A Note on Product-Form Solution for Queuing Networks with Poisson Arrivals and General Service-Time Distributions with Finite Means

Abstract

The steady-state joint probability distribution of queue lengths is obtained for queuing networks with Poisson arrivals m which some of the service-tune dlstnbunon funcuons are general (e g, not even differenuable). In particular, an analytical model for queuing networks which is more general than those considered to date is produced by using the concept of generalized function Previous results on the relationships between the properties of queuing discipline, product form, and local balance can be shown to hold m this more general setting. © 1982, ACM. All rights reserved.