An Approximation Method for Open Restricted Queueing Networks

Abstract

This paper presents an approximation method for analyzing open restricted queueing networks with exponential service time and Poisson arrivals. Analysis is made by node-by-node decomposition through the introduction of a pseudo-arrival rate and an effective service rate. The method is applied to example networks and evaluated by comparing the results obtained thereby with those by simulations or exact calculations. We find that this method provides a fairly good approximation procedure for obtaining system performance measures such as blocking probabilities, output rates, etc., in open restricted queueing networks.

Modeling Patient Flows Using a Queuing Network with Blocking

“…Hillier and Boling [9] is probably the first publication in this area. Since then, the method was further researched and extended by many publications [1,2,21,29]. Our study fundamentally applies the decomposition algorithm introduced by Takahashi et al [29], which dealt with blocking in an open queuing network system with feed-forward flows and finite buffers between stations.…”

“…Our work, however, extends their model by modifying their single-server model to a multiple-server model. To author's knowledge, the direct application of Takahashi et al [29] in the context of multiple servers is only found in Korporal et al [15], which analyzed the congestion level in a penitentiary system in the Netherlands.…”

“…The derivations of all equations shown in the first subsection can be found in standard queuing texts such as Gross and Harris [7]. The present extension to blocking is based largely on the work of Takahashi et al [29]. 2 There are few publications that analyze blocking with feedback flows.…”

“…Thus the Jackson approach needs to be modified to capture such interactions between stations. This can be accomplished by introducing the concept of "effective service time" [29]. To be more specific, suppose there are only two stations, i and i + 1, linked in tandem.…”

“…Accordingly, our network system is solved individually and independently from the last station and moving backwards. The method is generally known as the single node decomposition approximation [29].…”