Analysis of M/M/S queues with 1-limited service

In this paper, a multiple server queue, in which each server takes a vacation after serving one customer is studied. The arrival process is Poisson, service times are exponentially distributed and the duration of a vacation follows a phase distribution of order 2. Servers returning from vacation immediately take another vacation if no customers are waiting. A matrix geometric method is used to find the steady state joint probability of number of customers in the system and busy servers, and the mean and the second moment of number of customers and mean waiting time for this model. This queuing model can be used for the analysis of different kinds of communication networks, such as multi-slotted networks, multiple token rings, multiple server polling systems and mobile communication systems.