Analysis of Multi-Server Single Queue System with Multiple Phases

This paper extends and improves on the performance measures of the Single-Server Single Queue System with Multiple Phases. The extension results in a new Queuing System of MultiServer with Multiple Phases under the conditions of First Come First Served, infinite population source, Poisson arrivals and Erlang service time. Queuing properties such as expected total service time, its variance and some performance measures like the expected number of phases in the system, expected number of phases in the queue, expected number of customers in the queue, expected waiting times in the queue and in the system as well as the number of customers in the system have been derived in this work for this Multi-Server with Multiple Phases (M/E-k/s: (infinity/FCFS)) queuing model with k identified stages in series. These performance measures so obtained were compared with those of the already existing Single-Server with Multiple Phases (M/E-k/1: (infinity/FCFS) model. Numerical illustration indicates the efficiency and effectiveness of the latter over the former.