Analysis of GI/M/n/n queueing system with ordered entry and no waiting line

This paper deals with a multi-server, finite-capacity queuing system with recurrent input and no waiting line. The interarrival times are arbitrarily distributed whereas service times are exponentially distributed. Moreover, the servers are heterogeneous and independent of each other. Arriving customers choose the server with the lowest index number among the empty servers. When all servers are busy at a time of an arrival, that arrival must leave the system without being served. The semi-Markov process method is used to describe this model and embedded Markov chain of the process is obtained. Furthermore, the Laplace–Stieltjes transform of the distribution of interoverflow times is derived which is the main objective of the paper. Finally, it is offered a new formulation for the loss probability which provides more efficient and rapid calculation is proposed.