Dynamic Policy for Idling Time Preservation

Benjamin Legros ()
Additional contact information
Benjamin Legros: Métis Lab EM Normandie - EM Normandie - École de Management de Normandie = EM Normandie Business School

Post-Print from HAL

Abstract: Abstract This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back-office tasks. We model the system as a single-agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion-related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast-agent and heavy-traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.

Date: 2023
References: Add references at CitEc
Citations:

Published in Naval Research Logistics, 2023, 70 (1), pp.53-71. ⟨10.1002/nav.22086⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04877210

DOI: 10.1002/nav.22086

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().