Motivated by increasing popularity of delay sensitive applications, we investigate the queue stability in device-to-device (D2D) relay-assisted cellular networks. In contrast to prior works on D2D relay-assisted cellular networks, we incorporate practical properties of these networks such as bursty packet arrivals, user mobility and relays generating their own traffic. Assuming network topology evolving in IID fashion, we first evaluate the system stability region to quantify its delay performance. Subsequently, we formulate a policy for joint resource allocation and power control under a more realistic mobility scenario of generalized reflected random walk. Also, the throughput optimality of this policy is investigated. Simulation results are provided to give better understanding of queue stability in the network.