Multiple-Input Heavy-Traffic Real-Time Queues

A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered-earliest deadline first and first-in, first-out. The set of current lead times of the K streams is modeled as a K-dimensional vector of random counting measures on R, and the limit of this vector of measure-valued processes is obtained under heavy traffic conditions.