We derived the formulas to calculate the exact value of the optimal threshold, and we analyzed some extreme cases for the explicit expressions to connect the optimal threshold values to the queuing parameters.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Within the framework of this paper, we consider an M/M/2 queuing model where a threshold -on the queue size- type control is assumed for using (or not using) the slower server.
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Temel Bulgular & Veri:The optimization policy to control is based upon a mini-max criterion, which minimizes the maximum "first passage time to an idle period" for the servers.
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Sonuç & Katkı:We derived the formulas to calculate the exact value of the optimal threshold, and we analyzed some extreme cases for the explicit expressions to connect the optimal threshold values to the queuing parameters.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
Within the framework of this paper, we consider an M/M/2 queuing model where a threshold -on the queue size- type control is assumed for using (or not using) the slower server. The optimization policy to control is based upon a mini-max criterion, which minimizes the maximum "first passage time to an idle period" for the servers. We derived the formulas to calculate the exact value of the optimal threshold, and we analyzed some extreme cases for the explicit expressions to connect the optimal threshold values to the queuing parameters.
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Bu Makaleye Atıf Yap
ŞİŞ, M. K. (2022). A mini-max approach for finding thresholds to control M/M/2 queues. Istanbul University Journal of Electrical and Electronics Engineering, Cilt: 5 - Sayı: 2, 1353–1362. https://ajindex.com/articles/543846
L. Kleinrock, Queuing Systems, Vol. I: Theory, John Wiley fa Sons,Inc. 1975
L. Kleinrock, Queuing Systems, Vol. II: Theory, John Wiley & Sons,Inc. 1976
M. K. Sis A Dynamic Local Congestion Reducing Strategy Based on a Mini-Max Criterion, Ph.D. Dissertation Thesis, Polytechnic University 1994
P.E. Sarachik, "Congestion Reducing Dynamic Routing Strategies for Multidestination Traffic Networks", IEEE Trans on Commun., Vol. COM-24, No. 4, April 1984
S.Ross, "Applied Probability Models with Optimization Applications", (Chapter 6) Markov Decision Processes, Holden -Day, San Francisco, 1970
W. Lin and P.R, Kumar, "Optimal Control of a Queuing System with Two Heterogeneous Servers", IEEE Trans on Automat. Contr. Vol. AC-29, No. 8, August 1984
Floyd S. and Jacobson V, "Random Early detection Gateways in congestion avoidance", IEEE/ACM Transaction on Networking. Vol. 1, No. 3, 1993