Asymptotic behavior of earliest-deadline-first scheduling with a large number of flows

Providing quality-of-service in a wireless network where channels are unreliable will require an efficient scheduling algorithm that can offer certain statistical delay guarantees. In a system with a large number of users, providing such guarantees demands a careful design of an admission control scheme, which requires the characterization of the schedulable region. In this paper we propose a framework for designing an efficient admission control scheme based on the asymptotic behavior of the system as the system capacity increases with the number of users. We show that as the system capacity scales with the number of users in the system, the system behavior can be approximated by a deterministic process that can be computed recursively. Moreover, the fluctuation of system behavior around its expected behavior can be typically captured by Gaussian random variables whose parameters can be computed iteratively.