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PreprintCC BY-NC-ND 4.0arXiv

Whittle index approach to multi-server scheduling with convex delay costs and impatient customers

  • Samuli Aalto
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Abstract

We consider the dynamic scheduling problem in a multi-class M/G/N + M queue with convex delay costs and impatient customers that have exponential abandonment times. We apply the Whittle index approach to find a reasonable heuristic solution for this tricky problem. By assuming exponential abandonment times, we are able to make a very straightforward use of the results of the corresponding problem with patient customers presented in Queueing Systems, Vol. 110, Article no. 2, 2026. Our main theoretical achievements are proving that the closed version of the corresponding discrete-time problem is indexable and deriving an explicit expression for the Whittle index. The discrete-time results are utilized to develop the Whittle index policy for the original continuous-time scheduling problem.

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Cite

BibTeXRIS
BibTeX
@misc{aalto2026whittle,
  title = {{Whittle index approach to multi-server scheduling with convex delay costs and impatient customers}},
  author = {Samuli Aalto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19792},
  eprint = {2609.19792},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19792},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Whittle index approach to multi-server scheduling with convex delay costs and impatient customers
AU  - Samuli Aalto
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19792
UR  - https://arxiv.org/abs/2609.19792
AB  - We consider the dynamic scheduling problem in a multi-class M/G/N + M queue with convex delay costs and impatient customers that have exponential abandonment times. We apply the Whittle index approach to find a reasonable heuristic solution for this tricky problem. By assuming exponential abandonment times, we are able to make a very straightforward use of the results of the corresponding problem with patient customers presented in Queueing Systems, Vol. 110, Article no. 2, 2026. Our main theoretical achievements are proving that the closed version of the corresponding discrete-time problem is indexable and deriving an explicit expression for the Whittle index. The discrete-time results are utilized to develop the Whittle index policy for the original continuous-time scheduling problem.
ER  -