Fluid models for customer service web chat systems with interactive automated service

In addition to traditional call centers, companies have increasingly started developing a new type of customer contact center over the Internet, rather than using phone calls, where customers communicate with agents online through a website. Apart from lining up for an agent service, customers have the option of an interactive self-help response and thus can obtain faster service. In such a new customer contact center, managers are inclined to induce customers to use an automated service to reduce manpower costs. Under such circumstances, delay announcements play an important role in guiding customer behavior derived from an avoid-the-crowd option into a self-help choice. Motivated by this, we characterize the underlying stochastic processes by establishing a fluid model in overloaded regimes, and propose that the key to the model is a customer response resulting from system interactions based on a deterministic approximation. Furthermore, we prove that the fluid limit of the model is a unique solution to a complicated queueing system using differential equations. Based on numerical examples, the approximation is shown to be effective in overloaded regimes through comparisons with simulations.A key managerial insight is that the lower the service level is required for staffing, the more effective automated service and the guidance of delay announcement are.