Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks

The stochastic model assumed to govern the mobility of nodes in a mobile ad hoc network has a significant impact on the network's coverage, maximum throughput, and achievable throughput-delay 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. 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, closed-form 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 uniform distribution of nodes (except at the boundaries) in steady state.

[1]  Mingyan Liu,et al.  A general framework to construct stationary mobility models for the simulation of mobile networks , 2006, IEEE Transactions on Mobile Computing.

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

[3]  Michele Garetto,et al.  Analysis of random mobility models with PDE's , 2006, MobiHoc '06.

[4]  Kuang-Ching Wang,et al.  Exposure for collaborative detection using mobile sensor networks , 2005, IEEE International Conference on Mobile Adhoc and Sensor Systems Conference, 2005..

[5]  Eduardo Casilari-Pérez,et al.  An analytical model to estimate path duration in MANETs , 2006, MSWiM '06.

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

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

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

[9]  Xiaoyan Hong,et al.  A group mobility model for ad hoc wireless networks , 1999, MSWiM '99.

[10]  Asha Seth.  The Correlated Unrestricted Random Walk , 1963 .

[11]  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..

[12]  Ahmed Helmy,et al.  IMPORTANT: a framework to systematically analyze the Impact of Mobility on Performance of Routing Protocols for Adhoc Networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Walter Böhm.  The correlated random walk with boundaries: A combinatorial solution , 2000 .

[14]  Edward J. Coyle,et al.  State space expansions and the limiting behavior of quasi-birth-and-death processes , 1989, Advances in Applied Probability.

[15]  Kanwar Sen,et al.  Transition probability matrices for correlated random walks , 1980 .

[16]  Ness B. Shroff,et al.  Simplification of network dynamics in large systems , 2005, IEEE/ACM Transactions on Networking.

[17]  Ward Whitt,et al.  The Fourier-series method for inverting transforms of probability distributions , 1992, Queueing Syst. Theory Appl..

[18]  Shashi Phoha,et al.  Surveillance coverage of sensor networks under a random mobility strategy , 2003, Proceedings of IEEE Sensors 2003 (IEEE Cat. No.03CH37498).

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

[20]  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).

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

[22]  Ahmed Helmy,et al.  Weighted waypoint mobility model and its impact on ad hoc networks , 2005, MOCO.

[23]  D. G. Lampard,et al.  A random walk problem with correlation , 1972 .

[24]  J. Abate,et al.  Multi‐precision Laplace transform inversion , 2004 .

[25]  U. Narayan Bhat,et al.  Some explicit results for correlated random walks , 1989, Journal of Applied Probability.

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

[27]  Ahmed Helmy,et al.  A survey of mobility modeling and analysis in wireless adhoc networks , 2004 .

[28]  E. Coyle,et al.  Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks , 2006 .

[29]  Donald F. Towsley,et al.  Mobility improves coverage of sensor networks , 2005, MobiHoc '05.

[30]  Jean-Yves Le Boudec.  On the Stationary Distribution of Speed and Location of Random Waypoint , 2005, IEEE Trans. Mob. Comput..

[31]  Thomas R. Gross,et al.  A mobility model based on WLAN traces and its validation , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[32]  David Tse,et al.  Mobility increases the capacity of ad hoc wireless networks , 2002, TNET.

[33]  Distribution of path durations in mobile ad-hoc networks - Palm's Theorem to the rescue , 2006, Comput. Networks.

[34]  Edward J. Coyle,et al.  Transient analysis of quasi-birth-death processes , 1989 .

[35]  Ahmed Helmy,et al.  Modeling path duration distributions in MANETs and their impact on reactive routing protocols , 2004, IEEE Journal on Selected Areas in Communications.

[36]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[37]  Ness B. Shroff,et al.  Degenerate delay-capacity tradeoffs in ad-hoc networks with Brownian mobility , 2006, IEEE Transactions on Information Theory.

[38]  Kevin C. Almeroth,et al.  Real-world environment models for mobile network evaluation , 2005, IEEE Journal on Selected Areas in Communications.

[39]  Ward Whitt,et al.  An Introduction to Numerical Transform Inversion and Its Application to Probability Models , 2000 .

[40]  Yuan Lin Zhang,et al.  Some problems on a one-dimensional correlated random walk with various types of barrier , 1992, Journal of Applied Probability.

[41]  J. Gillis,et al.  Correlated random walk , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[42]  Yu-Chee Tseng,et al.  On Route Lifetime in Multihop Mobile Ad Hoc Networks , 2003, IEEE Trans. Mob. Comput..

[43]  Pascal von Rickenbach,et al.  Wireless Ad Hoc And sensor netWorks , 2007 .

[44]  Jorma T. Virtamo,et al.  Spatial node distribution of the random waypoint mobility model with applications , 2006, IEEE Transactions on Mobile Computing.

[45]  T.-L. Chin,et al.  Analytic modeling of detection latency in mobile sensor networks , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[46]  Donald F. Towsley,et al.  Properties of random direction models , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[47]  S. Goldstein.  ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION , 1951 .