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A Symmetrical Exponential Open Queue Network with Blocking and Feedback

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1 Author(s)
Perros, H.G. ; Department of Quantitative Methods, College of Business Administration, University of Illinois at Chicago Circle

The exponential open queue network model studied here consists of n symmetrical queues in parallel served by independent first-level servers in tandem with a second-level server. Blocking of the flow of units through a first-level server occurs each time the server completes a service. The server remains blocked until its blocking unit completes its service at the second-level server. An approximate expression of the probability distribution of the number of blocked first-level servers conditioned upon a service completion of a first-level server is obtained. This expression compares well with simulation data. Based on this distribution, an approximate expression of the queue-length probability distribution is derived assuming a processor-sharing type of service. The exact condition for stability of the queue network is also derived. Some potential applications are discussed, and a quantitative evaluation of the model is given through a case study.

Published in:

Software Engineering, IEEE Transactions on  (Volume:SE-7 ,  Issue: 4 )

Date of Publication:

July 1981

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