M(sub t)/G/infinity queues with sinusoidal arrival rates
Article Abstract:
Congestion peaks, lags and ranges are analyzed in an M(sub)t/G/infinity queuewherein the mean number of busy servers is a function of time with sinusoidal arrival rates arising from a nonhomogeneous Poisson distribution arrival process. Such a process implies that the full distribution per period is characterized by its mean. Analysis indicates that peak arrival rates are lagged by peak congestion, while congestion range is much samller than the range of offered load. Application of a linear operator to the arrival rate function represents an image of the mean function. Pointwise stationary and polynomial approximations for the mean number of busy servers are investigated in order to apply the results to Fourier series-treated general periodic arrival rate problems. These results are applicable to queue models wherein lost or delayed customers are experienced.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1993
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Planning queueing simulations
Article Abstract:
The estimation of the required length of the run of a simulation is a major problem in the planning of simulation experiments addressing the estimation of steady-state quantities related to queueing models. Simple heuristic formulas for one-run queueing simulations can be applied to the design of queueing experiments to aid in approximating queue lengths. The formulas are based on queues with heavy traffic limits and can be applied to stochastic processes reflecting Brownian motion, including the queue process in a standard GI/G/1 model. The formulas can be used to approximate the length of the simulation run in each application of an experiment.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1989
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