State-dependent response times via fluid limits in shortest remaining processing time queues

We consider a single server queue with renewal arrivals and i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. We provide a fluid model (or formal law of large numbers approximation) for this system. The foremost payoff of our fluid model is a fluid level approximation for the state-dependent response time of a job of arbitrary size, that is, the amount of time it spends in the system, given an arbitrary system configuration at the time of its arrival.