M/G/1M/G/1 queue with deterministic reneging times

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/1M/G/1 queue with reneging using level crossing analysis. An analytical solution is given for the M/H2/1M/H2/1 queue with deterministic reneging times and a numerical approach is presented for the more general M/G/1M/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%.