Article2013

Algorithms for Time-Varying Networks of Many-Server Fluid Queues

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Healthcare Operations and Scheduling Optimization

Abstract

Motivated by large-scale service systems with network structure, we introduced in a previous paper a time-varying open network of many-server fluid queues with customer abandonment from each queue and time-varying proportional routing among the queues, and showed how performance functions can be determined. The deterministic fluid model serves as an approximation for the corresponding non-Markovian stochastic network of many-server queues with Markovian routing, experiencing periods of overloading at the queues. In this paper we develop a new algorithm for the previous model and generalize the model to include non-exponential service-time distributions. In this paper we report results of implementing the algorithms and studying their computational complexity. We also conduct simulation experiments to confirm that the algorithms are effective in computing the performance functions and that these performance functions provide useful approximations for the corresponding stochastic models.

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References

2005Statistical Analysis of a Telephone Call Center 1985Applications of Queueing Theory 2007Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System 1982Applications of Queueing Theory 2006Fluid Models for Multiserver Queues with Abandonments 1998Strong approximations for Markovian service networks 1993Networks of infinite-server queues with nonstationary Poisson input 1983Applications of Queueing Theory.

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2017Approximations for the Queue Length Distributions of Time-Varying Many-Server Queues 2017Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing 2018Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment 2019Optimal Control of a Time-Varying Double-Ended Production Queueing Model 2017Queueing network models for analysis of nonstationary manufacturing systems 2022Energy harvesting cognitive radio networks with strategic users: A two-class queueing model with retrials

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