UC San Diego

In this thesis, we consider a multi-server, multiclass queue with reneging operating under the random order of service discipline. Interarrival times, service times, and patience times are assumed to be generally distributed. Under mild conditions, we establish a fluid limit theorem for a measure-valued process that keeps track of the remaining patience time for each job in the queue. We prove uniqueness for fluid model solutions in all but one case and study the asymptotic behavior of fluid model solutions as time goes to infinity.