Modeling Mobile Ticket Dispenser System with Impatient Clerk

The mobile ticket dispenser system (MTDS) allows customers to remotely draw tickets for service orders anywhere through a mobile handset. In our previous work, the MTDS was applied to a restaurant scenario in which both clerks and customers are patient, i.e., once a mobile ticketing (MT) customer remotely draws the ticket, his request can be served by the clerk when the clerk is available, regardless of when the customer arrives at the restaurant. In this paper, the MTDS is applied to a post office scenario in which the customers are patient, but the clerk is impatient since the original ticket drawn by the MT customer may be invalid if he/she does not arrive at the post office before his/her turn. In this case, the behavior of the MT customer is the same as the so-called in-person ticketing customer who needs to draw a ticket in person when he/she arrives at the service counter. We propose an analytical model to derive the probability that an MT customer misses his/her turn when he/she arrives at the post office. A discrete-event simulation model is developed to investigate the performance of the predicted time adjustment mechanism for the MTDS. We also use real data collected at a post office to observe the queuing behavior. Our study provides guidelines for arranging the time for an MT customer to arrive at the MTDS server.