Throughput of the Queue With Probabilistic Rejections

The queueing system with probabilistic job rejections based on the system occupancy has applications in engineering and logistics. It is also a natural extension of the most basic and commonly used FIFO queue with tail drop. In this paper, we analyze the throughput of such a system - a fundamental characteristic from a practical point of view. Specifically, we derive a formula for the number of jobs that the system processes in a time interval of arbitrary length (transient analysis), as well as a formula for the stationary throughput, i.e., the overall percentage of jobs passing successfully through the system. What is important, a general interarrival distribution is used in derivations, which enables modeling of a great variety of arrival streams. Theoretical results are accompanied by numeric calculations, in which the time-dependent and stationary throughput is calculated for different rejection probabilities, system loads, interarrival distributions, and initial system states.