Performance Analysis and Optimization of a Queueing Model for a Multi-skill Call Center in M-Design

This paper studies a queuing model of a multi-skill call center in M-design. In this model, there are two types of customers and three groups of servers who have different skills. Servers in Group 1 can only serve type 1 customers, servers in Group 2 can only serve type 2 customers, and servers in Group 3 can serve both type 1 and type 2 customers. We obtain the state-transition rates by using results from M/M/c/c and M/M/c queueing systems. Then, we establish equations for the steady-state probabilities of the system. Finally, we obtain the computational formula for the service level and we present an optimization of a staffing problem.