A simple Queuing System in the Case Where a Server Joins the System when the Queue Length Attains a Certain Length

Abstract

A simple queuing system with a queue-dependent server is considered. Assuming a finite waiting space in front of servers, we derive the system size distribution (the state probability) and the mean number of customers in the system for two servers. Furthermore, a method of diffusion approximation is applied for solving the system with general independent inter-arrival time and general service time distributions. Numerical examples for the mean number of customers in the system are given to compare an exact value with an approximate one.