Analysis of Restricted Queueing Networks - A Blocking Approach

In this paper we consider an open restricted queueing network with Poisson arrivals and exponential service times at stations and present an approximation method for analysis, made by node-by-node decomposition employing the concept of effective arrival rate and effective service rate. The steady state characteristics of the network system and of individual stations are obtained. Congestion due to blocking has been a severe problem in several health care studies, but among studies that apply queueing theory, those analyzing the blocking mechanism are still limited. This study applies to a health care system of infertility clinic considered as an open queueing network with blocking caused due to the capacity of the waiting space between stations. The method is illustrated with the help of an example network to study the efficiency of the approximation method. Finally a simulation study is performed to assess the transient behaviour of the network system. The blocking approach presented here for a simple model of a healthcare system can be easily adapted to any general open restricted queueing network.