A Retrial Queueing System with Preemptive Priority and Randomized Push-Out Mechanism

摘要

A single-server finite-buffer retrial system with a Poisson stream of arrivals and an exponential service time distribution is analyzed. If an arriving customer finds the buffer filled up, this customer joins a special retrial waiting group (orbit) in order to seek service again in an exponentially distributed period of time. The customers seeking service for the first time have the preemptive priority over retrial ones, thus, one can think of the original system as of the priority one with retrial customers being low-priority. We also introduce a randomized push-out buffer management mechanism, which makes it possible to control the loss probability of the high-priority and low-priority customers efficiently. It is shown that such queueing model can be reduced to a similar one but without retrial. Using the generating function technique, main probabilistic characteristics (e.g., loss probabilities) for both types of the customers are obtained. The dependency of the loss probabilities on the model parameters, i.e., the push-out and retrial probabilities, is investigated. Regions of the load parameters are found such that the system is locked for the low-priority customers, or such that there is a linear dependence of the loss probabilities on the push-out probability.