Low of large number limits of Limited Processor Sharing queues

Motivated by applications in computer and communication systems, we consider a pro-cessor sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriately scaled processor sharing queues. Key words and phrases. limited processor sharing, measure-valued process, fluid model, invariant manifold