APPROXIMATING A POINT PROCESS BY A RENEWAL PROCESS, II: SUPERPOSITION ARRIVAL PROCESSES TO QUEUES.

The author develops an approximation for a queue having an arrival process that is the superposition of independent renewal processes, i. e. , SIGMA Gl//i/G/1. This model is useful, for example, in analyzing networks of queues where the arrival process to an individual queue is the superposition of departure processes from other queues. If component arrival processes are approximated by renewal processes, the SIGMA Gl//i/G/1 model applies. The approximation proposed is a hybrid that combines two basic methods described by W. Whitt. All these methods approximate the complex superposition process by a renewal process and yield a Gl/G/1 queue that can be solved analytically or approximately. In the hybrid method, the moments of the intervals in the approximating renewal process are a convex combination of the moments determined by the basic methods.