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In customer support centers, a successful service interaction involves a dialogue between a customer and an agent. Both parties depend on one another for information and problem solving, and this interaction defines a co-produced service process. In this paper, we propose, develop, and compare new stochastic models for the co-production of service in a contact center. Using insights from service communication data, we model the service interactions using self-exciting and mutually exciting bivariate Hawkes processes, so that a correspondence from one party increases the likelihood of a response from the other party soon after. Moreover, our models incorporate both dynamic busyness factors that depend on the agent workload as well as dynamic factors that depend on the inner-mechanics of the interaction. To understand how well our Hawkes models describe the message-timestamps, we compare the goodness-of-fit of these models on contact center data from industry. We show that the word-count bivariate Hawkes model, which takes into account the mutual interaction and the amount of information provided by each party, fits the data the best. In addition to a great goodness-of-fit, the Hawkes models allow us to construct explicit expressions for the relationship between the correspondence rates of each party and the conversation progress. These formulae illustrate that the agent is more dominant in pacing the service along in the short term, but that the customer has a more profound effect on the duration of the conversation in the long run. Finally, we use our models to predict the future level of activity within a given conversation, through which we find that the bivariate Hawkes processes that incorporate the amount of information provided by each party or the sentiment expressed by the customer give us the most accurate predictions.

The Co-Production of Service: Modeling Service Times in Contact Centers Using Hawkes Processes