  This paper presents a heavy-traffic analysis of the behavior of a
single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in
which customers have deadlines and are served only until their deadlines
elapse. The performance of the system is measured by the fraction of reneged
work (the residual work lost due to elapsed deadlines) which is shown to be
minimized by the EDF policy. The evolution of the lead time distribution of
customers in queue is described by a measure-valued process. The heavy traffic
limit of this (properly scaled) process is shown to be a deterministic function
of the limit of the scaled workload process which, in turn, is identified to be
a doubly reflected Brownian motion. This paper complements previous work by
Doytchinov, Lehoczky and Shreve on the EDF discipline in which customers are
served to completion even after their deadlines elapse. The fraction of reneged
work in a heavily loaded system and the fraction of late work in the
corresponding system without reneging are compared using explicit formulas
based on the heavy traffic approximations. The formulas are validated by
simulation results.
