Multiple-input heavy-traffic real-time queues.
Customers with random service times and random due dates from \(K\) renewal streams arrive at their own buffer at a single server. The server serves the buffers which are nonempty according to a generalized processor sharing discipline (head-of-the-line with weights). The buffers are either FIFO or EDF (earliest deadline first). Service times, interarrival times and due dates are stream specific characterized by two moments with the usual independence assumptions. To describe the detailed state of the system a lead time profile for the system is introduced which describes for all customers present their time until dead line. Constructing the usual processes to describe the queueing and workload behaviour over the streams a sequence of rescaled systems with their associated processes under diffusion scaling for heavy traffic is investigated. For this sequence the heavy traffic limit is determined.
scientific article; zbMATH DE number 1906142