Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET)

Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET) 1 Syed S. Rizvi, 2 Aasia Riasat, and 3 Khaled M. Elleithy 1, 3 Computer Science and Engineering Department, University of Bridgeport, Bridgeport CT, 06601 2 Department of Computer Science, Institute of Business Management, Karachi, Pakistan {srizvi 1, elleithy 3 }@bridgeport.edu, aasia.riasat@cbm.edu.pk 2 Abstract-The capacity of mobile ad hoc network (MANET) is typically determined by the size of network, routing protocol, mobility and the interactions that occur between the nodes. Moreover, these critical parameters cause the loss rate that has severed impact on the performance of the MANET. This situation even becomes worst when these critical parameters are chosen inappropriately. This paper presents an analytical model that incorporates most of the critical parameters that can influence the capacity of MANET. Based on the analytical model, an efficient 3-phase algorithm is designed to optimize the performance of MANET in terms of increased capacity and reduced transmission delay. The proposed 3-pahse algorithm considers both delay-tolerant and delay-sensitive network traffics. In addition, the 3-phase algorithm can be used to approximate both the best and worst case capacities of MANET with the relaying and non-relaying nodes. Keywords Ad Hoc networks, capacity analysis, transmission delay, and bandwidth I. INTRODUCTION Much research has already been done for improving the performance of MANET [1, 2, 5]. The capacity of a fixed wireless network decreases as the number of nodes increases when all the nodes share a common wireless channel [1]. This scheme was shown to increase the capacity of the MANET in such a way that it remains constant as the total number of nodes increases in the system. More recently, [3] has proposed a two phase packet relaying technique. The main intention of this technique was to reduce the overall packet transmission delay. However, the delay experienced by packets under this strategy was shown to be large and it can be even infinite for a fixed number of nodes in the system, which has prompted more recent work presenting analysis of capacity and delay tradeoffs. However, the proposed 3-phase technique is highly efficient in such a way that it shows that the capacity of 1 Contact author: srizvi@bridgeport.edu MANET can be increased at the expense of comparatively small increased in the transmission delay. According to the analysis of Gupta and Kumar [1], the capacity region of network is defined as n(n-1) where n represents the number of nodes. Two types of capacities are typically measured: transport and throughput. The transport capacity is determined by multiplying bits and the distance per second where as the throughput capacity is expressed simply by bits per second. In a MANET, the transport capacity is approximated as O( n) bit-meter per second whereas the throughput capacity of each node is O(1/ n) bit per second. However, this analysis does not include the mobility of nodes. The proposed analytical model and 3-phase algorithm not only accounts the transport and throughput capacities of MANET but also considers the node mobility at one specific point. Our numerical and simulation analysis demonstrates that the capacity of MANET can be improved significantly if the critical parameters are set intelligently. II. ANALYTICAL MODEL FOR CAPACITY ANALYSIS AND TRANSMISSION DELAY Our proposed analytical model is based on the method proposed by Gupta and Kumar [1]. They considered a static model where all nodes are fixed and relaying is an allowable property of MANET. The node positions Xi are independent and identically-distributed in the open disk of a unit area. The destinations are chosen independently and the destination for each source node is chosen with respect to the node closest to a randomly chosen point on the disk. For such a static model, the upper and lower bounds on the asymptotically feasible throughput reaches to infinity for each pair of source and destination (S-D) [1]. However, the capacity of mobile nodes without relaying can also be computed [5]. This requires considering a model that consists of n nodes in an open disk of unit area where the radius can be approximated as 1/ π. Although, [3, 4] proved that the capacity of MANET is constant, but they did not determine the particular capacity at one certain point of time. In other words, the proposed algorithm considers the transmission time which involves one

particular pair of S-D. However, we use these 2 basic models to develop the proposed algorithm that considers both the delay time and the broadcasting between the nodes of MANET. A. Framework for a 3-Phase Algorithm We use special scheduling policy [3], called as π, for our 3- phase transmission algorithm. This scheduling policy (π) selects S-D pairs randomly in each time slot t. Our transmission algorism is divided into three phases. In the first phase, the transmission occurs only between the sender that has packets for transmission and the relay nodes as shown in Fig. 1. The relay nodes might have some part of packets which must be sent to the destination or between sender and destination if the nearest node of destination is sender node. In the second phase, these nodes move around in unit circle whose radius is 1/ π. During the second phase, no transmission is carried out among mobile nodes until the relay nodes approach an appropriate destination node. Even though, this mobility of nodes may cause a delay time, this can not be influenced to the total throughput. Lastly, the processing of third phases begins when the location of mobile relay nodes is near the destination node as shown in Fig. 2. In such a case, the transmission can occur immediately between the relay and the destination nodes or between the S-D pair. It should be noted in Fig. 2 that the first and the last phases of the proposed algorithm are interleaved in a sense that the processing of first phase occurs in even time slots where as the processing of the last phase occurs in odd time slots. B. Implementation of the Proposed 3-Phase Algorithm In order to implement the proposed algorithm, we use Fig. 2. Processing of the first and the third phase. The parameter L p is set to 2, L Tt is the transmission-time 2 packets, M is set to 3, P 0 is set to 2, P 1 is set to 1, P 2 is set to 2, and T t0, T t1, T t2 represents the required time to transmit 2, 1, 2 packets to the destination, respectively. scheduling model (π) that selects only one sender node which has 3 packets for transmission with one destination node within the unit circle which consists of n mobile nodes. Moreover, we assume that there are three mobile nodes which are located within the close proximity of the sender node. In other words, this second assumption implies that the transmissions can occurs at distance of order of 1/ n. In first phase, sender distributes each packet to 10 mobile nodes, so each mobile node (relay node) has a part of the sender packets. In the second phase, these mobile nodes move around the unit circle. If some relay node(s) which has the part of the sender s packet enters within the close proximity of destination node, the transmission occurs immediately. Finally, in the third phase, the relay node(s) transmits the part of the sender s packet to the appropriate destination node. Both second and the third phases of the proposed algorithm are repeated until the destination receives the entire packets. III. ANALYSIS OF BEST AND WORST CASE CAPACITIES FOR MANET Fig. 1. Processing of the first phase. The biggest rectangle is unit rectangle which is 1 m2. Small circle presents the distance at which nodes can communicate. This model has 12 mobile nodes and 3 relay nodes In this section, we present the analysis of the best and the worst case capacities for a MANET. Specifically, we show that how the proposed 3-phase algorithm can be implanted in order to compute the capacities for a MANET. A. The Worst Case Capacity For the worst cast capacity, it is assumed that the transmission occurs for the largest time. Also, we assume that

P i is the maximum number of packets that can be transmitted from the ith source node to a destination. The size of a transmitted packet between each pair of S-D can not exceed to L P. In the given scenario, each relay nodes may start transmission at different time. The packet transmission in MANET can be estimated as: Transmission S D L + P A 2L Property (1) P i P i = 0 where, M represents the number of relay nodes. Moreover, if relay nodes transmission occurs at different times, then L represents the transmission time between the Ti ith source and the other relay nodes. In addition, the source and the relay nodes are assumed to have the largest number of packets for transmission. Based on the above argument, the total transmission time can be approximated as follows: = Tt + Ti 0 Transmission Time L T Property (2) Using (1) and (2), we can derive a closed form expression for estimating the worst case capacity (WC capacity ) such as: WCcapacity A 2LP LTt + LTi Property (3) 0 where the total delay time is set to 0 B. The Best Case Capacity For the best case capacity, we consider the shortest transmission time between a pair of S-D. The shortest time is generated when the transmission starts simultaneously between the relay nodes and the destination node. This transmission time can be considered as a time in which the relay node has the largest packet size for transmission towards a destination. This time is the same as the transmission time between the source node and the relay node. This leads us to the following expression for the best case capacity: L P /L Ti Finally, we can combine the result of worst and the best case capacities. When the characteristics of property (3) are true, the total transmission throughput reaches to O(1) between node i and j at distance of order 1/ n. We also assume that there is no direct transmission exists between the source and the destination system. Taking this into account, one can approximate the best and the worst case capacities such as: M 1 lim 2 L L + T ( t) L L t > (t λ ( ) Property (4) P Tt ti P Tt 0 where λ ) is the throughput with respect to the transmission time. TABLE I THE RESULT OF RELAY MOBILE NETWORK WITHOUT REPRODUCTION NRN Ttime (sec) Delay (sec) Throughput 1 3 0.0112 3406232 14285.70 2 4 0.0096 5056653 16666.66 3 3 0.0112 3442331 14285.70 4 3 0.012 3515001 13333.32 5 5 0.0096 4160049 16666.66 6 8 0.0096 4758960 16666.66 7 6 0.012 5544597 13333.32 8 2 0.012 1378757 13333.32 NRN = THE NUMBER OF RELAY NODE, T TIME = TRANSMISSION TIME, DELAY = DELAY TIME C. Reducing Delay Time The delay time is always generated with a certain probability with respect to a certain complexity such as of O(1/n). In the given scenario, when the transmission occurs, relay nodes approach to appropriate destinations. The second phase of the proposed algorithm (see Fig. 2) can be effectively used to reduce the delay time by improving the probability (see Fig. 3 for delay reduction). We have shown that the second phase of the proposed algorithm improves this probability by asymmetrically distributing the packets that each relay node is supposed to transmit to other nodes. Based on the proposed approach, as the number of relay node increases that carry the identical packets, the probability of constructing the pairs of relay nodes and the destination nodes also increases. The improvement in the probability is in the order of O (c/n), c > 0. D. Numerical and Simulation Results Before we discuss the simulation results, it is worth Fig. 3. This picture shows the improvement to reduce the overall delay time. The biggest rectangle is a unit rectangle (1 m2 ) where as the small circle represents the distance at which nodes can communicate. This model has 12 mobile nodes, 3 relay nodes and 3 reproduced relay nodes.

