THE JOINT ARRIVAL AND DEPARTURE PROCESS FOR THE M/M/l QUEUE

Onno Boxma

16 citations0/0 files storedStatistica Neerlandica

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

Abstract

Abstract We consider the M/M/1‐queue and derive an explicit expression for the joint distribution of the number of arrivals and the number of departures in [0, t), given the number of customers initially present. The derivation is almost purely combinatorial, it avoids the use of generating functions, and immediately yields a simple probabilistic interpretation of the result.

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1956An Elementary Method of Solution of the Queueing Problem with a Single Server and Constant Parameters 1982Some New Results for the M/M/1 Queue

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1986The departure process for the M/M/1 queue 1999Transient behavior of a single-stage kanban system based on the queueing model 1995Lattice path counting andM/M/c queueing systems

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