A Uniformization Approach for the Dynamic Control of Queueing Systems with Abandonments

Benjamin Legros (), Oualid Jouini () and Ger Koole ()
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Benjamin Legros: EM Normandie, Laboratoire Métis, 75016 Paris, France
Oualid Jouini: CentraleSupélec, Université Paris-Saclay, Laboratoire Genie Industriel, 92290 Chatenay-Malabry, France
Ger Koole: Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands

Operations Research, 2018, vol. 66, issue 1, 200-209

Abstract: We consider queueing systems with general abandonment. Abandonment times are approximated by a particular Cox distribution with all phase exponential rates being the same. We prove that this distribution arbitrarily closely approximates any nonnegative distribution. By explicitly modeling the waiting time of the first customer in line, we obtain a natural bounded jump Markov process allowing for uniformization. This approach is useful to solve, via dynamic programming, various optimization problems where the objectives and/or constraints involve the distributions of the performance measures, not only their expected values. It is also useful for the performance analysis of queueing systems with general abandonment times.

Keywords: queueing systems; Markov chains; dynamic programming; uniformization; scheduling; optimization; Markov decision process; Cox distribution; general abandonments (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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