph coloring. Some of these schemes produce good results [2,14-16], e.g., PMNF. Figure 7 shows its solution. From Figure 7 we know that PMNF also needs 7 time slots.

Fig.6 Another negotiation result of our scheme

Fig.7 Assignment result of PMNF

Fig.8 Coloring quality comparison of different scales

We also compare the coloring quality of several schemes. RAND[2] executes easier than PMNF does and has been used in many channel assignment schemes. DRAND[7] has the same performance as of RAND on coloring quality. DLB[2-3] is the degree-based lower bound, which is defined as the maximal user degree plus one. This lower bound is very tight but can be used to approximate the optimal coloring solution. Figure 8 shows the comparison for different network scales. N users are deployed in a 100-by-100

square area. The regular transmission range is fixed to 25. The initial access index is set to the half of N. N increases from 10 to 60 by 10. We run 1000 simulations and take the average for each network scale. It can be seen from Figure 8 that PMNF has the solution closest to DLB. Due to the randomness, RAND/DRAND requires more time slots than PMNF does. Our scheme only needs a little more time slots than RAND does, while the coloring qualities are with the same order.

Fig.9 Coloring quality comparison of different radii

We also generate 1000 random topologies of 50 users. The initial access probability is set to 1/25. The radius ranges from 25 to 50 by 5. Figure 9 compares the coloring quality for different solutions. With the increase of the radius, each user has more neighbors, thus the time slot required are increased. The curves have the same trend as those of Figure 8, and the result of our scheme is also close to that of the centralized algorithms.

VII. CONCLUSIONS

We design a TDMA MAC scheme for ad hoc networks, which is a negotiation-based method with the assistance of a coordinator. Game theory has been utilized to model the negotiation procedure as a potential game. On coloring quality, the performance of our scheme is similar to that of the classical centralized TDMA solutions with distributed manner. In addition, it is scalable to the topology change. Moreover, there is a fairness benefit on it compared to CSMA/CA.

It remains future work to investigate the design rule for the time slot length and the efficient slot assignment method for users with different QoS requirements.

AcknowledgementsThe authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work was supported in part by National Science Fund for Distinguished Young

Scholars under Grant No.60725105; National Key Basic Research Program of China (973 Program) under Grant No. 2009CB320404; Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0852; National Natural Science Foundation of China under Grants No.60972047, 61072068 and 111 Project under Grant No.B08038.

Note1. In this paper, we use collision-free phase and TDMA phase

interchangeably.

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Biographies

Hui Leifang, is currently a Ph.D. candidate at Xidian University, Xi’an, China. She has been an IEEE student member since 2010. She was a visiting student to the Department of Electrical and Computer Engineering at University of Florida from 2008 to 2009. Her research interests include spectrum allocation, resource sharing and resource management in heterogeneous networks.

Li Jiandong, received the B.E., M.S. and Ph.D. degrees in electrical engineering from Xidian University, Xi’an, China, in 1982, 1985 and 1991 respectively. He has been a faculty member of Telecommunications Engineering at Xidian University since 1985, where he is currently a professor and director of State Key Laboratory of Integrated Service Networks. Prof. Li is a senior member of IEEE. He was a visiting professor to the Department of Electrical and Computer Engineering at Cornell University from 2002-2003. He was a member of Personal Communication Networks (PCN) specialist group for China 863 Communication High Technology Program during 1993-1994 and again 1999-2000. He also served as the General Vice Chair for COMSOCs Chinacom 2009. He was awarded as Distinguished Young Researcher and Changjiang Scholar from Ministry of Science and Technology, China. His major research interests include wireless communication theory, cognitive radio and signal processing. *The corresponding author. Email: [email protected]

Li Hongyan, received her M.S. degree in control engineering from Xi’an Jiaotong University, and the Ph.D. degree in signal and information processing from Xidian University, Xi’an, Shaanxi, China, in 1991 and 2000 respectively. She is currently a professor in the State Key Laboratory of Integrated Service Networks, Xidian University. Her research interests include wireless networking, cognitive networks, integration of heterogeneous network, and mobile ad hoc networks.

Ma Yinghong, received the B.S. degree in electronic information science and technology and the M.S. degree in communication & information system from North China Electric Power University, Baoding, Hebei, China, in 2003 and 2006, respectively. She is currently a Ph.D. candidate at Xidian University, Xi’an, Shaanxi, China. Her research interests focus on wireless communications and human-computer interaction techniques.