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

O. J. Boxma

Statistica Neerlandica, 1984, vol. 38, issue 3, 199-208

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.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:bla:stanee:v:38:y:1984:i:3:p:199-208

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