Disk drives are a common performance bottleneck in modern storage systems. To alleviate this, disk manufacturers employ a variety of I/O request scheduling strategies which aim to reduce disk head positioning time by dynamically reordering queueing requests. An analytical model of this phenomenon is best represented by an $M/G/1$ queue with queue length dependent service times. However, there is no general exact result for the response time distribution of this variety of queue with generalised service time distributions. In this paper, we present a novel approximation for the response time distribution of such a queue. We then apply this method to the specific case of a zoned disk drive which implements I/O request reordering. A key contribution is the derivation of realistic service time distributions with minimised positioning time. We derive analytical results for calculating not only the mean but also higher moments and the full distribution of I/O request response time. We validate our model against measurements from a real disk to demonstrate the accuracy of our approximation.
Information from pubs.doc.ic.ac.uk/qest2009-ipods.