The last, the least and the urgent...a story of three policies.

Resumen: In several queueing systems, arriving tasks or customers have service
and timing requirements. These systems with customer abandonment have a
long and rich history in queueing theory, and have several applications
in task scheduling in computer systems, operations research problems,
etc. A common point in all of these works is that they deal with
customers reneging from the system only while in the queue, and not
during service. However, in several applications, customers may also
leave during service, and the partial work performed by the system
during their stay is still useful.

We will therefore model this new type of partial service queues with
abandonment through a point process state representation. Building upon
the machinery of measure-valued processes that has been the backbone of
this line of research, we will show a common framework in which to
include several policies.

Finally, we will show that the deadline-oblivious policy (preemptive)
LCFS achieves exactly the same performance as Earliest-Deadline-First in
the fluid scale. This is a striking property, that makes this scenario
interesting, and overcomes the difficulty of estimating deadlines
entirely.

Joint work with Diego Goldsztajn and Fernando Paganini.