Martingale-Based Resource Partitioning Bounds for URLLC and eMBB Network Slicing in 5G

Network slicing is a key enabler for the coexistence of ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB) in 5G networks. However, allocating limited radio resources to heterogeneous slices while satisfying stringent quality-of-service (QoS) requirements remains challenging, particularly in the ultra-reliable regime where conventional effective-capacity-based approaches may lead to excessive resource allocation. To address this issue, this paper proposes a martingale-based resource block (RB) allocation framework for coexisting URLLC and eMBB slices. By constructing exponential martingale processes using the moment generating functions (MGFs) of the arrival and service processes and applying Doob's maximal inequality, explicit non-asymptotic upper bounds are derived for the URLLC delay violation probability and the eMBB backlog violation probability. Based on the resulting theoretical stability conditions, a low-complexity bisection algorithm is developed to determine the optimal martingale parameters, followed by a deterministic search algorithm to obtain the minimum RB requirements for both slices. Numerical results show that the analytical bounds effectively upper-bound the Monte Carlo simulation results. At a target violation probability of $10^{-6}$ for each slice, the proposed framework requires 44 RBs in total, satisfying the system capacity constraint of 50 RBs. Compared with the conventional effective-capacity baseline requiring 64 RBs, the proposed framework reduces total RB consumption by approximately 31.2% relative to the conventional effective-capacity baseline.