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. 4, pp. 395-402, July 1981, doi:10.1109/TSE.1981.234542