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 fo the actual peak congestion by the time of peak congestion in an infinite server model and then substituting the arrival rate at this tiem int he corresponding stationary finite server model. We show that the lagged PSA is always more accurate than the SPHA and results in dramatically smaller erros 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.
Green, Linda, and Peter Kolesar. "The lagged PSA for estimating peak congestion in multiserver Markovian queues with periodic arrival rates." Management Science 43, no. 1 (January 1997): 80-87.
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