Soraya Zertal

Queueing models of RAID systems with maxima of waiting times

A queueing model is developed that approximates the effect of synchronizations at parallel service completion instants. Exact results are first obtained for the maxima of independent exponential random variables with arbitrary parameters, and this is followed by a corresponding approximation for general random variables, which reduces to the exact result in the exponential case. This approximation is then used in a queueing model of RAID (Redundant Array of Independent Disks) systems, in which accesses to multiple disks occur concurrently and complete only when every disk involved has completed. We consider the two most common RAID variants, RAID0-1 and RAID5, as well as a multi-RAID system in which they coexist. This can be used to model adaptive multi-level RAID systems in which the RAID level appropriate to an application is selected dynamically. The random variables whose maximum has to be computed in these applications are disk response times, which are modelled by the waiting times in M/G/1 queues. To compute the mean value of their maximum requires the second moment of queueing time and we obtain this in terms of the third moment of disk service time, itself a function of seek time, rotational latency and block transfer time. Sub-models for these quantities are investigated and calibrated individually in detail. Validation against a hardware simulator shows good agreement at all traffic intensity levels, including the threshold for practical operation above which performance deteriorates sharply.

Queueing Models with Maxima of Service Times

We develop a queueing model that approximates the effect of synchronisations at parallel service completion instants. We first obtain exact results for the maxima of independent exponential random variables with arbitrary parameters and follow this with an approximation for general random variables, which reduces to the exact result in the exponential case. We use this in a queueing model of RAID (Redundant Array of Independent Disks) systems, in which accesses to multiple disks occur concurrently and complete only when every disk involved has completed. The random variables to be maximised are therefore disk response times which are modelled by the waiting times in an M/G/1 queue. To compute the mean value of their maximum requires the second moment of queueing time and we obtain this in terms of the third moment of disk service time, itself a function of seek time, rotational latency and block transfer time. These quantities are analysed individually in detail. Validation by simulation, with realistic hardware parameters and block sizes, shows generally good agreement at all traffic intensity levels, including the threshold above which performance deteriorates sharply.

Storage workload modelling by hidden Markov models: Application to Flash memory

A workload analysis technique is presented that processes data from operation type traces and creates a hidden Markov model (HMM) to represent the workload that generated those traces. The HMM can be used to create representative traces for performance models, such as simulators, avoiding the need to repeatedly acquire suitable traces. It can also be used to estimate the transition probabilities and rates of a Markov modulated arrival process directly, for use as input to an analytical performance model of Flash memory. The HMMs obtained from industrial workloads-both synthetic benchmarks, preprocessed by a file translation layer, and real, time-stamped user traces-are validated by comparing their autocorrelation functions and other statistics with those of the corresponding monitored time series. Further, the performance model applications, referred to above, are illustrated by numerical examples.

Response time distribution of flash memory accesses

Flash memory is becoming an increasingly important storage component among non-volatile storage devices. Its cost is decreasing dramatically and its performance continues to improve, which makes it a serious competitor for disks and a candidate for enterprise-tier storage devices of the future. Consequently, it is important to devise models and tools to analyse its behaviour and to evaluate its effects on a systems performance. We propose a Markov modulated fluid model with priority classes to investigate the response time characteristics of Flash memory accesses. This model can represent well the Flash access operation types, respecting the erase/write/read relative priorities and autocorrelations. We apply the model to estimate response time densities at the chip for an OLTP-type of workload and indicate the magnitude of the penalty suffered by writes under priority scheduling of read operations. The model is validated against a customised hardware simulator that uses input-traces typical of our Markovian workload description.

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.

Calibration of a Queueing Model of RAID Systems

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 models 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.

Bus Modelling in Zoned Disks RAID Storage Systems

A model of bus contention in a Multi-RAID storage architecture is presented. Based on an M/G/1 queue, the main issues are to determine the service time distribution that accurately represents the highly mixed input traffic of requests. This arises from the coexistence of different RAID organisations that generate several types of physical request (read/write for each RAID level) with different related sizes. The size distributions themselves are made more complex by the striping mechanism, with full/large/small stripes in RAID5. We show the impact of the bus traffic on the systems overall performance as predicted by the model and validated against a simulation of the hardware, using common workload assumptions.

A generic and open simulation tool for large multi-tiered hierarchical storage systems

Actual storage systems are very large, with complex and distributed architectural configurations, composed of various technologies devices. However, simulation, analysis and evaluation tools in the literature do not handle this complex design and these heterogeneous components. This paper presents OGSSim (Open and Generic Storage systems Simulation tool): a new simulation tool for such systems. Being generic to all devices technologies and open to diverse management strategies and architecture layouts, it fulfills all the storage systems needs in term of representativeness. Also, it has been validated against real systems, thus its accuracy makes it a useful tool for the conception of future storage systems, the choice of hardware components and the analysis of the adequacy between the applications needs and the management strategies combined with the configuration layout. This validation confirmed only a maximum of 15% of difference between real and simulated execution time. Also, OGSSim execution in a competitive time, just 3.5 sec for common workloads on a large system of 500 disks, makes it a challenging simulation and evaluation tool. Thus, it is the appropriate and accurate tool for modern storage systems conception, evaluation and maintenance.

Block shifting layout for efficient and robust large declustered storage systems

Modern disks are very large (SSDs, HDDs) and their capacities will certainly increase in the future. Storage systems use an important number of such devices to compose storage pools and fulfil the storage capacity demands. The result is a higher probability of a failure and a longer reconstruction duration. Consequently, the whole system is penalized as the response time is higher and a second failure will generate a data loss. In this paper, we propose a new method based on block shifting layout which increases the efficiency of a RAID declustered storage system and improves its robustness in both normal and failure modes. We define four mapping rules to reach these objectives. Conducted tests reveal that exploiting the coprime property between the number of devices and the block shifting factor leads to an optimal layout. It reduces significantly the redirection time proportionally to the number of disks, reaching 50% for 1000 disks and a negligeable memory cost as we avoid the use of a redirection table. It also allows the recovery of additional data in case of a second failure during the degraded mode which gives to our proposed method a huge interest for large storage systems comparing to other existing methods.

Investigating Flash memory wear levelling and execution modes

The impact of wear levelling on a Flash storage package and its access operations’ execution modes is investigated. First, a simple, static logical-to-physical mapping function is proposed and its implied wear levelling is assessed for different distributions of addresses, covering both uniform access and hotspots, as well as the Flash chip utilization within the whole package. Second, for each access mode, different preemptive and non-preemptive priority schemes are considered with a range of IO arrival rates, using Poisson-, Erlang- and Pareto-based arrival processes. The analysis of the impact of the execution modes on the performance of the Flash memory is undertaken using a hardware simulator. The results show clearly the good wear levelling obtained by the mapping functions, even in the presence of hotspots. In addition, the impact of the chosen execution mode on the whole storage package for each IO workload type is assessed, both qualitatively and quantitatively.