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A simple solution for the M/D/c waiting time distribution. (English) Zbl 0993.90026

Summary: A surprisingly simple and explicit expression for the waiting time distribution of the M/D/\(c\) queueing system is derived by a full probabilistic analysis, requiring neither generating functions nor Laplace transforms. Unlike the solutions known so far, this expression presents no numerical complications, not even for high traffic intensities. Finally, the result is proved explicitly to satisfy Erlang’s integral equation for the M/D/\(c\) queue, which has been somewhat problematic for the expressions known so far.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
90B10 Deterministic network models in operations research
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