M/G/1 queue with deterministic reneging times

We consider single-server and multi-server queues with deterministic reneging times motivated by the timeout mechanisms used in application servers.. A Volterra integral equation is developed using the level crossing analysis for the M/G/1 queue with reneging. An analytical solution is given for the M/HyperExponential/1 queue with deterministic reneging times and a numerical approach is presented for the M/G/1 queue with deterministic reneging times. We further present an approximation method for the expected waiting time in the M/G/n queue with deterministic reneging times. Approximations are verified via simulation and numerical results reveal that predictions are highly accurate with errors, in general, below 5%.

• Type: Journal
• Year: 2008
• Where: PE
• Authors: Wei Xiong, David L. Jagerman, Tayfur Altiok
• Keywords: Deterministic Reneging Times, Multi-server Queues, Optimization, PE 2008, Volterra Integral Equation