Approximate Analysis of a Multi - class Queue with Class - Dependent Window - Flow Control

A single server queue shared by N different classes of jobs is considered. Class i jobs arrive at the queue in a poisson fashion with a class dependent rate. The total number of class i jobs allowed to wait in the queue is wi, the window size of this class. A class i job that arrives to find wi class i jobs in the shared queue is forced to wait in an input queue. There is one input queue for each class. All classes receive the same service at the shared queue, which is exponentially distributed. An approximate decomposition algorithm is developed which permits to study any number of classes utilizing a numerical procedure for a particular two-class queue. Validation tests show that the approximation procedure is fairly accurate. The applicability of the algorithm to networks of queues is also discussed. * Supported in part by a grant from AIRMICS through the Center for Communications and Signal Processing, NC State University, and by the National Science Foundation under grant no: CCR-87-02258