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- Title
Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection.
- Authors
Zychlinski, Noa; Mandelbaum, Avishai; Momčilović, Petar
- 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 Gt/M/N/(N+H)<inline-graphic></inline-graphic> 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.
- Subjects
TIME-varying systems; QUEUING theory; STOCHASTIC systems; LIMITS (Mathematics); MATHEMATICAL models
- Publication
Queueing Systems, 2018, Vol 89, Issue 1/2, p15
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-018-9578-x