Analytical evaluation of average delay and maximum stable throughput along a typical two-way street for vehicular ad hoc networks in sparse situations

Abstract

Intermittent connectivity is an intrinsic feature of vehicular ad hoc networks (VANETs) in sparse situations. This type of network is in fact an example of delay and disruption tolerant networks (DTNs). In this paper, we focus on a typical two-way street and analytically evaluate the maximum stable throughput and the average delay for packet forwarding along the street. To this end, we map the mobility patterns of the vehicles with different speeds onto suitable parameters of a BCMP queueing network and derive the location density of vehicles. Then, we employ another queueing network in order to model opportunistic multi-hop packet forwarding along the street with respect to the specifications of MAC and routing schemes. We propose a two-mode MAC scheme suitable for DTNs with predictable mobility patterns. We also consider the effect of vehicles’ velocities and opportunistic relaying for routing schemes. In our analysis, we evaluate the average delay and the maximum stable throughput for the proposed MAC and routing schemes. In the last part of the paper, we show the efficiency of the proposed analytical approach by some numerical results and confirm our analysis by simulation.

Introduction

Vehicular ad hoc networks (VANETs) are essential parts of Intelligent Transportation Systems (ITSs). In a typical VANET, vehicles are mobile nodes comprising an ad hoc network. Also, some fixed nodes may exist. They facilitate the packet transmission process. Then, a typical VANET is comprised of two types of nodes, fixed and mobile (vehicles), in general. Usually the number of fixed nodes is not so much to remove the necessity of multi-hop packet transmission among mobile nodes. We consider an example of this type of VANET in this paper.

The number of vehicles in a typical street is a random process that is strongly dependent upon the arrival rate of vehicles as well as the mobility patterns of the vehicles at that street. In sparse situations, where the number of vehicles is low, connectivity among vehicles is not preserved. Then in this case, the street, as a part of a typical VANET, is actually a delay and disruption tolerant network (DTN). Up until now several papers focusing on DTNs have been published in the literature. A major part of them is concerning about suitable routing algorithms in DTNs [1], [2], [3], [4], [5], [6], [7]. Some of them have focused on increasing the delivery ratio by several versions of epidemic routing [4], [6]. Some of the others have considered routing schemes with respect to energy and memory concerns [2]. In this respect, a few papers have evaluated the level of cooperation [3]. And some research works have focused on throughput maximization by inserting special nodes [8].

The major parts of the above works have considered DTNs in general and not in special situations. In some applications some of the concerns considered in previous works are not important. For example, in VANETs energy and memory are not the main concerns. Furthermore, the mobility patterns of the vehicles are road restricted.

On the other hand, many papers have focused on different aspects of VANETs. Some of them have considered connectivity issue and mobility modeling [9], [10], [11], [12], [13]. Some research works have focused on efficient flooding and dissemination algorithms [14], [15]. And many research works have focused on designing new routing algorithms in different situations [16], [17], [18], [19]. One of the main concerns of the routing algorithms in VANETs reverts to decisions at intersections. This is of more crucial importance in sparse situations. In fact, an efficient packet forwarding technique for VANETs in sparse situations is carry and forward technique [19] as well as opportunistic multi-hop packet transmission. In other words, a mobile node or vehicle stores the packet and carries it by itself until it finds a suitable vehicle. Then, the packet is sent to the more suitable vehicle. This attribute is very effective and viable because of mobility of the vehicles.

In this paper, we focus on a part of a VANET in sparse situations that is a good example of DTNs. In this respect, a typical two-way street is considered and we evaluate the average delay and the maximum stable throughput for the packets generated along one way of the street. In fact, in a typical VANET, two types of services have been proposed, i.e., emergency services and conventional communication services. The key characteristic of emergency services relates to delay but for conventional services throughput plays a key role as well. Moreover, in several routing algorithms proposed for VANETs, the average delay along a typical street is a crucial parameter in decision-making at intersections [19], [20]. However, to the best of our knowledge an analytical evaluation of this parameter has not been proposed in the literature, especially in sparse situations. One of the main issues focused in this paper is proposing a solution to this problem. In this respect, we evaluate the average delay as well as the maximum stable throughput versus arrival rate of vehicles in the street. The arrival rate is sufficiently low such that the connectivity among vehicles is intermittent. In this respect, we consider two static nodes at two contiguous intersections, i.e., at the ends of a typical two-way street. The packets generated at one intersection (i.e., first static node at our VANET scenario) are marked and sent towards the other end of the street. We also consider conventional (unmarked) packets generated at the vehicles along the street. The destination of both types of the packets, i.e., marked and conventional ones, is at the other intersection (i.e., the second static nodes at our VANET scenario). In our analyses, we evaluate the average delay for the marked packets as well as the maximum stable throughput for all packets. It is worth noting that in a real-life scenario, the static nodes at intersections can be active public information displays (e.g., electronic billboards) that contain helpful information for all vehicles arriving at the street and also play the role of fixed relay stations [20]. Moreover, the marked packets can be some emergency packets, e.g., the status of probable crash or traffic load in the street. Furthermore, conventional packets include advertised broadcast packets from the stores and malls at the roadside of the street and the packets corresponding to communication services (e.g., VoIP, web browsing, etc.).

In our analytical approach, we map different components of the network, e.g., mobility patterns and the effective factors in multi-hop packet transmission process (i.e., MAC and routing) onto the components of several queueing networks [21]. By solving the related traffic equations we derive the desired performance metrics, i.e., the maximum stable throughput and the average delay. We also propose a two-mode MAC scheme and evaluate analytically the proposed MAC scheme as well as several routing schemes in view of the desired performance metrics. We will confirm our analytical results by extensive simulations.

Following this introduction, in Section 2, we discuss about the mobility modeling. Analytical modeling of packet forwarding process including MAC and routing schemes has been discussed in Section 3. We evaluate the average delay and the maximum stable throughput in Section 4. After several numerical results and simulations confirming the proposed analytical approach in Section 5, we conclude this paper in Section 6.