Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
The tightness in the ergodic analysis of regenerative queueing processes
Queueing Systems: Theory and Applications
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We consider an open Jackson type queueing network N with input epochs sequence I={Tn(0), n≥0}, T0(0)=0, assume another input $\tilde{I}$={$\widetilde{T}$n(0)} and denote δk=|$\widetilde{T}$k(0)−Tk(0)|, Δ0=0, Δn=max1≤k≤nδk, n≥1. Let {Tn} and {$\widetilde{T}$n} be the output points in network N and in modified network, $\widetilde{\mathcal{N}} $ with input $\tilde{I}$, accordingly. We study the long-run stability of the network output, establishing two-sided bounds for output perturbation via input perturbation. In particular, we obtain conditions that imply maxk≤n|Tk−$\widetilde{T}$k|=o(n1/r) with probability 1 as n→∞ for some r0. This result is also extended to continuous time. We consider successively separate station (service node), tandem and feedforward networks. Then we extend stability analysis to general (feedback) networks and show that in our setting these networks can be reduced to feedforward ones. Similar stability results are also obtained in terms of the number of departures. Application to a tandem network with the overloaded stations is considered.