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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3670 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3670 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3670 archive 351 disk0/00/00/36/51 2016-01-15 02:01:57 2021-08-27 17:14:14 2016-01-15 02:01:57 monograph show 2 Adan I.J.B.F. Waarsenburg W.A. van de Wessels J. AL1368 pub iis_met iis_mod prog_mda In this paper we study a system consisting of parallel identical servers and a common queue. The service times are Erlang-r distributed and the interarrival times are Erlang-k distributed. The service discipline is first-come first-served. Bertsimas has proved that the equilibrium probability for a saturated state can be written as a linear combination of geometric terms. In the present paper it is shown that the coefficients also have a geometric form. It is also shown how the factors may be found efficiently. The present paper uses a direct approach for solving the equilibrium equations rather than a generating function approach as Bertsimas does. The direct approach was inspired by previous work of two of the authors on the shortest queue problem, in particular, and on the two-dimensional random walk, more generally. Although the paper extends results of Bertsimas it is self-contained. 1992-07 published WP-92-047 WP-92-047 10 2510 public working_paper IIASA, Laxenburg, Austria 17 FALSE info:eu-repo/semantics/book