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<p>Motivated by the challenges inherent in high-frequency appointment scheduling systems, we explore the scaling behavior of customer unpunctuality in arrival patterns and its impact on service dynamics. In particular, we characterize the asymptotic limits of unpunctual arrivals within the appointment system and establish corresponding limiting results for the associated single-server queueing process. Our findings reveal that, while the limiting arrival process is Poisson and the prelimit process is well approximated by a Poisson process, the Poisson approximation can fail dramatically at the queueing level.</p>

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When scheduled arrivals behave like Poisson - until they don’t

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Koen De Turck,
  • Dieter Fiems

摘要

Motivated by the challenges inherent in high-frequency appointment scheduling systems, we explore the scaling behavior of customer unpunctuality in arrival patterns and its impact on service dynamics. In particular, we characterize the asymptotic limits of unpunctual arrivals within the appointment system and establish corresponding limiting results for the associated single-server queueing process. Our findings reveal that, while the limiting arrival process is Poisson and the prelimit process is well approximated by a Poisson process, the Poisson approximation can fail dramatically at the queueing level.