Optimal design of a multi-server queueing system with delay information

The purpose of this paper is to provide a framework for the optimal design of queueing systems of call centers with delay information. The main decisions in the design of such systems are the number of servers, the appropriate control to announce delay anticipated.

This paper models a multi-server queueing system as an M/M/S+M queue with customer reactions. Based on customer psychology in waiting experiences, a number of different service-level definitions are structured and the explicit computation of their performance measures is performed. This paper characterizes the level of satisfaction with delay information to modulate customer reactions. Optimality is defined as the number of agents that maximize revenues net of staffing costs.

Numerical studies show that the solutions to optimal design of staffing levels and delay information exhibit interesting differences, especially U-shaped curve for optimal staffing level. Experiments show how call center managers can determine economically optimal anticipated delay and number of servers so that they could control the trade-off between revenue loss and customer satisfaction.

Many results that pertain to announcing delay information, customer reactions, and links to satisfaction with delay information have not been established in previous studies, however, this paper analytically characterizes these performance measures for staffing call centers.