1. To Queue or Not to Queue? Physical queues can be really stressful and exhausting…

2. What Is a Ticket Queue? Examples: banks, hospitals, motor vehicles registration, tax offices, visa offices, post offices, theme parks…

3. Characteristics of Ticket Queues For customers: –Reduce stress level in a calm environment –Less anxiety on defending my position in the line –More productive use of waiting time –Better security, privacy For service provider: –Improve customer satisfaction, more loyal customers –Attract more business, increase market share –Reduce staff stress level and increase their efficiency –Collect business intelligence –Making dynamic decisions on staffing levels, customer routing However, –customers natural tendency is to assume all positions are real customers, ignore the possibility that some have balked –Balking customers create empty queueing positions – underutilization of service capacity

4. Research Questions Extensive research has been done on performance evaluation and management of queues with impatient customers that have no information or complete information of N (actual number of customers) To the best of our knowledge, no research has been done on ticket queues that has partial information of N How to evaluate performance of ticket queue? –What are the distributions of D (ticket difference) and N ? –What is the balking rate and system utilization? –What is customers expected waiting time given his ticket position? How to improve service performance of a ticket queue (reduce the balking rate)?

5. A Markov Chain Model Step 1. Aggregate all states with |x| = L and n L K into a super state S L, L = 1,2,…,K. MC with super states has a finite state space and can be modeled as a quasi birth- death (QBD) process and admits matrix product form solution. Step 2. Back to the original MC obtain steady state probabilities of states |x| = L and n l K recursively, using the known probabilities derived in Step 1.

6. State Reduction and Approximation However, because of intermixing of joining/balking customers, the state space grows exponentially: K=20, it is nearly 10 million ! State reduction idea: –Separate joining and balking customers into two queues –Only keep track of total number of customers in each queue, joining customers have higher service priority The original and modified systems would have similar stochastic behavior if intermixing of joining and balking customers occurs rarely in ticket queue. such phenomena were observed in our simulations The number of states in the modified system is polynomial K 2 + 1

7. Accuracy of Approximation

8. Comparison of Ticket and Physical Queue The two systems show most significant differences in balking rate when customers are impatient and traffic is heavy. Significant region: Heavy traffic and Impatient customers; impact of info loss most severe Moderate region: moderate traffic and relatively patient customers; impact of info loss moderate; Insignificant region: light traffic and patient customers, impact of info loss is minimum

9. Improvement to Ticket Queue Improvement : In addition to the ticket number, provide the expected waiting time information, based on his ticket position New information corrects customers over estimation of waiting time Improved system always yields a balking rate virtually identical to that of physical queue (M/M/1/K)

10. Contributions Intelligent ticket queue management system has become ever more popular in service industry and government offices alike We introduce the first analytical model of ticket queue We obtain insights on the impact of information loss in the ticket queue on key service performance measures and propose a remedy to correct it We develop efficient and effective evaluation tools that can help management to quantify service performance, benchmark performance gap with physical queue, and implement improvement when it is called for Ticket queue needs to go beyond simply issuing tickets

11. Future Research Multiple servers, multiple job classes General inter-arrival or service time distributions Probabilistic balking behavior and reneging (intelligent ticket technology is able to collect rich information of customer s behavior) Provide customers with dynamic information in a ticket queue with both balking and reneging customers – E.g., amusement parks use the pager system to schedule ride and show times and communicate with their customers in virtual queues – Restaurant Pagers, provide timely info benefit both customers and service provider

13. Contributions Intelligent ticket queue management system has become ever more popular in service industry and government offices alike We introduce the first analytical model of ticket queue We obtain insights on the impact of information loss in the ticket queue on key service performance measures and propose a remedy to correct it We develop efficient and effective evaluation tools that can help management to quantify service performance, benchmark performance gap with physical queue, and implement improvement when it is called for Ticket queue needs to go beyond simply issuing tickets