A Note on Approximating Peak Congestion in M<html_ent glyph="@lt;" ascii="<"></html_ent>sub<html_ent glyph="@gt;" ascii=">"></html_ent>t<html_ent glyph="@lt;" ascii="<"></html_ent>/sub<html_ent glyph="@gt;" ascii=">"></html_ent>/G/ Queues with Sinusoidal Arrivals

W e study the M / G / queue where customers arrive according to a sinusoidal function Xt = + A sin(27rt/T) and the service rate is u. We show that the expected number of customers in the system during peak congestion can be closely approximated by (X + A) / p for service distributions with coefficient of variation between 0 and 1. Motivated by a result derived by Eick, Massey, and Whitt that the time lag of the peak congestion from the peak of the customer arrivals is 1/2 4 for models with deterministic service times, we show that the time lag for exponential service times is closely approximated by 1 / [. Based on a cycle length of 24 hours and regardless of the values of other system parameters, these approximations are of the order of 1% accuracy for ,u = 1, and the accuracy increases rapidly with increasing iy. (Queues; Nonstationarity; Approximations)