Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time

In this paper, we analyze a multi-server queueing system with marked Markov arrival process of two types customers and phase-type distribution service time depending on the type customer. Customers both are assumed to be impatient renege from buffers after an exponentially distributed number times. The strategy flexible provisioning priorities is analyzed. It assumes randomized choice buffers, probabilities dependent relation between in priority finite buffer fixed threshold value. To simplify construction underlying chain derivation explicit form its generator, use so-called generalized distribution. shown that created fits category asymptotically quasi-Toeplitz chains. Using fact, show considered ergodic for any value parameters compute stationary Expressions key performance measures presented. Numerical results how control affect system’s measurements given. can used managerial purposes it crucial take correlation into account.