  In customer support contact centers, every service interaction involves a
messaging dialogue between a customer and an agent; together, they exchange
information, solve problems, and collectively co-produce the service. Because
the service progression is shaped by the history of conversation so far, we
propose a bivariate, marked Hawkes process cluster model of the customer-agent
interaction. To evaluate our stochastic model of service, we apply it to an
industry contact center dataset containing nearly 5 million messages. Through
both a novel residual analysis comparison and several Monte Carlo
goodness-of-fit tests, we show that the Hawkes cluster model indeed captures
dynamics at the heart of the service and also surpasses classic models that do
not incorporate the service history. Furthermore, in an entirely data-driven
simulation, we demonstrate how this history-dependent model can be leveraged
operationally to inform a prediction-based routing policy. We show that
widely-used and well-studied customer routing policies can be outperformed with
simple modifications according to the Hawkes model. Through analysis of a
stylized model proposed in the contact center literature, we prove that service
heterogeneity can cause this underperformance and, moreover, that such
heterogeneity will occur if service closures are not carefully managed.
