Modeling the process of information relay through inter-vehicle communication

In a new paradigm of the decentralized traffic information system as a recent thrust in the Intelligent Transportation Systems (ITS), vehicles form ad hoc mobile networks, and information may be propagated between vehicles through wireless communication with a short transmission range. Fundamental to the system design is effective information propagation. In this paper, we study information propagation along a traffic stream on which presence of equipped vehicles follows an independent homogeneous Poisson process. We define a relay process in which only the furthest equipped vehicle within each transmission range continues the relay, and model it as a transient Markov process. We present closed form formulas for the expected value and variance of propagation distance in the case without transmission delay. We also study the expected number of relays and the expected propagation distance in the case with transmission delay. The results make transparent the relationship between propagation distance, equipped vehicle density and transmission range. In addition, we study the probability distribution of propagation distance, and find that the Gamma distribution could be used as a good practical means of approximation especially when the number of equipped vehicles is large within a transmission range. The Gamma-like behavior is also observed on heterogeneous traffic. It is noted that the relay process has many other applications as well. (c) 2006 Elsevier Ltd. All rights reserved.