Abstract
We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.
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References
Arazi A, Ben-Jacob E, Yechiali U (2004) Bridging genetic networks and queueing theory. Physica A 332:585–616
Artalejo JR (2000) G-networks: a versatile approach for work removal in queueing networks. Eur J Oper Res 126(2):233–249
Chase C, Serrano J, Ramadge PJ (1993) Periodicity and chaos from switched flow systems: contrasting examples of discretely controlled continuous systems. IEEE T Automat Contr 38(1):70–83
Gelenbe E (1991) Product-form queueing networks with negative and positive customers. J Appl Prob 28:656–663
Thompson JMT, Stewart HB (1986) Nonlinear dynamics and chaos: geometrical methods for engineers and scientists. Wiley, New York
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Arazi, A., Ben-Jacob, E. & Yechiali, U. Controlling an oscillating Jackson-type network having state-dependent service rates. Math Meth Oper Res 62, 453–466 (2005). https://doi.org/10.1007/s00186-005-0041-5
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DOI: https://doi.org/10.1007/s00186-005-0041-5