Issue No. 04 - July (1981 vol. 7)
H.G. Perros , 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.
two-level service, Approximations, blocking, exponential, feedback, open queue networks
H.G. Perros, "A Symmetrical Exponential Open Queue Network with Blocking and Feedback", IEEE Transactions on Software Engineering, vol. 7, no. , pp. 395-402, July 1981, doi:10.1109/TSE.1981.234542