Stationary waiting time distribution in G|M|n|r with random renovation policy

Abstract

Recent recommendation RFC 7567 by IETF indicates that the problem of active queue management remains vital for modern communications networks and the development of new active queue management is required. Queueing system with renovation when customers upon service completion pushes-out other customers residing in the queue with a given probability distribution may have potential application as an alternative active queue management. In this paper one presents the analytic method for the computation of the customer’s stationary waiting time distribution in G|M|n|r queue with random renovation under FCFS (and non-preemptive LCFS) scheduling in the terms of Laplace-Stieltjets transform. The method is illustrated by one particular case: stationary waiting time distribution of the customer, which either received service or was pushed-out under FCFS scheduling.