A Multi-Class Fluid Model for a Contact Center with Skill-Based Routing

A multi-class deterministic fluid model is proposed to describe and improve the performance of a customer contact center with skill-based routing. The fluid model can be regarded as an approximation for a stochastic queueing system with multiple customer classes and multiple server groups, with customer abandonment and non-exponential service-time and time-to-abandon distributions. The fluid model is attractive to provide a rough analysis of large systems, with high arrival rate and many servers. Even though the fluid model evolves deterministically, the service-time distributions and time-to-abandon distributions beyond their means play a critical role. The fluid model can be used for staffing, routing and system design, because it is possible to formulate tractable optimization problems.