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Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection

Noa Zychlinski (), Avishai Mandelbaum () and Petar Momčilović ()
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Noa Zychlinski: Technion – Israel Institute of Technology
Avishai Mandelbaum: Technion – Israel Institute of Technology
Petar Momčilović: University of Florida

Queueing Systems: Theory and Applications, 2018, vol. 89, issue 1, No 3, 15-47

Abstract: Abstract In this paper, we develop time-varying fluid models for tandem networks with blocking. Beyond having their own intrinsic value, these mathematical models are also limits of corresponding many-server stochastic systems. We begin by analyzing a two-station tandem network with a general time-varying arrival rate, a finite waiting room before the first station, and no waiting room between the stations. In this model, customers that are referred from the first station to the second when the latter is saturated (blocked) are forced to wait in the first station while occupying a server there. The finite waiting room before the first station causes customer loss and, therefore, requires reflection analysis. We then specialize our model to a single station (many-server fluid limit of the $$G_t/M/N/(N +H)$$ G t / M / N / ( N + H ) queue), generalize it to k stations in tandem, and allow finite internal waiting rooms. Our models yield operational insights into network performance, specifically on the effects of line length, bottleneck location, waiting room size, and the interaction among these effects.

Keywords: Fluid models; Tandem queueing networks with blocking; Time-varying queues; Reflection; Flow lines with blocking; Functional Strong Law of Large Numbers; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:spr:queues:v:89:y:2018:i:1:d:10.1007_s11134-018-9578-x