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We present a heavy traffic analysis for a single server queue with renewalarrivals and generally distributed i.i.d. service times, in which the serveremploys the Shortest Remaining Processing Time (SRPT) policy. Under typicalheavy traffic assumptions, we prove a diffusion limit theorem for ameasure-valued state descriptor, from which we conclude a similar theorem forthe queue length process. These results allow us to make some observations onthe queue length optimality of SRPT. In particular, they provide the sharpestillustration of the well-known tension between queue length optimality andquality of service for this policy.

Diffusion limits for shortest remaining processing time queues