Processor Sharing (PS) queues were originally introduced to analyze the
performance of time-sharing in computer networks. Nowadays, PS queues
are one of the most popular congestion models for TCP traffic on the
Internet. Under the PS discipline, each customer in the system receives
the same service rate.

Motivated by obtaining a better understanding of the impact of reneging
(e.g. aborting the download of a file) in communication
networks, we consider a PS queue in overload where customers may leave
after a certain amount of time, before their service is finished.
Under the PS service discipline, such behavior is unwelcome, since it
always implies that some work is done in vain. Therefore, when the queue
is in overload, the actual throughput can be much lower than the total
service rate.

We consider a fluid approximation of this queue, which is accurate
when both the arrival rate and service rate is large. We apply this fluid
approximation to analyze the impact of reneging on system performance
in PS queues. By studying several examples, we show that the impact can be
quite substantial and propose an admission control scheme to reduce its
effect.

This talk is based on joint work with Christian Gromoll (Stanford) and
Philippe Robert (INRIA).