Operations Research, Systems Engineering and Industrial Engineering Commons^™

Multi-Threshold Control Of The Bmap/Sm/1/K Queue With Group Services, Alexander Dudin N., Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated.