A Scheme of Bandwidth Demands Capture and Resource Allocation Based on Martingale Theory Under Statistical End-to-End Delay QoS Constraints

Statistical end-to-end (E2E) delay quality-of-service (QoS) provisioning is pivotal for ultra-reliable low-latency communication (URLLC) in 5G/B5G networks. Based on martingale theory, we propose an E2E delay analysis framework for paths with heterogeneous service processes. Martingales related to the arrival and service processes are constructed, and bias scale functions are defined via martingale parameters to characterize the statistical features of the accumulated arrival and service. A service index is introduced to model the service capability of the tandem queuing system in the martingale domain. By combining the service index with the Doob maximum inequality, a tight upper bound of the E2E delay violation probability is derived. For the parallel transmission pattern constructed for URLLC traffic, a bandwidth demand capture and reliability decomposition (BDC-RD) scheme is designed, which obtains the bandwidth requirements of all involved nodes and decomposes the reliability requirement across different E2E paths. Guided by the martingale-based upper bound, an optimization problem for QoS provisioning is formulated and solved by the particle swarm optimization (PSO) algorithm, achieving the decoupling between the statistical QoS requirements and the desired bandwidth of each node. In the radio access network, a physical-layer resource allocation algorithm is proposed under the bandwidth demand constraints, and a closed-form solution of the power consumption is derived. The effectiveness of the proposed BDC-RD scheme and the physical-layer resource allocation algorithm is verified. The PSO solutions are shown to be close to the global optimum by comparison with the global-optimum lower bound obtained by the branch-and-bound search. The superiority of the theoretical result on the delay violation probability is demonstrated.