IPA for spillover volume in a fluid queue with retransmissions

This paper considers the application of IPA to the average buffer overflow (spillover) in a fluid queue as a function of the buffer size. The queue acts as a leaky bucket where access inflow fluid is discharged when the buffer is full. Associated with each fluid "molecule" there is a timer, so that discharged fluid becomes part of the inflow process at a later time. The paper derives the IPA derivative in a form that is nonparametric (model free) and easily computable from the sample path. Prior works concerning finite-buffer queues have treated spillover fluid as lost, and this paper is the first (in the context of IPA for fluid queues) to consider an explicit retransmission model. It explores a basic principle that will motivate future investigations of realistic networks.