A Delay Performance Analysis and Wireless Resource Allocation Scheme Based on Martingale Theory

Statistical delay quality of service (QoS) provisioning is crucial for ultra-reliable low-latency communications (URLLCs). In this paper, a precise delay performance analysis framework is proposed based on martingale theory and a wireless resource configuration scheme is designed. A tight upper bound of delay violation probability is conducted for the aggregated traffic composed of bursty flows and independent identically distributed (i.i.d.) flows. A martingale of aggregated arrival processes is constructed. Based on the definition of martingale processes, the martingale parameters are determined by considering the statistical features of flows, which expose the impacts of heterogeneous flows entangled with each other on system delay. A stopping time event related to delay is defined. Leveraging the stopping time theory of martingale processes, the complementary cumulative distribution function of delay is captured, which reveals the implicit relationship among aggregated traffic, service schemes, and delay performance. Guided by the theoretical upper bound of delay violation probability, a bandwidth estimation algorithm is proposed, which facilitates the decoupling of the statistical delay QoS requirements as the bandwidth demands. Subject to the bandwidth demands, a wireless resource allocation problem is formulated. Based on the Lagrangian convex optimization framework, the closed form of the transmission power is obtained. Simulations verify the effectiveness of the martingale-based delay performance analysis method and power allocation scheme.