  A single-server queuing model is considered with customers that have
deadlines. If a customer's deadline elapses before service is offered, the
customer abandons the system (customers do not abandon while being served).
When the server becomes available, it offers service to the customer having
earliest deadline among those that are in the queue. We obtain a fluid limit of
the queue length and abandonment processes and for the occupation measure of
deadlines, in the form of measure-valued processes. We characterize the limit
by means of a Skorohod problem in a time-varying domain, which has an explicit
solution. The fluid limits also describe a certain process called the frontier,
that is well known to play a key role in systems operating under this
scheduling policy.

Probability