Queues with Message Discard at Non-zero Cost

摘要

Some systems discard messages that wait in the queue longer than a certain threshold. Identifying such messages and discarding them takes the processor a fixed amount of time. That time is considerably smaller than an average service time, but greater than zero, therefore the models for queuing systems with reneging do not apply. This paper provides a model for such queues. It describes a method of deriving exact formulas for the distribution of waiting times, and proposes simple, yet accurate approximations. The paper then analyzes the model and discusses the properties of such systems.