Efficient and accurate Lyapunov function-based truncation technique for multi-dimensional Markov chains with applications to discriminatory processor sharing and priority queues

Online service providers aim to satisfy the tail performance requirements of customers through Service-Level Objectives (SLOs). One approach to ensure tail performance requirements is to model the service as a Markov chain and obtain its steady-state probability distribution. However, obtaining the distribution can be challenging, if not impossible, for certain types of Markov chains, such as those with multi-dimensional or infinite state-space and state-dependent transitions. Examples include M/M/1 with Discriminatory Processor Sharing (DPS) and preemptive M/M/c with multiple priority classes and customer abandonment.