Mobility Modeling for Vehicular Communication Networks

Newly manufactured vehicles are no longer the simple mechanical devices that we once knew. Each vehicle is a smart body of various sensors that can measure different attributes. Recently, efforts have been made to deploy communication capabilities in vehicles and the transport infrastructure, leading to a potential of vehicular ad hoc networks (VANETs) [1–3]. In 1999, the United States Federal Communications Commission (FCC) allocated 75 MHz of radio spectrum in the 5.9 GHz band to be used for Dedicated Short Range Communication (DSRC) by intelligent transportation systems (ITS). The DSRC spectrum has seven 10MHz channels, one control channel (CCH) and six service channels (SCHs). In 2008, the European Telecommunications Standards Institute (ETSI) allocated 30 MHz of spectrum in the 5.9 GHz band for ITS. In 2014, the United States (U.S.) National Highway Traffic Safety Administration (NHTSA) announced that it had been working with the U.S. department of transportation on regulations that would eventually mandate vehicular communication capabilities in new light vehicles by 2017 [4]. An envisioned VANET will consist of (1) vehicles with on-board sensing and transmitting units which form the network nodes; (2) stationary road side units (RSUs) deployed on the sides of roads and connected to the Internet; and (3) a set of wireless channels from the DSRC spectrum. An illustration of a VANET infrastructure is shown in Fig. 1.1.

Consider a connected VANET on a multi-lane highway with no on or off ramps. This brief focuses on a single lane with lane changes implicitly captured in the adopted mobility model. A single lane from a multi-lane highway is chosen instead of a single-lane highway, in order to be more realistic in a highway scenario. A vehicle can overtake a slower leading vehicle, if possible, and accelerate towards its desired speed. Assume that the highway is in a steady traffic flow condition defined by a time-invariant vehicle density. Let D denote the vehicle density in vehicle per kilometer. Three levels of D are considered: low, intermediate, and high vehicle densities as in Table 1.​1 However, in this research the case when the vehicle density is changing among the three levels is not considered. Additionally, this work does not consider the case of increasing/decreasing vehicle density within the same level of density. The system model focuses only on a single direction traffic flow. All the vehicles have the same transmission range, denoted by R. Any two nodes at a distance less than R from each other are one hop neighbors. The set of vehicles, that are within the coverage range R of a vehicle, is referred to as vehicle’s one-hop neighborhood as illustrated in Fig. 2.1a. The length of a hop is defined as the distance to the furthest node within the transmission range of a reference node, which is upper bounded by R as illustrated in Fig. 2.1b. The furthest node within the transmission range of a reference vehicle is referred to as hop edge node. Let H denote the hop length with respect to a reference node. Assume that the transmission range is much larger than the width of the highway such that a node can communicate with any node within a longitudinal distance of R from it. Time is partitioned with a constant step size. Let X _i be the distance headway between node i and node i + 1, \(i = 0,1,2,\ldots\). The distance headway is the distance between two identical points on two consecutive vehicles on the same lane. Define \(X_{i} =\{ X_{i}(m),m = 0,1,2\ldots \}\) to be a discrete-time stochastic process of the ith distance headway, where X _i (m) is a random variable representing the distance headway of node i at the mth time step. At any time step, \(X_{i}(m) \in [\alpha,X_{\text{max}}]\) for all i, m ≥ 0, where α and X _max is the minimum and maximum distance headway, respectively. Furthermore, assume that the distance headways (X _i for all i ≥ 0) are independent with identical statistical behaviors. For notation simplicity, the index i from X _i is omitted when referring to an arbitrary distance headway. In this analysis, the 0th time step refers to the time when the network has just established. A two-hop neighborhood between two reference vehicles is the set of vehicles between two reference vehicles that are connected via two-hop connection. Let \(\mathbb{X}_{H2}\) denote the sequence of distance headways between two reference vehicles that are two-hop apart as illustrated in Fig. 2.1c. The set of nodes between the two-hop vehicles is referred to as vehicle’s two-hop neighborhood. The vehicles are assumed to be distributed on the highway according to a stationary probability distribution of the distance headways when the network is first established. Let μ and \(\sigma\) be the mean and the standard deviation of the distance headway in meters, respectively, where μ = 1000∕D and \(\sigma\) are constant system parameters and take different values according to the vehicle density. Throughout this brief, \(F_{Y }(y),P_{Y }(y),f_{Y }(y),Q_{Y }(y),\) and E[Y ] are used to denote the cumulative distribution function (cdf), the probability mass function (pmf), the probability density function (pdf), the probability generating function, and the expectation of random variable Y, respectively.

Unlike traditional mobile ad hoc networks, the high node mobility in VANETs can cause frequent network topology changes and fragmentations. As discussed in Sect. 1.​3, any change in network topology is directly or indirectly related to the change in distance headways among vehicles. This chapter presents a novel microscopic mobility model to facilitate VANET analysis. Firstly, A discrete-time finite-state Markov chain with state dependent transition probabilities is proposed to model the distance headway. The model captures the time variations of a distance headway and its dependency on distance headway value. Secondly, highway vehicular traffic is simulated using microscopic vehicle traffic simulator, VISSIM. Vehicle trajectory data collected from highways in the U.S. and that simulated by VISSIM are used to demonstrate the validity of the proposed mobility model for three vehicle density ranges. Finally, the proposed mobility model is extended to a group mobility model that describes the time variations of a system of distance headways between two non-consecutive vehicles. Using lumpability theory, a Markov chain with reduced state-space is proposed to represent the mobility of a group of vehicles.

Network topology in VANETs is subject to fragmentations and frequent changes due to vehicle mobility. Moreover, VANETs are susceptible to vehicle density variations from time to time throughout the day. This imposes new challenges in maintaining a connection between vehicular nodes. As discussed in Sect. 1.​3, the frequent changes in VANET topology may degrade the performance of network protocols. In this chapter, the spatiotemporal variations in VANET topology are analyzed. Two parameters are used to describe the network topology, the communication link and vehicle’s neighbors. Firstly, the length of the communication link is analyzed using mesoscopic vehicle mobility models. Secondly, the proposed microscopic mobility model is utilized to derive the communication link duration. Thirdly, the lumped Markov chain is relaxed to an edge-lumped Markov chain and the probability distribution of the time period between successive changes in vehicle’s one-hop neighborhood is derived. Furthermore, queueing theory is utilized to model the limiting behavior of the common VNs of two reference vehicles that are two-hop away. The overlapping region of the coverage ranges of the two-hop vehicles is modeled as a storage buffer in a two-state random environment. Using G/G/1 queuing theory, the steady-state distribution of the number of common VNs is approximated. Numerical results are presented to evaluate the proposed models, which demonstrate a close agreement between analytical and simulation results.

VANETs are promising additions to our future intelligent transportation systems, that have captured world-wide attention from auto companies, academics, and government agencies. Realizing V2I and V2V communications will enable many safety and infotainment applications that can revolutionize the transport infrastructure.