Analysis of Multi-server Loss Queueing System with the Batch Marked Markov Arrival Process

A multi-server queueing system with various types of customers arriving in accordance with a Batch Marked Markov Arrival Process (BMMAP) is considered. The service times have exponential distribution with the rate corresponding to the type of customer. The system does not have a buffer. The customer acceptance discipline is assumed to be partial admission. The operation of the system is described by a multi-dimensional continuous time Markov chain. The stationary distribution of the states of the chain and the key system indicators (such as loss probabilities of customers of different types and the sojourn time distribution) are computed. The results are illustrated numerically. © 2021, Springer Nature Switzerland AG.