K competing queues with customer abandonment: optimality of a generalised $$c \mu $$ c μ -rule by the Smoothed Rate Truncation method

S. Bhulai (), H. Blok () and F. M. Spieksma ()
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S. Bhulai: Vrije Universiteit Amsterdam
H. Blok: Eindhoven University of Technology
F. M. Spieksma: Universiteit Leiden

Annals of Operations Research, 2022, vol. 317, issue 2, No 4, 387-416

Abstract: Abstract We consider a K-competing queues system with the additional feature of customer abandonment. Without abandonment, it is optimal to allocate the server to a queue according to the $$c \mu $$ c μ -rule. To derive a similar rule for the system with abandonment, we model the system as a continuous-time Markov decision process. Due to impatience, the Markov decision process has unbounded jump rates as a function of the state. Hence it is not uniformisable, and so far there has been no systematic direct way to analyse this. The Smoothed Rate Truncation principle is a technique designed to make an unbounded rate process uniformisable, while preserving the properties of interest. Together with theory securing continuity in the limit, this provides a framework to analyse unbounded rate Markov decision processes. With this approach, we have been able to find close-fitting conditions guaranteeing optimality of a strict priority rule.

Keywords: Competing queues; Abandonments; Unbounded transition rates; Smoothed Rate Truncation; Markov decision processes; Generalised $$c \mu $$ c μ -rule; Uniformisation; 90C40; 60K25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-019-03131-3

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