Measurements and approximations to describe the offered traffic and predict the average workload in a single-server queue

Measurements and approximations are proposed to describe the variability of offered traffic to a queue and predict the average workload in the queue. The principal traffic measurement considered is a normalized version of the variance of the total input of work as a function of time, which is called the index of dispersion for work (IDW). Given ample traffic data, the IDW can easily be estimated using sample averages. Given a mathematical model, such as a multiclass queue in which each class has GI/G/1 offered traffic, the IDW can often be calculated analytically, or approximated by using the limits as t approaches 0 and t approaches ∞. The basic premise is that the average workload is primarily determined by the offered traffic, beyond the offered load (the deterministic rate work arrives), through the IDW. Support is provided for this premise, and it is shown how the average workload can be predicted from the IDW or basic model parameters