GENERALIZED QUEUING DISCIPLINE FOR PRODUCT FORM NETWORK SOLUTIONS

Certain queuemg discaphnes, such as processor sharing, the preemptive last-come-first-served discipline, and the infinite server queue, are known to result in network eqmltbnum state probabihties that have a convenient product form A generalization of the above dlsciphnes is introduced The general class is presented in the form of a parametenzed disciphne, called the last-batch-processor-sharing (LBPS) discipline The eqmhbrlum state probabilities for disciplines of the LBPS class are shown, and, by use of the concept of local balance, at is shown that arbitrary networks of LBPS queues have product form eqmlibrium state probabilities It as also shown that within the class of symmetric dlsciphnes, the LBPS form is necessary ff the product form solution is to be obtained for general service time dtstrlbutmns A dasctphne is symmetric ff the processor assignments to the customers in the queue depend on total queue occupancy and queue position (relatwe arrival time) only Generahzations of the LBPS rule beyond the symmetric dlsciphnes are discussed A multiple customer-class form of the LBPS disclphne is also demonstrated, and it is shown to have the local balance property. © 1979, ACM. All rights reserved.