# Performance Analysis of D2D Communication with Retransmission Mechanism in Cellular Networks
## 1 Introduction
Furthermore, in several works addressing the queuing model for D2D communications with retransmission schemes [22; 23], the authors did not describe the packet retransmission process by the feedback queuing model. In this paper, we construct a spatiotemporal traffic model with a retransmission strategy to evaluate the performance of D2D underlay cellular networks, where the data packets' arrival is initiated randomly and the departure is governed by the received signal-to-interference-plus-noise ratio (SINR). The main contributions of this paper include three parts: Firstly, from the perspective of spatial distribution, we employ the tools of stochastic geometry to derive the coverage probability of D2D user. Secondly, from the temporal domain perspective, the exact queueing behavior of D2D users with the retransmission mechanism in D2D underlay cellular networks is developed by queuing theory, in which sporadic data generation instead of saturated traffic affect the interference state and further network QoS performance evaluation. Third, an embedded Markov chain is used to model the queue length state transition. The steady-state probability distribution is computed using an iterative solution, and the expressions of performance metrics are obtained. The main contributions and outcomes of this paper are as follows:  
* We develop a stochastic traffic model to model a retransmission mechanism for D2D underlay communication. By using the stochastic geometry model for a user's position, interference levels experienced by D2D users are also quantified, and simple formulas of coverage probability are derived. A queuing model with feedback is adopted to analyze the performance of dynamic traffic for a D2D underlay cellular network. * The retransmission strategy is modeled as feedback queuing to explore the effects of the number of retransmission attempts on key system parameters. In order to analyze the queuing behavior in the buffer, we formulate it as an embedded Markov chain and compute its steady-state distribution by the iterative solution. The closed-form expressions of performance metrics, namely the average queue length, mean throughput, average packet delay, and packet dropping probability, are obtained. * Simulation results indicate that the dropping probability and average throughput are affected by setting an appropriate number of retransmission attempts. The dropping probability gradually decreases as the retransmission attempts increase. However, when the arrival rate is comparatively high, the optimal throughput is reached after fewer retransmission attempts because of the limited buffer. Simulation results show the validity and rationality of the theoretical analysis. The remainder of this paper is structured as follows. Section 2 reviews related works, and Section 3 describes the system model. Section 4 gives the details and transmission strategy of the feedback queuing model applied to D2D communication and the transition probability matrix of the embedded Markov chain. Section 5 introduces the solving process of the steady-state probability distribution in detail. Expressions of the performance metrics, namely average queue length, average throughput, average packet delay, and packet dropping probability, are derived. In Section 6, the simulation results are reported, and they demonstrate the validity and rationality of the theoretical analysis. Finally, a brief conclusion and possible future work are presented in Section 7.