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We consider a single-server queue with renewal arrivals and i.i.d. servicetimes, in which the server employs either the preemptive Shortest RemainingProcessing Time (SRPT) policy, or its non-preemptive variant, Shortest JobFirst (SJF). We show that for given stochastic primitives (initial condition,arrival and service processes), the model has the same fluid limit under eitherpolicy. In particular, we conclude that the well-known queue length optimalityof preemptive SRPT is also achieved, asymptotically on fluid scale, by thesimpler-to-implement SJF policy. We also conclude that on fluid scale, SJF andSRPT achieve the same performance with respect to response times of thelongest-waiting jobs in the system.

Invariance of fluid limits for the Shortest Remaining Processing Time and Shortest Job First policies