Asymptotic Product-Form Steady State for Generalized Jackson Networks in Multiscale Heavy Traffic

Product-Form Steady-State Approximation of Generalized Jackson Networks In “Asymptotic Product-Form Steady State for Generalized Jackson Networks in Multiscale Heavy Traffic,” Dai, Glynn, and Xu revisit a long-standing question in queueing network theory. For open Jackson networks in which interarrival and service distributions are exponential, steady-state queue lengths are independent and admit a product-form distribution, making performance analysis tractable and scalable. For generalized Jackson networks with general primitive distributions, the product-form structure no longer holds. The authors show that under a multiscale heavy traffic condition—where different stations operate at widely separated levels of congestion—the stationary distribution of suitably scaled queue lengths admits an asymptotic product-form limit. In this limit, each component is exponentially distributed, with a rate that depends only on the first two moments of the primitive distributions. This result, along with its recent generalizations, creates the potential for a scalable performance analysis tool for generalized Jackson networks and beyond.