We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of ℝ2. The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street. Models in this Coxian framework can characterize streets of different lengths and orientations forming intersections or T-junctions. The lengths of the streets can be infinite or finite and mutually independent or dependent. We analyze the reliability of communication for different models, where reliability is the probability that a vehicle at an intersection, a T-junction, or a general location can receive a message successfully from a transmitter at a certain distance. Further, we introduce a notion of equivalence between vehicular models, which means that a representative model can be used as a proxy for other models in terms of reliability. Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants.

A comprehensive vehicular network analysis requires modeling the street system and vehicle locations. Even when Poisson point processes (PPPs) are used to model the vehicle locations on each street, the analysis is barely tractable. That holds for even a simple average-based performance metric—the success probability, which is a special case of the fine-grained metric, the meta distribution (MD) of the signal-to-interference ratio (SIR). To address this issue, we propose the transdimensional approach as an alternative. Here, the union of 1D PPPs on the streets is simplified to the transdimensional PPP (TPPP), a superposition of 1D and 2D PPPs. The TPPP includes the 1D PPPs on the streets passing through the receiving vehicle and models the remaining vehicles as a 2D PPP ignoring their street geometry. Through the SIR MD analysis, we show that the TPPP provides good approximations to the more cumbrous models with streets characterized by Poisson line/stick processes; and we prove that the accuracy of the TPPP further improves under shadowing. Lastly, we use the MD results to control network congestion by adjusting the transmit rate while maintaining a target fraction of reliable links. A key insight is that the success probability is an inadequate measure of congestion as it does not capture the reliabilities of the individual links.

Poisson line processes (PLPs) describe a street system as a random collection of lines. Poisson point processes (PPPs) model vehicle locations on each line or street as random points. The characterization of vehicular networks as their combination, i.e., the PLP-PPP model, is relevant and widely used in the literature. However, the analytical expression for even a simple performance metric such as the probability of successful message reception in the PLP-PPP is quite complex and provides little insights into the network behavior. Here, we propose a transdimensional Poisson model-superposition of the 1D and 2D PPPs- as an alternative. It considers the vehicles on the same line as the receiving vehicle as a 1D PPP and the vehicles on the other streets as random points on the 2D plane neglecting their street geometry. We show that the success probability in the proposed transdimensional model is tractable and provides a tight approximation to that of the PLP- PPP. Also, it is asymptotically exact on both the upper and lower tails of the success probability.

We consider a vehicular network with an underlying regular street system formed by horizontally and vertically oriented streets. We model vehicle locations on each street using Poisson point processes, and each vehicle transmits with some probability following slotted ALOHA. Each receiving vehicle connects to its partner-transmitting vehicle based on the following schemes: 1) Nearest-transmitter reception (NTR), 2) Nearest-transmitter reception with selective thinning (NTR-II), and 3) Nearest-receiver transmission (NRT). In NTR and NTR-II, each receiver receives from its nearest transmitter, whereas in NRT, each transmitter transmits to its nearest receiver. NTR-II is a modified version of NTR, where the transmitters not closest to any of the receivers remain idle. Under each scheme, we calculate the probabilities of successful reception for the general and intersection users, i.e., vehicles not at intersections and at intersections. We study how the nearest-transmitter/receiver distance properties in each scheme differ for general and intersection users, and in turn, how those properties affect their probabilities of successful reception. Also, we show that we can obtain higher data rates in NTR and NTR-II compared to NRT in the high-reliability regime.

The analysis of vehicle-to-vehicle communications is generally limited to vehicles on street segments, which are modeled using 1-D point processes. However, it is essential to model the intersections which are crucial for vehicle safety. In this paper, we focus on orthogonal street systems involving intersections with Poisson distributed vehicles on each street. We derive analytical expressions for the success probabilities of two types of users-- the typical general user and the typical intersection user. We show that the the orthogonal street system shares some properties of both 1-D and 2-D Poisson networks. Specifically, the vehicles on the street system behave like 1-D and 2-D Poisson point processes of vehicles in the high-reliability and low-reliability regimes, respectively. Also, we deduce that the success probability of the typical general/intersection user is upper bounded by the minimum of the success probabilities of the 1-D and 2-D Poisson networks.

We integrate a wireless powered communication network with a cooperative cognitive radio network, where multiple secondary users (SUs) powered wirelessly by a hybrid access point (HAP) help a primary user relay the data. As a reward for the cooperation, the secondary network gains the spectrum access where SUs transmit to HAP using time division multiple access. To maximize the sum throughput of SUs, we present a secondary sum-throughput optimal resource allocation (STORA) scheme. Under the constraint of meeting target primary rate, the STORA scheme chooses the optimal set of relaying SUs and jointly performs the time and energy allocation for SUs. In particular, by exploiting the structure of the optimal solution, we find the order in which SUs are prioritized to relay primary data. Since the STORA scheme focuses on the sum throughput, it becomes inconsiderate toward individual SU throughput, resulting in low fairness. To enhance fairness, we investigate three resource allocation schemes, which are: 1) equal time allocation; 2) minimum throughput maximization; and 3) proportional time allocation. Simulation results reveal the tradeoff between sum throughput and fairness. The minimum throughput maximization scheme is the fairest one as each SU gets the same throughput, but yields the least SU sum throughput.

This paper considers the cooperation between primary and secondary users at information and energy levels when both users are energy harvesting nodes. In particular, a secondary transmitter helps relaying the primary message, and in turn, gains the spectrum access as a reward. Also, the primary transmitter supplies energy to the secondary transmitter if the latter is energy-constrained, which facilitates an uninterrupted cooperation. We address this two-level cooperation over a finite horizon with the finite battery constraint at the secondary transmitter. While promising the rate-guaranteed service to both primary and secondary users, we aim to maximize the primary rate. We develop an iterative algorithm that obtains the optimal offline power policies for primary and secondary users. To acquire insights about the structure of the optimal solution, we examine specific scenarios. Furthermore, we investigate the effects of the secondary rate constraint and finite battery on the primary rate and the probability of cooperation. We show that the joint information and energy cooperation increases the chances of cooperation and achieves significant rate gains over only information cooperation.