Approximations for Chat Service Systems Using Many-Server Diffusion Limits

We study a queueing model of customer service chat (CSC) systems. A unique feature of these queueing systems is that a single agent can serve multiple customers simultaneously. We prove the convergence of the queueing process to di↵erent di↵usion processes in a many server heavy-tra c regime in three di↵erent cases. Using this result, we are able o↵er approximations for the steady state performance measures such as the number of customers in the system, the abandonment probability and the sojourn time of a customer. Our numerical experiments show that proposed approximations are accurate in various cases.