Abstract. RAID systems are widely deployed, both as standalone storage solutions and as the building blocks of modern virtualised storage platforms. An accurate model of RAID system performance is therefore critical to understanding storage system performance. To this end, this paper presents a queueing network-based model of RAID systems comprised of zoned disks and operating at RAID level 0-1 or 5. The contribution over previous work is twofold. Firstly, our analysis approximates full I/O request response time distributions rather than just mean values. This provides the ability to reason about response time quantiles and higher moments of response time -both of which are useful in the context of modern quality of service requirements. Secondly, we validate our model against measurements from a real RAID system rather than a software simulation. The close agreement between predicted and observed response time distributions gives a high level of confidence in the validity of our model.

Abstract. RAID systems are ubiquitously deployed in storage environments, both as standalone storage solutions and as fundamental components of virtualised storage platforms. Accurate models of their performance are crucial to delivering storage infrastructures that meet given quality of service requirements. To this end, this paper presents a flexible fork-join queueing simulation model of RAID systems that are comprised of zoned disk drives and which operate under RAID levels 01 or 5. The simulator takes as input I/O workloads that are heterogeneous in terms of request size and that exhibit burstiness, and its primary output metric is I/O request response time distribution. We also study the effects of heavy workload, taking into account the request-reordering optimisations employed by modern disk drives. All simulation results are validated against device measurements.

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vious measures can be easily derived. Analytical queueing network models of RAID performance [4,9, 12, 18, 19] deWe present and validate an enhanced analytical queueing veloped prior to [10] approximate only the mean response network model ofzoned RAID. The modelfocuses on RAID time of the system. We note that RAID performance can levels 01 and 5, and yields the distribution ofI/O request also be modelled using other techniques including simularesponse time. Whereas our previous work could only suption [4, 12], table-based [2] and black-box modelling [13]. port arrival streams ofI/O requests of the same type, the Our RAID model is developed in a bottom-up hierarchimodelpresented here supports heterogeneous streams with cal fashion. We begin by modelling each disk drive in the a mixture ofread and write requests. This improved realism array as a single M/G/1 queue. We then abstract the RAID is made possible through multiclass extensions to our exas a fork-join queueing network [3] in which each disk in isting model. When combined with priority queueing, this the array is represented by an M/G/1 queue. In an N-queue development also enables more accurate modelling of the fork-join network (see Fig. 1) each incoming job is split way subtasks ofRAID 5 write requests are scheduled. In into N subtasks at the fork point. Each of these subtasks all cases we derive analytical results for calculating not queues for service at a parallel service node before joining only the mean but also higher moments and the full distria queue for the join point. When all N subtasks in the job bution ofI/O request response time. We validate our model are at the head of their respective join queues, they rejoin against measurements from a real RAID system.(synchronise) at the join point.Pi Q

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 phenomena 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 M X /G/1 queue, and a RAID system as a fork-join queueing network of M X /G/1 queues. We find the response time distribution for a randomly 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.