Stability of generalized Jackson networks with infinite supply of work

Abstract

A general Jackson network (GJN) with infinite supply of work is considered. By fluid limit model, the author finds that the Markov process describing the dynamics of the GJN with infinite supply of work is positive Harris recurrent if the corresponding fluid model is stable. Furthermore, the author proves that the fluid model is stable if the usual traffic condition holds.

Nonergodic Jackson networks with infinite supply–local stabilization and local equilibrium analysis

“…Early work using this concept of infinite supply are, [LY75] using IVQ attached to an M/G/1 queueing system to utilize idle times. More recent are [Guo08] where generalized Jackson networks are considered and [KNW09] where a push-pull network with infinite supply is investigated. The work of Guo [Guo08] and of Guo, Lefeber, Nazarathy, Weiss, Zhang [GLN13] is on general multi-class queueing networks with IVQs under different scheduling policies for the servers.…”

“…More recent are [Guo08] where generalized Jackson networks are considered and [KNW09] where a push-pull network with infinite supply is investigated. The work of Guo [Guo08] and of Guo, Lefeber, Nazarathy, Weiss, Zhang [GLN13] is on general multi-class queueing networks with IVQs under different scheduling policies for the servers. These policies guide the nodes' decisions how to dedicate their activities to either the regular standard queues or the infinite virtual queues.…”

“…For some early work using this concept of infinite supply see [11], where IVQ attached to an M/G/1 queueing system was used to utilize idle times. For more recent examples see [5] where generalized Jackson networks were considered and [10] where a push-pull network with infinite supply was investigated.…”

“…The work of Guo [5] and Guo et al [6] was on general multiclass queueing networks with IVQs under different scheduling policies for the servers. These policies guide the nodes' decisions on how to dedicate their activities to either the regular standard queues or the infinite virtual queues.…”