Abstract:
In this paper we consider a finite capacity queuing system in which arrivals
are governed by a Markovian arrival process. The system is attended by two
exponential servers, who offer services in groups of varying sizes. The service
rates may depend on the number of customers in service. Using Markov theory,
we study this finite capacity queuing model in detail by obtaining numerically
stable expressions for (a) the steady-state queue length densities at arrivals and
at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary
waiting time distribution of an admitted customer at points of arrivals. The
stationary waiting time distribution is shown to be of phase type when the
interarrival times are of phase type. Efficient algorithmic procedures for
computing the steady-state queue length densities and other system performance
measures are discussed. A conjecture on the nature of the mean waiting time is
proposed. Some illustrative numerical examples are presented.
