Using bulk arrivals to model i/o request response time distributions in zoned disks and raid systems

Abstract

Useful analytical models of storage system performance must support the characteristics exhibited by real I/O workloads. Two essential features are the ability to cater for bursty arrival streams and to support a given distribution of I/O request size. This paper develops and applies the theory of bulk arrivals in queueing networks to support these phenom- ena in models of I/O request response time in zoned disks and RAID systems, with a specific focus on RAID levels 01 and 5. We represent a single disk as an MX/G/1 queue, and a RAID system as a fork-join queueing network of MX/G/1 queues. We find the response time distribution for a ran- domly placed request within a random bulk arrival. We also use the fact that the response time of a random request with size sampled from some distribution will be the same as that of an entire batch whose size has the same distribution. In both cases, we validate our models against measurements from a zoned disk drive and a RAID platform. Copyright © 2009 ICST.