Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11134-007-9028-7
Title: A semidefinite optimization approach to the steady-state analysis of queueing systems
Authors: Bertsimas, D.
Natarajan, K. 
Keywords: Semidefinite optimization
Steady-state distribution
Waiting time
Issue Date: May-2007
Citation: Bertsimas, D., Natarajan, K. (2007-05). A semidefinite optimization approach to the steady-state analysis of queueing systems. Queueing Systems 56 (1) : 27-39. ScholarBank@NUS Repository. https://doi.org/10.1007/s11134-007-9028-7
Abstract: Computing the steady-state distribution in Markov chains for general distributions and general state space is a computationally challenging problem. In this paper, we consider the steady-state stochastic model Wd = g(W, X)where the equality is in distribution. Given partial distributional information on the random variables X, we want to estimate information on the distribution of the steady-state vector W. Such models naturally occur in queueing systems, where the goal is to find bounds on moments of the waiting time under moment information on the service and interarrival times. In this paper, we propose an approach based on semidefinite optimization to find such bounds. We show that the classical Kingman's and Daley's bounds for the expected waiting time in a GI/GI/1 queue are special cases of the proposed approach. We also report computational results in the queueing context that indicate the method is promising. © Springer Science+Business Media, LLC 2007.
Source Title: Queueing Systems
URI: http://scholarbank.nus.edu.sg/handle/10635/102755
ISSN: 02570130
DOI: 10.1007/s11134-007-9028-7
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