Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities

A single-server non-pre-emptive priority queueing system of a finite capacity with many types customers is analyzed. Inter-arrival times can be correlated and batch arrivals are allowed. Possible unreliability the server, implying loss customer or necessity its service from early beginning some phase service, taken into account. Initial priorities provided to various at arrival moment varied (increased decreased) after random amount time during stay in buffer. Such type queues arises modeling operation emergency care systems, information, perishable goods delivering etc. The stationary behavior described by state multi-dimensional continuous-time Markov chain upper-Hessenberg block structure generator. distribution states important characteristics calculated. presented numerical examples illustrate opportunities quantitatively evaluate impact buffer customers’ mean rate on most system. possibility solving optimization problems briefly shown.