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<p>In stochastic service systems, growing customer demands and high service volatility combine to challenge the efficient operation of service disciplines in multiple dimensions. Priority mechanisms offer an effective approach for managing demand heterogeneity and congestion, thereby generating revenue and improving service quality. However, both preemptive priority and non-preemptive priority schemes exhibit inherent limitations. To address the deficiencies arising from implementing either scheme independently, this study develops a switching mechanism between these priority types and proposes a fully observable mixed priority model. In such a model, the priority customer (type-I customer) has non-preemptive priority over the ordinary customer (type-II customer) when the priority queue length is not greater than a fixed value <i>L</i>. In turn, the priority mechanism will be transferred from non-preemptive to preemptive once the length of the priority queue exceeds <i>L</i>. The expected delays for both priority and ordinary customers are derived in closed form. The expected wait time of a priority customer is revealed to not necessarily increase with the length of the priority queue under the <i>L</i>-policy, as the future-arriving priority customers may generate a positive external effect. In addition, considering that priority and ordinary customers are two stakeholders with different “market power,” a noncooperative game is established by capturing the noncooperative interactions among them. The equilibrium strategic behaviors of both kinds of customers are investigated, which are shown to be state-dependent. Finally, the sensitivity of customers’ strategic behavior on key system parameters is explored by implementing numerical experiments.</p>

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Performance evaluation and equilibrium strategies for a mixed priority queueing system

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Sheng Zhu,
  • Xuege Han,
  • Jinting Wang,
  • Zhongbin Wang

摘要

In stochastic service systems, growing customer demands and high service volatility combine to challenge the efficient operation of service disciplines in multiple dimensions. Priority mechanisms offer an effective approach for managing demand heterogeneity and congestion, thereby generating revenue and improving service quality. However, both preemptive priority and non-preemptive priority schemes exhibit inherent limitations. To address the deficiencies arising from implementing either scheme independently, this study develops a switching mechanism between these priority types and proposes a fully observable mixed priority model. In such a model, the priority customer (type-I customer) has non-preemptive priority over the ordinary customer (type-II customer) when the priority queue length is not greater than a fixed value L. In turn, the priority mechanism will be transferred from non-preemptive to preemptive once the length of the priority queue exceeds L. The expected delays for both priority and ordinary customers are derived in closed form. The expected wait time of a priority customer is revealed to not necessarily increase with the length of the priority queue under the L-policy, as the future-arriving priority customers may generate a positive external effect. In addition, considering that priority and ordinary customers are two stakeholders with different “market power,” a noncooperative game is established by capturing the noncooperative interactions among them. The equilibrium strategic behaviors of both kinds of customers are investigated, which are shown to be state-dependent. Finally, the sensitivity of customers’ strategic behavior on key system parameters is explored by implementing numerical experiments.