A Fourier approach to the study of cyclic behaviour of networks

This paper presents a method of analysis for cyclo-stationary queueing systems. These are queues where either or both of the arrival rate into the queue and the departure rate out of the queue have cyclic variations. This technique is particularly useful when the period of the cyclic traffic is not vastly greater than the interarrival times. The method of analysis is based on using Fourier series with complex coefficients to describe the cyclo-stationary probabilities for different states of the system. All other performance measures can be calculated from these coefficients