Fluid Limit of a Heavily Loaded EDF Queue with Impatient Customers
2008, v.14, Issue 1, 131-158
In this paper, we present the fluid limit of a heavily loaded Earliest Deadline First queue with impatient customers, represented by a measure-valued process keeping track of the time-credits of the customers. This fluid limit is the deterministic solution of an integrated transport equation in the space of tempered distribution. We then use this fluid limit to derive fluid approximations of the processes counting respectively the number of lost customers and the size of the queue.
Keywords: fluid limit,measure-valued Markov process,queueing theory