Spatial node distribution of the random waypoint mobility model with applications

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.

[1]  Mathew D. Penrose,et al.  Extremes for the minimal spanning tree on normally distributed points , 1998, Advances in Applied Probability.

[2]  Eric W. Weisstein.  Disk Line Picking , 2000 .

[3]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

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

[5]  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).

[6]  Mathew D. Penrose,et al.  On k-connectivity for a geometric random graph , 1999, Random Struct. Algorithms.

[7]  J. Broch,et al.  Dynamic source routing in ad hoc wireless networks , 1998 .

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

[9]  Hannes Hartenstein,et al.  Stochastic Properties of the Random Waypoint Mobility Model , 2004, Wirel. Networks.

[10]  M. Penrose.  On k-connectivity for a geometric random graph , 1999, Random Struct. Algorithms.

[11]  Patrick Thiran,et al.  Connectivity in ad-hoc and hybrid networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[12]  Christian Bettstetter,et al.  On the Connectivity of Ad Hoc Networks , 2004, Comput. J..

[13]  Peter P. Pham,et al.  Performance analysis of reactive shortest path and multipath routing mechanism with load balance , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[14]  Esa Hyytiä,et al.  Spatial Node Distribution in the Random Waypoint Mobility Model , 2004 .

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

[16]  David Tse,et al.  Mobility increases the capacity of ad-hoc wireless networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[17]  Peng-Jun Wan,et al.  Asymptotic critical transmission radius and critical neighbor number for k-connectivity in wireless ad hoc networks , 2004, MobiHoc '04.

[18]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

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

[20]  Tracy Camp,et al.  Stationary distributions for the random waypoint mobility model , 2004, IEEE Transactions on Mobile Computing.

[21]  Jorma T. Virtamo,et al.  Random waypoint model in n-dimensional space , 2005, Oper. Res. Lett..

[22]  Jean-Yves Le Boudec,et al.  Perfect simulation and stationarity of a class of mobility models , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[23]  Esa Hyytiä,et al.  Connectivity Properties of Random Waypoint Mobility Model for Ad Hoc Networks , 2005, Med-Hoc-Net.

[24]  Esa Hyytiä,et al.  Traffic load in a dense wireless multihop network , 2005, PE-WASUN '05.

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

[26]  J.-Y. Le Boudec.  On the stationary distribution of speed and location of random waypoint , 2005, IEEE Transactions on Mobile Computing.