Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
Stability of two families of queueing networks and a discussion of fluid limits
Queueing Systems: Theory and Applications
A Two-Node Jackson Network With Infinite Supply Of Work
Probability in the Engineering and Informational Sciences
Maximum Pressure Policies in Stochastic Processing Networks
Operations Research
Analysis of a simple Markovian re-entrant line with infinite supply of work under the LBFS policy
Queueing Systems: Theory and Applications
The asymptotic variance rate of the output process of finite capacity birth-death queues
Queueing Systems: Theory and Applications
Positive harris recurrence and diffusion scale analysis of a push pull queueing network
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Operations Research Letters
The variance of departure processes: puzzling behavior and open problems
Queueing Systems: Theory and Applications
Dynamic server allocation for unstable queueing networks with flexible servers
Queueing Systems: Theory and Applications
Stability of multi-class queueing networks with infinite virtual queues
Queueing Systems: Theory and Applications
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We consider a push pull queueing network with two servers and two types of job which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the Kumar-Seidman Rybko-Stolyar (KSRS) multi-class queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of job are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a re-entrant line with an infinite supply of work.