On a Stochastic Delay Bound for Disrupted Vehicle-to-Infrastructure Communication with Random Traffic* Atef Abdrabou and Weihua Zhuang Dept. of Elec. & Comp. Eng., University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 Abstract— This paper studies the multihop packet delivery delay in a disrupted vehicle-to-infrastructure communication scenario, where an end-to-end connected path is not likely to exist between a vehicle and the nearest road side unit (RSU) due to the intermittent connectivity between adjacent vehicles. We present an analytical framework that takes into account the randomness of vehicle traffic and the statistical variation of the disrupted communication channel. Our framework employs the effective bandwidth theory and its dual, the effective capacity concept, in order to obtain the maximum distance between adjacent RSUs that stochastically limits the worst case packet delivery delay to a certain maximum value (i.e., allows only an arbitrarily small fraction of packets received by the RSU from the farthest vehicle to exceed a required delay bound). Simulation results demonstrate that our analytical framework is accurate in determining the separation distance between RSUs that probabilistically limit the worst case delay bound. Keywords – Delay, multihop, vehicular ad hoc network, vehicle-to-infrastructure, disrupted connectivity, road side unit placement. I. I NTRODUCTION Many vehicles today are already equipped with wireless communication devices that can facilitate vehicle-to-vehicle and vehicle-to-infrastructure communications. Therefore, ve- hicular ad hoc networks (VANETs) recently have started to attract attention from many researchers in both industry and academia. Federal Communications Commission (FCC) has allocated 5.850 - 5.925 GHz band to promote vehicular communications for safe and efficient highways. This band is planned to be used in the emerging radio standard for Dedicated Short-Range Communications (DSRC) [1] [2] that supports an Intelligent Transport Systems (ITS) with public safety and private operations for roadside-to-vehicle and inter- vehicle communications. Basically, wireless connectivity and special sensors de- ployed in vehicles can be utilized to continuously report real-time traffic and environmental data (e.g., information about driving habits, roadway congestion, pollution levels), and also to provide access to email, news and entertainment applications. However, for vehicular communication networks to become a reality, a number of technical challenges have to be addressed. Data traffic initiated by vehicles is expected to be random and bursty in nature. As RSUs represent gateways to the infrastructure of the ITS system, vehicles convey their real time information and Internet access requests to RSUs. RSUs also send responses to Internet queries and road information to vehicles. However, it is difficult, in terms of infrastructure * This research was supported by a research grant from the Natural Science and Engineering Research Council (NSERC) of Canada. cost, to cover roads with a large number of RSUs so that every vehicle can always be connected to at least one nearby RSU during its trip in the area under control of the ITS system. Instead, vehicle-to-vehicle communications should be used in a multihop fashion in order to allow vehicles to connect to the out-of-transmission range RSUs with a reasonable number of RSUs covering the road. It is difficult to maintain an end-to- end connection between a vehicle and an RSU, while vehicles are moving with high speeds, especially on roads with a low vehicle density. Moreover, achieving a reasonable packet trans- mission delay over a disrupted multihop connection between a vehicle and an RSU is a big challenge. Our research objective in this paper is to present an an- alytical framework that helps to approximately estimate the minimum number of RSUs required to cover a road segment with a probabilistic vehicle-to-RSU delay guarantee, given that an intermittent multihop connectivity exists between vehicles and RSUs and vehicles are sending bursty traffic. We exploit both the effective bandwidth theory and its dual, the effective capacity concept, in order to determine an RSU density on a road that guarantees a required maximum vehicle-to-RSU delay with a certain pre-determined delay violation probability (based on the application needs). In the literature, most of research works related to disrupted connectivity in vehicular ad hoc networks focus on connectivity analysis [3] [4] and average message delay evaluation [4] [5]. To the best of our knowledge, no other study in the literature relates packet de- livery delay to RSUs with random vehicle traffic and disrupted connectivity modeling. II. SYSTEM MODEL A. Network Configuration a L Moving Vehicles Fixed RSUs 2G a L Moving Vehicles Fixed RSUs 2G Fig. 1. An illustration of network configuration. Consider a one dimensional road. Consider one segment of the road as a straight line of length a meters, where two adjacent RSUs are separated by L meters as shown in Figure 1. The transmission range for vehicles and RSUs is denoted by G. Initially, vehicles are distributed uniformly over the road segment. Following the same approach as in [6], it can This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings. 978-1-4244-4148-8/09/$25.00 ©2009