Abstract
We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between the servers positive recurrent. We analyze two specific policies in detail, obtaining steady state distributions. We perform extensive calculations of expected queue lengths under these policies. We compare this network with the Kumar–Seidman–Rybko–Stolyar network, in which there are two random streams of arriving jobs rather than infinite supply of work.
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Research supported in part by Israel Science Foundation Grants 249/02 and 454/05 and by European Network of Excellence Euro-NGI.
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Kopzon, A., Nazarathy, Y. & Weiss, G. A Push–Pull Network with Infinite Supply of Work. Queueing Syst 62, 75–111 (2009). https://doi.org/10.1007/s11134-009-9121-1
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DOI: https://doi.org/10.1007/s11134-009-9121-1
Keywords
- Queueing
- Manufacturing
- Markovian multiclass queueing networks
- Infinite supply of work
- Infinite virtual queues
- Threshold policies
- Maximum pressure policies
- Kumar–Seidman–Rybko–Stolyar network