Approximation to the Transient Solution of theM/Ek/1 Queue
J. D. Griffiths, G. M. Leonenko, J. E. Williams
INFORMS Journal on Computing · 2008 · Volume 20 · Issue 4
Abstract
This paper considers the Erlang queueing system M/E k /1, where customers arrive at random at mean rate λ and the service times have an Erlang distribution with parameter k and mean service rate μ. It is difficult to obtain a transient solution in explicit form to the queue equations because of their complex structure. We propose a simple method of computing W q ( t )—the mean waiting time of a customer arriving in the queue at time t , based on an exponential function approximation.
Keywords
queues, approximations, numerical methods
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