Approximations for chat service systems using many-server diffusion limits

Tezcan, T and Cui, L (2016) Approximations for chat service systems using many-server diffusion limits. Mathematics of Operations Research, 41 (3). pp. 775-807. ISSN 0364-765X

Abstract

We study a queueing model of customer service chat 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 different diffusion processes in a many-server heavy-traffic regime in three different cases. Using this result, we are able to offer 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.