A multiserver queue with Markovian arrivals and group services with thresholds

The authors consider a multiserver queueing system in which arrivals are governed by a Markovian arrival process. The system is attended by K identical exponential servers. Under a dynamic probabilistic service rule which depends on two threshold parameters, this model is studied as a Markov process. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic key performance measures of the system are developed. Some numerical examples are discussed.