Abstract
We study customer service chat (CSC) systems with generally distributed service and patience times by developing measure-valued processes to model and analyze the system dynamics. We first prove that these processes are tight in the many-server asymptotic regime and then show that their limits satisfy a set of fluid model equations. We then establish the invariant states of these limits and use these invariant states to obtain (non-asymptotic) approximations for various performance metrics of CSC systems in the steady state. We also demonstrate the accuracy of these approximations using extensive numerical experiments. These approximations allow us to establish the impact of service and patience time distributions on the system performance and to devise effective dynamic routing policies.
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