Martingale-Based URLLC Slice Customization for the Provisioning of Reliability With Regard to End-to-End Latency

End-to-end (E2E) reliability provisioning is critical for network slice customization. Leveraging martingale theory, we construct an analysis framework of the reliability with regard to E2E latency for the multihop system, where service processes provided by wireless nodes and networking nodes are heterogeneous. Based on the Wald martingale constructions of arrival processes and service processes, tandem service descriptor is defined to embody the features of tandem service mode for the targeted flow. Arrival bias and service bias are derived to describe the fluctuations of arrival and service processes, respectively. Relying on the Doob maximum inequality of martingales, a tight upper bound of the unreliability regard to E2E latency is captured. Packet duplication and hot-backup parallel transmission patterns are adopted for network reliability enhancement. A reliability decomposition and bandwidth abstraction algorithm is proposed, which achieves the decoupling between the statistical reliability requirement and the desired bandwidth of each node. Slice instantiation is performed in the access network and the core network, respectively. In the wireless access network, a long-term stochastic optimization problem is formulated with reliability requirements constraint. Lyapunov drift-plus-penalty (DPP) optimization theory is explored to transform the intractable long-term optimization problem into dynamic evolutionary per-slot optimization problems. We yield the closed-form solutions of user scheduling and power allocation. In the core network, the forwarding rates in the networking nodes for the targeted flow are obtained.