The Lagged PSA for Estimating Peak Congestion in Multiserver Markovian Queues with Periodic Arrival Rates

We propose using a modification of the simple peak hour approximation (SPHA) for estimating peak congestion in multiserver queueing systems with exponential service times and time-varying periodic Poisson arrivals. This lagged pointwise stationary approximation (lagged PSA) is obtained by first estimating the time of the actual peak congestion by the time of peak congestion in an infinite server model and then substituting the arrival rate at this time in the corresponding stationary finite server model. We show that the lagged PSA is always more accurate than the SPHA and results in dramatically smaller errors when average service times are greater than a half an hour (based on a 24 hour period). More importantly, the lagged PSA reliably identifies proper staffing levels to meet targeted performance levels to keep congestion low.