The M/M/c queue with mass exodus and mass arrivals when empty

Junping Li

21 citations0/0 files storedJournal of Applied Probability

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

Abstract

In this paper we consider an M/M/c queue modified to allow both mass arrivals when the system is empty and the workload to be removed. Properties of queues which terminate when the server becomes idle are firstly developed. Recurrence properties, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no mass exodus. All of these results are then generalized to allow for the removal of the entire workload. In particular, we obtain the Laplace transformation of the transition probability for the absorptive M/M/c queue.

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References

1977Fundamentals of Queueing Theory.1987Applied Probability and Queues 2003Applied Probability and Queues 1985Fundamentals of queueing theory (2nd ed.).1991Product-form queueing networks with negative and positive customers 1986Fundamentals of Queueing Theory.2000G-networks: A versatile approach for work removal in queueing networks 1991Queues with negative arrivals

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2017MX/M/c Queue with catastrophes and state-dependent control at idle time

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