Stationary distributions for the random waypoint mobility model

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]  Christian Wagner,et al.  The Spatial Node Distribution of the Random Waypoint Mobility Model , 2002, WMAN.

[2]  Mingyan Liu,et al.  Sound mobility models , 2003, MobiCom '03.

[3]  Paolo Santi,et al.  A Statistical Analysis of the Long-Run Node Spatial Distribution in Mobile Ad Hoc Networks , 2002, MSWiM '02.

[4]  J. Gates.  Introduction to Probability and its Applications , 1992 .

[5]  Tracy Camp,et al.  Improving the Accuracy of Random Waypoint Simulations Through Steady-State Initialization , 2004 .

[6]  David A. Maltz,et al.  A performance comparison of multi-hop wireless ad hoc network routing protocols , 1998, MobiCom '98.

[7]  Louise E. Moser,et al.  An analysis of the optimum node density for ad hoc mobile networks , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[8]  Paolo Santi,et al.  The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks , 2003, IEEE Trans. Mob. Comput..

[9]  Tracy Camp,et al.  A survey of mobility models for ad hoc network research , 2002, Wirel. Commun. Mob. Comput..

[10]  David A. Maltz,et al.  Dynamic Source Routing in Ad Hoc Wireless Networks , 1994, Mobidata.

[11]  Tracy Camp,et al.  Performance comparison of two location based routing protocols for ad hoc networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[12]  Christian Bettstetter,et al.  Smooth is better than sharp: a random mobility model for simulation of wireless networks , 2001, MSWIM '01.

[13]  Hannes Hartenstein,et al.  Stochastic properties of the random waypoint mobility model: epoch length, direction distribution, and cell change rate , 2002, MSWiM '02.

[14]  Mingyan Liu,et al.  Random waypoint considered harmful , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).