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Calibration of a Queueing Model of RAID Systems

Peter G. Harrison, Soraya Zertal

Conference or Workshop Paper
PASM 2004, 1st International Workshop on Practical Applications of Stochastic Modelling
March, 2005
Electronic Notes in Theoretical Computer Science
Volume 128
Issue 4
DOI 10.1016/j.entcs.2005.01.017

A recent queueing-based modelling methodology of RAID systems compared the mean disk access times of the two most common variants, RAID0-1 and RAID5, as well as a multi-RAID system in which they coexist. Accesses to multiple disks occur concurrently for each logical (user) request and complete only when every disk involved has completed. The models therefore needed to estimate the mean value of the maximum of the individual disk response times, each of which is modelled by the waiting time of an M/G/1 queue. This mean-max value was approximated in terms of the second moment of queueing time which in turn required the third moment of disk service time, itself a function of seek time, rotational latency and block transfer time. To achieve consistently good agreement with an event-driven simulator of the physical hardware and system software requires careful calibration of the resulting model's parameters and validation of its assumptions. This calibration and validation process involves detailed analysis of sub-models to reveal the restrictions necessary on the domain of real-world operating parameters that facilitate a viable predictive model. The process yields significant insight into several of the abstract subsystems involved that may be utilised in a range of practical modelling studies; for example, the effect of approximating a bank of parallel queues with synchronised arrivals by a bank of identical, independent queues. The final comparison against the hardware simulator shows excellent agreement, far surpassing that of the original model.

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