A multiserver queueing system with a finite buffer, blocking of a semi-Markovian input flow of customers, and removal of all customers from the system

Abstract

A multiserver queueing system with a finite buffer, phase-type service at each server, and a semi-Markovian input flow of customers is considered. Arrival of customers at the system can be blocked during certain time intervals. The first customer arriving at the system after the arrival is unblocked removes all the customers from the system. A method is developed for calculating the stationary distribution of the number of customers in the system, and mathematical relationships for the mean time of a customer’s residence in the system are obtained.