In recent days, queuing systems with impatient customers have gain considerable interest. In this talk we consider queuing systems in which each arriving customer has a deadline and the customer leaves the system if he/she does not reach the server before his/her deadline elapses. Earliest-Deadline-First (EDF) policy has proven optimal in certain sense for these systems. We start with a single server queuing system working under EDF scheduling policy and establish the LLN limits for the queue measures and reneged customers. We show that the LLN limits of queue lengths are related to a Skorohod reflection problem in a time-varying domain. Extension of these results to other queuing systems will also be discussed.
This talk is based on a joint work with Rami Atar and Haya Kaspi.