Stochastic Offered Load Processes in Service Systems

Many challenges arise in the operations management of service systems with uncertain time-varying arrivals, non-exponential service and patience times, and complex network structures. Stochastic offered load processes have been shown to provide useful insights in capacity planning and performance analysis of large-scale service systems. In this talk, we focus on stochastic offered load processes in non-Markovian many-server queueing systems with dependence among interarrival times and among service times. Dependence among interarrival times commonly occurs when some of the arrivals are overflows from another system; the arrival process is more bursty as a consequence.  Dependent service times can occur in many systems. For example, in a hospital emergency room, there may be multiple patients associated with the same medical incident, so that their required treatment can be highly correlated.

  The goal is to study the impact of these forms of dependence upon system performance and capacity planning. We derive the approximate stationary and transient distributions of stochastic offered load processes by proving a functional central limit theorem under the assumptions that the sequence of interarrival times satisfies a functional central limit theorem and the sequence of service times satisfies certain mixing conditions.  We show how the stationary and transient distributions can be used to give effective approximations of delay probabilities and provide insights on staffing (a refined square root staffing rule) for such systems.