Equilibrium Joining Strategies for Queues in Two-Phase Random Environment
Abstract
We study equilibrium joining strategies in an M/M/1-type queueing system with strategic customers operating in a two-phase random environment described as a continuous-time Markov process. Strategic customers, upon arrival, choose whether to join or to balk based on available information and anticipated utility, considering the trade-off between reward from service and waiting cost. Four observation scenarios are analysed: fully observable (both queue length and environment phase are disclosed to a customer upon arrival), queue-only observable, environment-only observable, and fully unobservable. In each case, equilibrium joining strategies are analysed. In the environment-only observable and fully unobservable cases, explicit solutions and equilibrium conditions are derived under rapid oscillations and under very slow transitions between environment phases.
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BibTeX
@misc{avrachenkov2026equilibrium,
title = {{Equilibrium Joining Strategies for Queues in Two-Phase Random Environment}},
author = {Konstantin Avrachenkov and Uri Yechiali},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32345},
eprint = {2609.32345},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32345},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Equilibrium Joining Strategies for Queues in Two-Phase Random Environment
AU - Konstantin Avrachenkov
AU - Uri Yechiali
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32345
UR - https://arxiv.org/abs/2609.32345
AB - We study equilibrium joining strategies in an M/M/1-type queueing system with strategic customers operating in a two-phase random environment described as a continuous-time Markov process. Strategic customers, upon arrival, choose whether to join or to balk based on available information and anticipated utility, considering the trade-off between reward from service and waiting cost. Four observation scenarios are analysed: fully observable (both queue length and environment phase are disclosed to a customer upon arrival), queue-only observable, environment-only observable, and fully unobservable. In each case, equilibrium joining strategies are analysed. In the environment-only observable and fully unobservable cases, explicit solutions and equilibrium conditions are derived under rapid oscillations and under very slow transitions between environment phases.
ER -