Abstract
Motivated by applications in biological systems, we show for certain multiclass queueing networks that time-dependent distributions for the multiclass queue-lengths can have a factorized form which reduces the problem of computing such distributions to a similar problem for related single-class queueing networks. We give an example of the application of this result to an enzymatic processing network.
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This research was supported in part by the National Institute of General Medical Sciences of the National Institutes of Health (GM079333 and GM089976). Research of RJW was supported in part by NSF grant DMS-0906535.
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Mather, W.H., Hasty, J., Tsimring, L.S. et al. Factorized time-dependent distributions for certain multiclass queueing networks and an application to enzymatic processing networks. Queueing Syst 69, 313–328 (2011). https://doi.org/10.1007/s11134-011-9216-3
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DOI: https://doi.org/10.1007/s11134-011-9216-3
Keywords
- Multiclass queueing network
- Homogeneous Kelly-type stations
- State-dependent routing
- Reneging
- Product form
- Stationary distribution
- State-space collapse
- Dimension reduction
- Correlation
- Intracellular networks
- Enzymatic processing
- Ultrasensitivity of signal propagation