The impact of balking queues on n-redundancy in computer systems

We study the steady state queue length probabilities for a queueing system for file downloading in which files are stored with redundancy. In particular, we address how the ability of a download file request to leave the system after seeing the queue length but before joining the queue. While it has been thoroughly proven that redundancy improves the performance of queueing systems, previous work has failed to address the inclusion of request loss affects a queueing system with redundancy. We develop a model for a queueing system with redundancy and request loss based on the Supermarket Model. Using that model, we solve for steady state queue length distribution and provide numerical results comparing systems with and without request loss. These numerical simulations show that in a queueing system with redundancy and request loss, the probability of having a particular number of requests in the system decreases as the number increases.Arts and Sciences, Irving K. Barber School of (Okanagan)Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)Graduat