Analyzing Queues Using Variance-Time Curves

Queuing theory has become a standard tool for analyzing the performance of complex systems such as communications networks, computers and manufacturing facilities. However, these systems often differ significantly from the more tractable mathematical models. For example, these systems often have complicated (not nearly Poisson) offered traffic (arrival Processes). We discuss insights that can be gained by focusing on variance-time curves of the offered traffic. The Variance-time curves can be estimated from measurements or calculated from model parameters. In addition to providing a useful description of the variability of the offered traffic, the variance- time curves can be used to generate approximations for standard performance measures such as the mean steady-state workload in a queue.