Staffing to Stabilize Blocking in Loss Models with Time-varying Arrival Rates

The modified-offered-load approximation can be used to choose a staffing function (the time-varying number of servers) to stabilize delay probabilities at target levels in multi-server delay models with time-varying arrival rates, with or without customer abandonment. In contrast, as we confirm with simulations, it is not possible to stabilize blocking probabilities to the same extent in corresponding loss models, without extra waiting space, because these probabilities necessarily change dramatically after each staffing change. Nevertheless, blocking probabilities can be stabilized provided that we either randomize the times of staffing changes or average the blocking probabilities over a suitably small time interval. We develop systematic procedures and study how to choose the averaging parameters.