Multichannel Queueing Systems with Regenerative Input Flow

Larisa Grigor'evna Afanas'eva · Andrey Tkachenko

17 citations0/0 files storedTheory of Probability and Its Applications

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

We consider the multichannel queueing system with nonidentical servers and regenerative input flow. The necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, the ergodicity condition for queues with unreliable servers is obtained. Suggested approaches are used to prove the ergodic theorem for systems with limitations. We also consider the hierarchical networks of queueing systems.

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1962The stability of a queue with non-independent inter-arrival and service times 1962A Waiting Line with Interrupted Service, Including Priorities 1970Multiple channel queues in heavy traffic. I 1955On the theory of queues with many servers 1979A Markovian Queue with N Servers Subject to Breakdowns and Repairs 1965Some Limit Theorems in the Theory of Mass Service, II Multiple Channels Systems 1997The tightness in the ergodic analysis of regenerative queueing processes 2004Weak Regeneration in Modeling of Queueing Processes

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