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A Discrete Single Server Queue With Markovian Arrivals And Phase Type Group Services, Attahiru Sule Alfa, K. Laurie Dolhun, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric …