This Article 
 Bibliographic References 
 Add to: 
Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks
November 2007 (vol. 6 no. 11)
pp. 1218-1229
The stochastic model assumed to govern the mobility of nodes in a mobile ad hoc network have been shown to significantly affect the network’s coverage, maximum throughput, and achievable throughputdelay tradeoffs. In this paper, we compare several mobility models, including the random walk, random waypoint and Manhattan models, on the basis of the number of states visited in a fixed time, the time to visit every state in a region, and the effect of the number of wandering nodes on the time to first entrance to a set of states. These metrics for a mobility model are useful for assessing the achievable event detection rates in surveillance applications where wireless-sensor-equipped vehicles are used to detect events of interest in a city. We also consider mobility models based on Correlated Random Walks, which can account for time dependency, geographical restrictions, and nonzero drift. We demonstrate that these models are analytically tractable by using a matrix-analytic approach to derive new, closedform results in both the time- and transform-domains for the probability that a node is at any location at any time for both semi-infinite and finite one-dimensional lattices. We also derive first entrance time distributions for these walks. We find that a correlated random walk (i) covers more ground in a given amount of time and takes a smaller amount of time to cover an area completely than a random walk with the same average transition rate; (ii) has a smaller first entrance time to small sets of states than the random waypoint and random walk models and (iii) leads to a uniform distribution of nodes (except at the boundaries) in steady state.

[1] G. Bianchi, “Performance Analysis of the IEEE 802.11 Distributed Coordination Function,” IEEE J. Selected Areas in Comm., vol. 18, no. 3, pp. 353-547, Mar. 2000.
[2] B. Zhou, A. Marshall, and T.-H. Lee, “The Non-Responsive Receiver Problem in Mobile Ad-Hoc Networks,” IEEE Comm. Letters, vol. 9, no. 11, pp. 973-975, 2005.
[3] S. Keshav, An Engineering Approach to Computer Networking: ATM Networks, the Internet and the Telephone Network. Addison-Wesley, 1997.
[4] N. Abramson, “The ALOHA System—Another Alternative for Computer Communications,” Proc. Am. Federation of Information Processing Soc. Conf., vol. 37, pp. 295-298, 1970.
[5] L.G. Roberts, “ALOHA Packet System with and without Slots and Capture,” Computer Comm. Rev., vol. 5, no. 2, Apr. 1975.
[6] P. Karn, “MACA—A New Channel Access Method for Packet Radio,” Proc. ARRL/CRRL Amatuer Radio Computer Networking Conf., pp. 134-140, 1990.
[7] IEEE 802.11 Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Standard 802.11, 1997.
[8] S. Xu and T. Saadawi, “Revealing the Problems with 802.11 Medium Access Control Protocol in Multi-Hop Wireless Ad Hoc Networks,” Computer Networks, vol. 38, pp. 531-548, 2002.
[9] T. Nandagopal, T. Kim, X. Gao, and V. Bharghavan, “Achieving MAC Layer Fairness in Wireless Packet Networks,” Proc. ACM MobiCom, Aug. 2000.
[10] V. Bharghavan, “MACAW: A Media Access Protocol for Wireless LANs,” Proc. ACM SIGCOMM, pp. 212-225, 1994.
[11] F. Cali, M. Conti, and E. Gregori, “Dynamic Tuning of the IEEE 802.11 Protocol to Achieve a Theoretical Throughput Limit,” IEEE/ACM Trans. Networking, vol. 8, no. 6, pp. 785-799, Dec. 2000.
[12] Y. Kwon, Y. Fang, and H. Latchman, “A Novel MAC Protocol with Fast Collision Resolution for Wireless LANs,” Proc. IEEE INFOCOM, Apr. 2003.
[13] S.J. Golestani, “A Self-Clocked Fair Queueing for Broadband Applications,” Proc. IEEE INFOCOM, pp. 636-646, Apr. 1994.
[14] J.L. Sobrinho and A.S. Krishnakumar, “Quality-of-Service in AdHoc Carrier Sense Multiple Access Wireless Networks,” IEEE J. Selected Areas in Comm., vol. 17, pp. 1353-1368, Aug. 1999.
[15] ETSI HIPERLAN/1 Standard, European Telecommunications Standards Inst., Oct. 2000, http:/
[16] A. Lindgren, A. Almquist, and O. Schelén, “Quality of Service Schemes for IEEE 802.11 Wireless LANs—An Evaluation,” J.Special Topics in Mobile Networking and Applications (MONET), special issue on performance evaluation of QoS architectures in mobile networks, vol. 8, no. 3, pp. 223-235, June 2003.
[17] Z.G. Abichar and J.M. Chang, “CONTI: Constant-Time Contention Resolution for WLAN Access,” Lecture Notes in Computer Science, vol. 3462, pp. 358-369, Jan. 2005.
[18] R. Jain, A. Durresi, and G. Babic, “Throughput Fairness Index: An Explanation,” ATM Forum/99-0045, Feb. 1999.

Index Terms:
MANET, mobility models, correlated random walk, random walk, random waypoint model
Seema Bandyopadhyay, Edward J. Coyle, Tillmann Falck, "Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks," IEEE Transactions on Mobile Computing, vol. 6, no. 11, pp. 1218-1229, Nov. 2007, doi:10.1109/TMC.2007.1014
Usage of this product signifies your acceptance of the Terms of Use.