A Two-Phase BMAP|G|1|N → PH|1|M – 1 System with Blocking

Authors:
D. Breuer;A. N. Dudin;V. I. Klimenok;G. V. Tsarenkov
Affiliations:
University of Tier, Tier, Germany;Belarussian State University, Minsk, Belarus;Belarussian State University, Minsk, Belarus;Belarussian State University, Minsk, Belarus
Venue:
Automation and Remote Control
Year:
2004

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Abstract

The stationary probability distribution of a two-phase queueing system with a finite or an infinite buffer for the first phase and a finite buffer for the second phase is derived. The input flow of the system is a batch Markov arrival process. Both phases have single-servers. The service time distribution is arbitrary for the first phase and of phase-type for the second phase. If the buffer of the second phase is full at the instant of completion of service at the first phase, the first server is blocked until the buffer is freed.