Call Center: the Waiting Time of Priority Customers

This paper compares two disciplines for serving prioritized customers in a call center, modeled as non-preemptive M/M/1 queues. Under the static priority discipline each customer holds a fixed priority, which guarantees that high-priority customers are served first but leaves low-priority customers exposed to unbounded waits as load approaches capacity. Under the dynamic priority discipline a customer's priority grows with time spent waiting, through a priority function of order r. We derive the expected waiting time for each priority class, show that the dynamic model converges to the static model as r approaches 0 and to first-come-first-served as r grows without bound, and verify the results by simulation. The simulation also shows that the dynamic discipline narrows the spread of waiting times between classes, and that, conditional on waiting, waiting times are well approximated by an exponential distribution with mean W_j/rho. The order parameter r gives a call center designer a direct way to set the relative service levels of each priority group. Simulation code, figure scripts and parameters are included for reproduction.