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Stationary Distributions for the Random Waypoint Mobility Model
January 2004 (vol. 3 no. 1)
pp. 99-108

Abstract—In simulations of mobile ad hoc networks, the probability distribution governing the movement of the nodes typically varies over time and converges to a "steady-state” distribution, known in the probability literature as the stationary distribution. Some published simulation results ignore this initialization discrepancy. For those results that attempt to account for this discrepancy, the practice is to discard an initial sequence of observations from a simulation in the hope that the remaining values will closely represent the stationary distribution. This approach is inefficient and not always reliable. However, if the initial locations and speeds of the nodes are chosen from the stationary distribution, convergence is immediate and no data need be discarded. We derive the stationary distributions for location, speed, and pause time for the random waypoint mobility model. We then show how to implement the random waypoint mobility model in order to construct more efficient and reliable simulations for mobile ad hoc networks. Simulation results, which verify the correctness of our method, are included. In addition, implementation of our method for the NS-2 simulator is available.

[1] T. Camp, J. Boleng, and V. Davies, A Survey of Mobility Models for Ad Hoc Network Research Wireless Comm.&Mobile Computing (WCMC): Special Issue on Mobile Ad Hoc Networking: Research, Trends, and Applications, vol. 2, no. 5, pp. 483-502, 2001.
[2] J. Yoon, M. Liu, and B. Noble, Random Waypoint Considered Harmful Proc. 21st Ann. Joint Conf. IEEE Computer and Comm. Soc. (INFOCOM 2003), pp. 1312-1321, Apr. 2003.
[3] J. Yoon, M. Liu, and B. Noble, Sound Mobility Models Proc. ACM/IEEE Int'l Conf. Mobile Computing and Networking (MOBICOM '03), pp. 205-216, Sept. 2003.
[4] T. Camp, J. Boleng, B. Williams, L. Wilcox, and W. Navidi, Performance Comparison of Two Location Based Routing Protocols for Ad Hoc Networks Proc. 20th Ann. Joint Conf. IEEE Computer and Comm. Soc. (INFOCOM 2002), pp. 1678-1687, June 2002.
[5] D. Johnson and D. Maltz, Dynamic Source Routing in Ad Hoc Wireless Networks Mobile Computing, T. Imelinsky and H. Korth, eds., pp. 153-181, Kluwer Academic Publishers, 1996.
[6] J. Broch, D. Maltz, D. Johnson, Y. Hu, and J. Jetcheva, Multi-Hop Wireless Ad Hoc Network Routing Protocols Proc. ACM/IEEE Int'l Conf. Mobile Computing and Networking (MOBICOM '98), pp. 85-97, Oct. 1998.
[7] Monarch Project, Wireless and Mobility Extensions to ns-2,http://www.monarch.cs.rice.educmu-ns.html , 2003.
[8] E.M. Royer, P.M. Melliar-Smith, and L.E. Moser, An Analysis of the Optimum Node Density for Ad hoc Mobile Networks Proc. IEEE Int'l Conf. Comm. (ICC 2001), pp. 857-861, June 2001.
[9] C. Bettstetter and C. Wagner, The Spatial Node Distribution of the Random Waypoint Mobility Model Proc. First German Workshop Mobile Ad-Hoc Networks (WMAN), pp. 41-58, 2002.
[10] C. Bettstetter, G. Resta, and P. Santi, The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks Technical Report TUM-LKN 2002/01, Technische Universität München, Inst. Comm. Network, Munich, Germany, Sept. 2002.
[11] W. Feller, An Introduction to Probability and Its Applications, vol. II, second ed. New York: John Wiley&Sons, 1970.
[12] C. Bettstetter, Smooth is Better Than Sharp: A Random Mobility Model for Simulation of Wireless Networks Proc. Fourth ACM Int'l Workshop Modeling, Analysis, and Simulation of Wireless and Mobile Systems (MSWiM '01), pp. 19-27, July 2001.
[13] Random Distances within a Rectangle and between Rectangles Bull. Calcutta Math. Soc., vol. 2, pp. 17-24, 1951.
[14] C. Bettstetter, H. Hartenstein, and X. Perez-Costa, Stochastic Properties of the Random Waypoint Mobility Model: Epoch Length, Direction Distribution, and Cell Change Rate Proc. Fifth ACM Int'l Workshop Modeling, Analysis, and Simulation of Wireless and Mobile Systems (MSWiM '02), pp. 7-14, Sept. 2002.
[15] D. Blough, G. Resta, and P. Santi, A Statistical Analysis of the Long-Run Node Spatial Distribution in Mobile Ad Hoc Networks Proc. Fifth ACM Int'l Workshop Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM '02), pp. 30-37, Sept. 2002.
[16] The VINT Project, The Network Simulator-ns-2,http://www. isi.edu/nsnamns/, 2003.
[17] Scalable Network Technologies, Qualnet,http:/www.scalable-networks.com, 2003.
[18] W. Navidi, T. Camp, and N. Bauer, Improving the Accuracy of Random Waypoint Simulations Through Steady-State Initialization Technical Report MCS-03-08, The Colorado School of Mines, Golden, CO, June 2003.

Index Terms:
Simulation of mobile ad hoc networks, random waypoint mobility model, mobility models.
Citation:
William Navidi, Tracy Camp, "Stationary Distributions for the Random Waypoint Mobility Model," IEEE Transactions on Mobile Computing, vol. 3, no. 1, pp. 99-108, Jan. 2004, doi:10.1109/TMC.2004.1261820
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