Analysis of a Queue with Slowdown of Non-priority Customers

A multi-server priority queueing system with non-priority customers delay in an auxiliary buffer is analysed. Customer arrival is defined by a marked Markovian arrival process ($MMAP$). The service time has a phase-type distribution. Customers can renege from the buffers. The process of the system states is defined by a multidimensional Markov chain with level-dependent behavior. The generator of this chain is derived. The expressions for computation of the main performance characteristics of the system are obtained.