Abstract—A queueing model is developed for a multi-RAID storage system implemented on modern zoned disks, using fine, accurate access time functions. An extension of a previous analytical model that utilizes Fork-Join composition of M/G/1 queues, it describes zoning directly in terms of the probability distributions or moments of the model’s components, such as seek time, rotational latency and data transfer time. These quantities are calculated directly using the principles of operation of the hardware. This is in contrast to estimating them from simulations and theoretical bounds, as in previous zoned disk models. The resulting multi-RAID model turns out to be accurate, when its performance predictions, characterized here by the mean of queueing and response times, are compared with simulation, and also scalable; not only for the zoned technology but also for alternate ones.

Abstract. This paper studies the performance of Peer-to-Peer Storage Systems (P2PSS) in terms of data lifetime and availability. Two schemes for recovering lost data are modeled through absorbing Markov chains and their performance are evaluated and compared. The first scheme relies on a centralized controller that can recover multiple losses at once, whereas the second scheme is distributed and recovers one loss at a time. The impact of each system parameter on the performance is evaluated, and guidelines are derived on how to engineer the system and tune its key parameters in order to provide desired lifetime and/or availability of data. We find that, in stable environments such as local area or research laboratory networks where machines are usually highly available, the distributed-repair scheme offers a reliable, scalable and cheap storage/backup solution. This is in contrast with the case of highly dynamic environments, where the distributed-repair scheme is inefficient as long as the storage overhead is kept reasonable. P2PSS with centralized-repair scheme are efficient in any environment but have the disadvantage of relying on a centralized authority. Our analysis also suggests that the use of large size fragments reduces the efficiency of the recovery mechanism. 1

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. 1

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 extensions 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

The peer-to-peer (P2P) paradigm have emerged as a cheap, scalable, self-repairing and fault-tolerant storage solution. This solution relies on erasure codes to generate additional redundant fragments of each “block of data ” in order to increase the reliability and availability and overcome the churn. When the amount of unreachable fragments attains a predefined threshold, due to permanent departures or long disconnections of peers, a recovery process is initiated to compensate the missing fragments, requiring multiple fragments of data of a given “block ” to be downloaded in parallel for an enhanced service. Recent modeling efforts that address the availability and the durability of data have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the “real ” distribution of the recovery process. This work aims at filling this gap and better understanding the behavior of these systems through simulation while taking into consideration the heterogeneity of peers, the underlying network topologies, the propagation delays and the transport protocol. To that end, the distributed storage protocol is implemented in the NS-2 network simulator. This paper describes a realistic simulation model that captures the behavior of P2P storage systems. We provide some experiments results that show how modeling the availability and durability can be impacted by the recovery times distribution which is impacted in turn by the characteristics of the the network and the context.

We present the Java Modelling Tools (JMT) suite, an integrated framework of Java tools for performance evaluation of computer systems using queueing models. The suite offers a rich user interface that simplifies the definition of performance models by means of wizard dialogs and of a graphical design workspace. The performance evaluation features of JMT span a wide range of state-of-the-art methodologies including discreteevent simulation, mean value analysis of product-form networks, analytical identification of bottleneck resources in multiclass environments, and workload characterization with fuzzy clustering. The discrete-event simulator supports several advanced modeling features such as finite capacity regions, load-dependent service times, bursty processes, forkand-join nodes, and implements spectral estimation for analysis of simulative results. The suite is open-source, released under the GNU general public license (GPL), and it is available for free download at

Building on our prior work in [8], we present an improved model for for large partial stripe following full stripe writes in RAID 5. This was necessary because we observed that our previous model tended to underestimate measured results. To date, we have only validated these models against RAID systems with at most four disks. Here we validate our improved model, and also our existing models for other read and write configurations, against measurements taken from an eight disk RAID array. 1

Abstract—Peer-to-peer storage systems rely on data fragmentation and distributed storage. Unreachable fragments are continuously recovered, requiring multiple fragments of data (constituting a “block”) to be downloaded in parallel. Recent modeling efforts have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the “real ” distribution of the recovery process. This work aims at filling this gap through a simulation study. To that end, we implement the distributed storage protocol in the NS-2 network simulator and run a total of seven experiments covering a large variety of scenarios. We show that the fragment download time follows approximately an exponential distribution. We also show that the block download time and the recovery time essentially follow a hypo-exponential distribution with many distinct phases (maximum of as many exponentials). We use expectation maximization and least square estimation algorithms to fit the empirical distributions. We also provide a good approximation of the number of phases of the hypo-exponential distribution that applies in all scenarios considered. Last, we test the goodness of our fits using statistical (Kolmogorov-Smirnov test) and graphical methods. I.

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.

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