Abstract. Accurately estimating node density in Vehicular Ad hoc Networks, VANETs, is a challenging and crucial task. Various approaches exist, yet none takes advantage of physical layer parameters in a distributed fashion. This paper describes a framework that allows individual nodes to estimate the node density of their surrounding network independent of beacon messages and other infrastructurebased information. The proposal relies on three factors: 1) a discrete event simulator to estimate the average number of nodes transmitting simultaneously; 2) a realistic channel model for VANETs environment; and 3) a node density estimation technique. This work provides every vehicle on the road with two equations indicating the relation between 1) received signal strength versus simultaneously transmitting nodes, and 2) simultaneously transmitting nodes versus node density. Access to these equations enables individual nodes to estimate their real-time surrounding node density. The system is designed to work for the most complicated scenarios where nodes have no information about the topology of the network and, accordingly, the results indicate that the system is reasonably reliable and accurate. The outcome of this work has various applications and can be used for any protocol that is affected by node density.

The broadcast performance of the 802.11 wireless protocol depends on several factors. One of the important factor is the number of nodes simultaneously contending for the shared channel. The Medium Access Control (MAC) technique of 802.11 is called the Distributed Coordination Function (DCF). DCF is a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) scheme with binary slotted exponential backoff. A collision is the result of two or more stations transmitting simultaneously. Given the simplicity of the DCF scheme, it was adapted for Dedicated Short Range Communication (DSRC) based vehicular communication. A broadcast mechanism is used to disseminate emergency and safety related messages in a vehicular network. Emergency and safety related messages have a strict end-to-end latency of 100 ms and a Packet Delivery Ratio (PDR) of 90% and above. The PDR can be evaluated through the packet loss probability. The packet loss probabilityPL is given by, PL = 1−(1-Pe)(1-PC), where Pe is the probability of channel error and PC is the probability of collision. Pe depends on several environmental and operating factors and thus cannot be improved. The only way to reduce PL is by reducing PC. Currently, expensive radio hardware are used to measure PL. Several adaptive algorithms are available to reduce PC. In this paper, we establish a closed relation between PC and the Stirling number of the second kind. Simulation results are presented and compared with the analytical model for accuracy. Our simulation results show an accuracy of 99.9% compared with the analytical model. Even on a smaller sample size, our simulation results show an accuracy of 95% and above. Based on our analytical model, vehicles can precisely estimate these real-time requirements with the least expensive hardware available. Also, once the distribution of PC and PL are known, one can precisely determine the distribution of Pe.

Accurately estimating node density in Vehicular Ad hoc Networks (VANETs) is a challenging and crucial task. Various approaches exist yet none are able to deliver an accurate estimation in all situations especially in presence of collision in highly saturated networks. This paper describes an adaptive framework that allows individual nodes to estimate the real-time node density of their surrounding network. Our solution performs well in all situations even in chaotic channel conditions by retrieving information from collisions. This provides every vehicle on the road with two equations indicating the relation between 1) received signal strength versus simultaneously transmitting nodes, and 2) the relation between simultaneously transmitting nodes versus node density. These equations and frequently sampled received power levels enable individual nodes to estimate their real-time surrounding node density. Our proposal adapts to different environments and can address fast changes in configuration of the network and property of the channel in VANETs. Our experimental results indicate that the method yields reliable estimation in an acceptable time frame.

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