Research Communication | Open Access
Volume 2021 | Communication ID 155
Volume 2021 | Communication ID 155
| The Diffusion approximation of the multiclass processor sharing queue |
Mohamed Ghazali, Abdelghani Ben Tahar
Received |
Accepted |
Published |
January 30, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: We consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or re-enter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. The goal is to prove a diffusion approximation theorem for the queue length process. We use a measure valued process that tracks the residual service times, and show that under heavy traffic assumptions, the diffusion scaled measure valued ...