title: Transient analysis of the Erlang A model.
abstract: We consider the Erlang A model, or [Formula: see text] queue, with Poisson arrivals, exponential service times, andmparallel 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 [Formula: see text] queue, theM/M/mqueue, and theM/M/m/mloss model. We also obtain some corresponding results for diffusion approximations to these models.
authors.affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 815 South Morgan Street, Chicago, IL 60607-7045 USA.
authors.forename: Charles
authors.initials: C
authors.lastname: Knessl
authors.affiliation: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
authors.forename: Johan S H
authors.initials: JS
authors.lastname: van Leeuwaarden
keywords: Complex analysis; Erlang A model; QED regime; Queueing theory; Time-dependent analysis