We consider customer service chat (CSC) systems where customers can receive real time service from agents using an instant messaging (IM) application over the Internet. A unique feature of these systems is that agents can serve multiple customers simultaneously. The number of customers that an agent is serving, referred to as the level of that agent, determines the rate at which each customer assigned to that agent receives service.
We aim to answer several important operational management questions arising in practice. We first consider the staffing problem in CSC systems with impatient customers where the objective is to minimize the number of agents while providing a certain service level with exponential service and abandonment times. The service level is measured in terms of the proportion of customers who abandons the system in the long run.
We also propose effective routing policies based on a static planning LP. We show that these routing policies minimize the proportion of abandoning customers in the long run asymptotically for large systems.Then we prove that the staffing solution obtained from a staffing LP, when used with the proposed routing policies, is asymptotically optimal. Finally we determine what the maximum level of multi-tasking for agents should be. We discuss the extensions of our results to general service and abandonment times.