Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers
建立票号队列的马尔可夫链模型，分析其与物理队列的性能差距，并提出通过提供预期等待时间来提升服务水平的改进方案。
Queueing systems managed by ticket technology are widely used in service industries as well as government offices. Upon arriving at a ticket queue, each customer is issued a numbered ticket. The number currently being served is displayed. An arriving customer balks if the difference between his ticket number and the displayed number exceeds his patience level. We propose a Markov chain model of a ticket queue and develop effective evaluation tools. These tools can help management quantify the service level and identify the performance gap between the ticket queue and the conventional physical queue, in which a waiting line is formed. We gain insights about the ways customer service is affected by information loss in the ticket queue. In particular, we show that ticket and physical queues have significantly different balking probabilities when customer patience is low and the system traffic is heavy. We also propose an improvement to the ticket queue that provides each customer with his expected waiting time conditioned on his observed number difference, which is shown to raise the performance of the ticket queue to that of the physical queue.