When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence

When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence Service times of customers often depend on the delay they experience in queue, as was recently demonstrated empirically in restaurants, call centers, and intensive care units. Two forms of dependence mechanisms in service systems with customer abandonment are studied in this paper: First, the service requirement of a customer may evolve while waiting in queue. Second, customers may arrive to the system with an exogenous service and patience time that are stochastically dependent. Because either dependence mechanism can have significant impacts on a system's performance, it should be identified and taken into consideration for performance evaluation and decision-making purposes. However, identifying the source of dependence from observed data is hard because both the service times and patience times are censored due to customer abandonment. Further, even if the dependence is known to be the latter exogenous one, there remains the difficult task of fitting a joint service-patience times distribution to the censored data. In “When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence”, Wu, Bassamboo, and Perry provide a solution to address these statistical challenges.

Enhance System Utilization and Business Revenue with AI-based Queue Reservation System

Queue management is a crucial part of service industry. Business has to deal with the uncertainty of arrival customer and the trade-off between the costs of providing capacity and customer satisfaction. Matching service capacity with the arrival customer is difficult so the system utilization is low in the low periods and customers have to wait for a long time in the peak period. Due to long waiting, some customer abandons the queue before receiving service. Customer abandonment affects business revenue and the system utilization. To relieve the effect of the customer abandonment, this paper aims to propose Artificial Neural Network based waiting time predictor with queue reservation system. The proposed system increases the system utilization and increase customer satisfaction at the same time. Instead of abandonment, customers can reserve their place in queue if the waiting time is too long and they can do other activities while waiting. Moreover, the proposed system provides the accurate estimated waiting time to each customer instead of queue-length. The accurate waiting time enables arrival customers to better decide on the reservation options. 95% of our predicted waiting time is accurate within 5 minutes. Comparing to the system without the queue reservation system, the system utilization and the number of the arrival customer completed service improve 13% and 54% respectively

STAFFING TO STABILIZE BLOCKING IN LOSS MODELS WITH TIME-VARYING ARRIVAL RATES

The modified-offered-load approximation can be used to choose a staffing function (the time-varying number of servers) to stabilize delay probabilities at target levels in multi-server delay models with time-varying arrival rates, with or without customer abandonment. In contrast, as we confirm with simulations, it is not possible to stabilize blocking probabilities to the same extent in corresponding loss models, without extra waiting space, because these probabilities necessarily change dramatically after each staffing change. Nevertheless, blocking probabilities can be stabilized provided that we either randomize the times of staffing changes or average the blocking probabilities over a suitably small time interval. We develop systematic procedures and study how to choose the averaging parameters.