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<p>We study an M/M/1 queueing system with two stages and impatient customers. When affected by the external environment, customers in different stages have different levels of impatience. In stage 1, reneging is forbidden, while in stage 2, customers renege at an exponential rate. We mainly study the impact of the waiting space in stage 2 on customers’ decisions, system profit and social welfare. It is shown that the customers’ balking threshold is independent of the renege rate. Moreover, we find that there exist unique optimal values of the waiting space in stage 2 that maximize the system profit or the social welfare. As traffic intensity increases, we discuss the variation in the system profit and social welfare, as well as the variation in the optimal waiting space in stage 2. In particular, when the traffic intensity is moderate and the capacity of stage 1 is small, our findings indicate that setting an appropriate value of the waiting space in stage 2 can effectively improve system profit and social welfare.</p>

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Equilibrium Behavior in a Two-Stage Reneging Queue with Impatient Customers

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Ying-Ying Pan,
  • Jing-Chuan Zhang,
  • Zai-Ming Liu

摘要

We study an M/M/1 queueing system with two stages and impatient customers. When affected by the external environment, customers in different stages have different levels of impatience. In stage 1, reneging is forbidden, while in stage 2, customers renege at an exponential rate. We mainly study the impact of the waiting space in stage 2 on customers’ decisions, system profit and social welfare. It is shown that the customers’ balking threshold is independent of the renege rate. Moreover, we find that there exist unique optimal values of the waiting space in stage 2 that maximize the system profit or the social welfare. As traffic intensity increases, we discuss the variation in the system profit and social welfare, as well as the variation in the optimal waiting space in stage 2. In particular, when the traffic intensity is moderate and the capacity of stage 1 is small, our findings indicate that setting an appropriate value of the waiting space in stage 2 can effectively improve system profit and social welfare.