Analyzing a Tandem Fluid Queueing Model with Stochastic Capacity and Spillback
Abstract
The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time properties of this model. Our analysis focuses on the system of two fluid queueing links in series. The upstream link has a constant capacity (saturation rate) and an infinite buffer size. The downstream link has a stochastic capacity and a finite buffer size. Queue spillback occurs when the the downstream link is full. We derive a necessary condition and a sufficient condition for the total queue length to be bounded on average. The necessary (resp. sufficient) condition leads to an upper (resp. lower) bound for the throughput of the two-link system. Using our results, we analyze the sensitivity of throughput of the two-link system with respect to the frequency and intensity of capacity disruptions, and to the buffer size. In addition, we discuss how our analysis can be extended to feedback-controlled systems and to networks consisting of merges and splits.
Cite
@article{arxiv.1905.02100,
title = {Analyzing a Tandem Fluid Queueing Model with Stochastic Capacity and Spillback},
author = {Li Jin and Saurabh Amin},
journal= {arXiv preprint arXiv:1905.02100},
year = {2019}
}