This article is cited in 3 papers

Queuing Systems

The $MAP+MAP/PH/1/N$ queuing system with single and batch arrivals of customers

S. A. Dudin

Belarussian State University, Minsk, Belarus

Abstract: The single-server queuing system with finite buffer was considered. The customers may arrive one-by-one or in batches. Arrivals of single customers and their batches obey the Markov input processes. The customers from a batch taken for servicing come one at a time at the exponentially distributed time intervals. The numbers of customers in batches are distributed geometrically. The time of customer servicing has a phase-type distribution. The numbers of batches and single customers that may be simultaneously accepted by the system are controllable parameters. The joint distribution of the number of batches and the number of customers in system, loss probabilities, distribution of the time of batch sojourn, and problems of optimization were analyzed.

PACS: 02.50.Fz

Presented by the member of Editorial Board: V. V. Rykov

Received: 30.06.2008

 English version: Automation and Remote Control, 2009, 70:5, 872–884

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