Operations Research, Systems Engineering and Industrial Engineering Commons^™

A Finite Capacity Queue With Markovian Arrivals And Two Servers With Group Services, Srinivas Chakravarthy, Attahiru S. Alfa

Industrial & Manufacturing Engineering Publications

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 …