A simple solution for the M/D/c waiting time distribution

Authors:
G. J. Franx
Affiliations:
Department of Mathematics and Computer Science, Free University of Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Venue:
Operations Research Letters
Year:
2001

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Abstract

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.