Scheduling of multi-class multi-server queueing systems with abandonments

Ayesta, Urtzi and Jacko, Peter and Novak, Vladimir (2017) Scheduling of multi-class multi-server queueing systems with abandonments. Journal of Scheduling, 20 (2). pp. 129-145. ISSN 1094-6136

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Abstract

Many real-world situations involve queueing systems in which customers may abandon if service does not start sufficiently quickly. We study a comprehensive model of multi-class queue scheduling accounting for customer abandonment, with the objective of minimizing the total discounted or time-average sum of linear waiting costs, completion rewards, and abandonment penalties of customers in the system. We assume the service times and abandoning times are exponentially distributed. We solve analytically the case in which there is one server and there are one or two customers in the system and obtain an optimal policy. For the general case, we use the framework of restless bandits to analytically design a novel simple index rule with a natural interpretation. We show that the proposed rule achieves near-optimal or asymptotically optimal performance both in single- and multi-server cases, both in overload and underload regimes, and both in idling and non-idling systems.

Item Type: Journal Article
Journal or Publication Title: Journal of Scheduling
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10951-015-0456-7
Uncontrolled Keywords: /dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
Departments: Lancaster University Management School > Management Science
ID Code: 76960
Deposited By: ep_importer_pure
Deposited On: 03 Dec 2015 08:52
Refereed?: Yes
Published?: Published
Last Modified: 17 Feb 2020 02:43
URI: https://eprints.lancs.ac.uk/id/eprint/76960

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