Fig. 4. This picture shows the location of mobile nodes in the simulation. The unit rectangle is 1 m2. The red, blue, and green nodes represent the source, destination, and the relay node, respectively. Simulation consists of 3 relay nodes and 100 regular nodes mentioning some of our key assumptions. We assume that the location of a mobile node may change randomly as shown in Fig. 4. In addition, each node has enough buffer size with the maximum capacity of 80 kbps. We also assume that the packet size is typically 8 bits. For the sake of simulation, we consider a network that consists of 100 nodes where each node may transmit 10 packets. The simulation is run over a long period of time and the results are presented in Table I. It should be noted in Table I that the achievable throughput exists between the best and the worst case capacities. The proposed algorithm provides reduced delay time as shown in Table I. IV. CONCLUSION This paper presented an analytical model that uses special scheduling policy for the random selection of the S-D pairs. Based on the analytical model, we designed an efficient 3- pahse algorithm that can be effectively used to analyze the capacities of MANET. The proposed algorithm considers the random selection of S-D pair which is essential in order to produce the correct approximation of best and worst case capacities. Our results have shown that the capacity of MANET can be improved by using the proposed algorithm. Also, the numerical results suggest that the transmission delay can be reduced even in the presence of node mobility. REFERENCES [1] Piyush Gupta and P.Kumar, The capacity of wireless networks, IEEE Transactions on Information Theory, Vol. 46, pp. 388-404, 2000. [2] L. Jinyang, C. Blake, S. Douglas, D. Couto, I. Lee, and R. Morris, Capacity of Ad Hoc Wireless Networks, In the proceedings of the 7 th ACM International Conference on Mobile Computing and Networking, pp. 61 69, Rome, Italy, July 2001. [3] M. Grossglauser and T. David, Mobility increases the capacity of Ad-hoc wireless networks, IEEE/ACM Transactions on Networking, Vol.10, no. 4, pp. 477 486, 2002. [4] C. Schindelhauer, T. Lukovszki, S. Rührup, K. Volbert, Worst case mobility in Ad Hoc networks, Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures, pp. 230 239, 2003. [5] C.-K. Toh, Maximum Battery Life Routing to Support Ubiquitous Mobile Computing in Wireless Ad Hoc Networks, IEEE Communications Magazine, Vol. 39, no. 6, pp. 138-147 June 2001. [6] A.J. Goldsmith and S.B. Wicker, "Design challenge for energy constrained ad-hoc wireless networks," IEEE Wireless, Communication, vol.4, pp.8 9, Aug. 2002. Authors Biographies SYED S. RIZVI is a Ph.D. student of Computer Engineering at University of Bridgeport. He received a B.S. in Computer Engineering from Sir Syed University of Engineering and Technology and an M.S. in Computer Engineering from Old Dominion University in 2001 and 2005 respectively. In the past, he has done research on bioinformatics projects where he investigated the use of Linux based cluster search engines for finding the desired proteins in input and outputs sequences from multiple databases. For last one year, his research focused primarily on the modeling and simulation of wide range parallel/distributed systems and the web based training applications. Syed Rizvi is the author of 75 scholarly publications in various areas. His current research focuses on the design, implementation and comparisons of algorithms in the areas of multiuser communications, multipath signals detection, multi-access interference estimation, computational complexity and combinatorial optimization of multiuser receivers, peer-to-peer networking, and reconfigurable coprocessor and FPGA based architectures. AASIA RIASAT is an Associate Professor of Computer Science at Collage of Business Management (CBM) since May 2006. She received an M.S.C. in Computer Science from the University of Sindh, and an M.S in Computer Science from Old Dominion University in 2005. For last one year, she is working as one of the active members of the wireless and mobile communications (WMC) lab research group of University of Bridgeport, Bridgeport CT. In WMC research group, she is mainly responsible for simulation design for all the research work. Aasia Riasat is the author or co-author of several scholarly publications in various areas. Her research interests

include modeling and simulation, web-based visualization, virtual reality, data compression, and algorithms optimization. KHALED ELLEITHY received the B.Sc. degree in computer science and automatic control from Alexandria University in 1983, the MS Degree in computer networks from the same university in 1986, and the MS and Ph.D. degrees in computer science from The Center for Advanced Computer Studies at the University of Louisiana at Lafayette in 1988 and 1990, respectively. From 1983 to 1986, he was with the Computer Science Department, Alexandria University, Egypt, as a lecturer. From September 1990 to May 1995 he worked as an assistant professor at the Department of Computer Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. From May 1995 to December 2000, he has worked as an Associate Professor in the same department. In January 2000, Dr. Elleithy has joined the Department of Computer Science and Engineering in University.