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doi:10.1016/j.peva.2007.07.003 
Copyright © 2007 Elsevier Ltd All rights reserved.
M/G/1 queue with deterministic reneging times
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Received 27 June 2006;
revised 18 July 2007;
accepted 23 July 2007.
Available online 28 July 2007.
Abstract
We consider a single-server queue with a deterministic reneging time motivated by the timeout mechanism used in application servers in distributed computing environments. We have employed a Volterra integral equation to study the M/G/1 queue with reneging using level crossing analysis. An analytical solution is given for the M/H2/1 queue with deterministic reneging times and a numerical approach is presented for the more general M/G/1 queue. The numerical approach is verified via simulation and the results reveal that predictions are highly accurate with errors that are in general below 0.5%.
Keywords: M/G/1 queue; Reneging; Level crossing; Volterra integral equation; Timeout mechanism
