Transient analysis of the Erlang A model

Charles Knessl () and Johan Leeuwaarden ()

Mathematical Methods of Operations Research, 2015, vol. 82, issue 2, 143-173

Abstract: We consider the Erlang A model, or $$M/M/m+M$$ M / M / m + M queue, with Poisson arrivals, exponential service times, and m parallel servers, and the property that waiting customers abandon the queue after an exponential time. The queue length process is in this case a birth–death process, for which we obtain explicit expressions for the Laplace transforms of the time-dependent distribution and the first passage time. These two transient characteristics were generally presumed to be intractable. Solving for the Laplace transforms involves using Green’s functions and contour integrals related to hypergeometric functions. Our results are specialized to the $$M/M/\infty $$ M / M / ∞ queue, the M / M / m queue, and the M / M / m / m loss model. We also obtain some corresponding results for diffusion approximations to these models. Copyright The Author(s) 2015

Keywords: Erlang A model; Queueing theory; Complex analysis; QED regime; Time-dependent analysis (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00186-015-0498-9

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