Scaling limits for processor sharing models 
Bert Zwart , Ph.D.
CocaCola Associate Professor, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
January 25, 2008
ABSTRACT
Processor Sharing (PS) queues were originally introduced to analyze the performance of timesharing 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. To analyze such systems rigorously, it is necessary to consider stochastic processes that are measurevalued, which complicates the analysis.
Motivated by this, we consider scaling (in particular law of large number) limits for several variations and extensions of the PS queue. In particular, 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 law of large number limit for this system, which leads to a fluid approximation.
We apply this fluid approximation to analyze the impact of reneging on system performance in PS queues.
