Stability of Multichannel Queueing Systems with Interruptions and Regenerative Input Flow

L.G. Afanassieva, A. Tkachenko

2019, v.25, Issue 4, 723-745

ABSTRACT

Multichannel queueing system with heterogeneous servers, regenerative input flow, and interruptions of the service is considered. Consecutive moments of the breakdowns are defined by the renewal process. The breakdowns of the servers may occur at any time even if they are not occupied by customers. Two main service disciplines are studied: preemptive repeat different service discipline and preemptive resume service discipline. Exploiting synchronization method we establish the necessary and sufficient conditions for stability of the system. It is shown that the necessary and sufficient stability condition for the preemptive repeat different service discipline cannot be expressed in terms of mean values of the input flow, service times, and repair times as is usually the case.

Keywords: multichannel system, regenerative flow, stability, interruption, vacation, unreliable servers

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