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<p>When a large crowd forms in a service system, customers’ service experience and service providers’ operating expenses will be greatly degraded by the negative effect of mass gathering. We examine a queueing system where customers exhibit gathering aversion, and consider customers’ overlapping number and time during their sojourn time as metrics to characterize the negative effects of gathering. We develop a mathematical framework to evaluate these two metrics, allowing us to characterize equilibrium balking thresholds and their bounds. Closed-form expressions for key system performance metrics such as average overlapping number and time in equilibrium are derived to assess the overall gathering levels of customers in the system, and their tradeoffs with other system performance metrics like throughput and social welfare are analyzed. Our findings reveal that increasing staffing levels does not always reduce gathering, as lower traffic can attract more customers to enter, leading to even increased gathering. As a result, increasing the staffing level does not necessarily enhance social welfare as customer gathering increases. We also analyze the strategy of pooling queues, finding that although the pooled system has a united service space, its advantage over the dedicated system is significant in reducing customers’ gathering when their arrival rate is large, due to the pooled space that discourages gathering-averse customers from entering. Furthermore, we evaluate the impact of shortening opening hours, showing that it may not discourage customers from entering. Instead, it can exacerbate congestion when the arrival rate is low due to the condensed arrival process. Lastly, we explore how gathering sensitivity influences system performance, finding that greater aversion to gathering will always degrade throughput. However, customers’ social welfare may increase as fewer of them choose to enter the system, thereby reducing the wait times and gathering levels. We also find that imposing an additional admission fee can help reduce congestion in the system and improve overall social welfare. These insights provide practical guidance for designing queueing systems that account for customer behavior and operational efficiency.</p>

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Managing queueing systems with gathering-averse customers: staffing, pooling, and opening hours

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Jin Xu,
  • Dening Huang,
  • Young Myoung Ko,
  • Jamol Pender

摘要

When a large crowd forms in a service system, customers’ service experience and service providers’ operating expenses will be greatly degraded by the negative effect of mass gathering. We examine a queueing system where customers exhibit gathering aversion, and consider customers’ overlapping number and time during their sojourn time as metrics to characterize the negative effects of gathering. We develop a mathematical framework to evaluate these two metrics, allowing us to characterize equilibrium balking thresholds and their bounds. Closed-form expressions for key system performance metrics such as average overlapping number and time in equilibrium are derived to assess the overall gathering levels of customers in the system, and their tradeoffs with other system performance metrics like throughput and social welfare are analyzed. Our findings reveal that increasing staffing levels does not always reduce gathering, as lower traffic can attract more customers to enter, leading to even increased gathering. As a result, increasing the staffing level does not necessarily enhance social welfare as customer gathering increases. We also analyze the strategy of pooling queues, finding that although the pooled system has a united service space, its advantage over the dedicated system is significant in reducing customers’ gathering when their arrival rate is large, due to the pooled space that discourages gathering-averse customers from entering. Furthermore, we evaluate the impact of shortening opening hours, showing that it may not discourage customers from entering. Instead, it can exacerbate congestion when the arrival rate is low due to the condensed arrival process. Lastly, we explore how gathering sensitivity influences system performance, finding that greater aversion to gathering will always degrade throughput. However, customers’ social welfare may increase as fewer of them choose to enter the system, thereby reducing the wait times and gathering levels. We also find that imposing an additional admission fee can help reduce congestion in the system and improve overall social welfare. These insights provide practical guidance for designing queueing systems that account for customer behavior and operational efficiency.