Markov Process Simulations of Service Systems with Concurrent Hawkes Service Interactions

In multi-tasked services such as in messaging-based contact centers, parallel service interactions share a mutual dependence through the agent’s concurrency. Here, we introduce Markov process simulation methods for bivariate Hawkes cluster service models that are not Markovian by default due to their concurrency dependence. To do so, we propose an alternate construction that maintains extra "shadow" variables for how the process would be under other concurrency levels. We prove that this construction yields an equivalent Markov process, and we show through numerical experiments that its corresponding simulation algorithm is significantly more efficient than the non-Markovian alternatives.