Abigail S. Lebrecht

Analytical and Simulation Modelling of Zoned RAID Systems

RAID systems are ubiquitously deployed in storage environments, both as standalone storage solutions and as fundamental components of virtualized 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 composed 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 optimizations employed by modern disk drives. All simulation results are validated against device measurements and compared with existing analytical queueing network models for the development of the models.

A Performance Model of Zoned Disk Drives with I/O Request Reordering

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 sucha queue. We then apply this method to the specific case of azoned 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.

A Response Time Distribution Model for Zoned RAID

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.

Modelling Zoned RAID Systems Using Fork-Join Queueing Simulation

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.

Modelling and Validation of Response Times in Zoned RAID

We present and validate an enhanced analytical queueing network model of zoned RAID. The model focuses on RAID levels 01 and 5, and yields the distribution of I/O request response time. Whereas our previous work could only support arrival streams of I/O requests of the same type, the model presented here supports heterogeneous streams with a mixture of read and write requests. This improved realism is made possible through multiclass extentions to our existing model. When combined with priority queueing, this development also enables more accurate modelling of the way subtasks of RAID 5 write requests are scheduled. In all cases 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 RAID system.

Using bulk arrivals to model I/O request response time distributions in zoned disks and RAID systems

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 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 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.