Disk arrays were proposed in the 1980s as a way to use parallelism between multiple disks to improve aggregate I/O performance. Today they appear in the product lines of most major computer manufacturers. This paper gives a comprehensive overview of disk arrays and provides a framework in which to organize current and future work. The paper first introduces disk technology and reviews the driving forces that have popularized disk arrays: performance and reliability. It then discusses the two architectural techniques used in disk arrays: striping across multiple disks to improve performance and redundancy to improve reliability. Next, the paper describes seven disk array architectures, called RAID (Redundant Arrays of Inexpensive Disks) levels 0-6 and compares their performance, cost, and reliability. It goes on to discuss advanced research and implementation topics such as refining the basic RAID levels to improve performance and designing algorithms to maintain data consistency. Last, the paper describes six disk array prototypes or products and discusses future opportunities for research. The paper includes an annotated bibliography of disk array-related literature.

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both con guring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytic performance models of disk arrays are di cult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. In this paper, we develop, validate and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytic model. Finally, we apply the analytic model to derive an equation for the optimal unit of data striping in disk arrays. 1

This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solution methodology.

The fork-join queue models parallel resources where arriving jobs divide into various number of sub-tasks that are assigned to unique devices within the parallel resource. Each device in the parallel resource is modeled  ¢¡ £  ¢¡¥ ¤ by queueing servers. A job completes execution and departs the parallel resource after all its sub-tasks complete execution. This paper analyzes ¦-server fork-join queues where arriving jobs divide into ¤¨§�©�§ are assigned to unique servers of the fork-join queue. There is no known closed-form solution for ¦��� � fork-join queues. The paper presents an O(log K) algorithm for computing the mean response time pessimistic and optimistic bounds and for computing the mean response time approximation of the fork-join queue. The error bounds for the response time bounds and approximation are presented. Index Terms: fork-join synchronization, performance evaluation, parallel computer and storage systems. 1

This paper discusses analytic solution methods for queueing models with multiple waiting lines. The methods are briefly illustrated, using key models like the 2 × 2 switch, the shortest queue and the cyclic polling system. AMS subject classification: 60K25, 90B22.

This paper gives an exact analysis of mean response time of fork-join systems. The response time is shown to be the sum of parallel wait and parallel service times which are analogous to wait and service times in nonparallel systems. It is shown that the parallel service time of a job is dependent on the state at arrival time of the job. A formal parallel wait time analysis, similar to the wait time analysis of non-parallel systems is also given. The analysis is carried out using event/time sequence (ET-S) trees, a simple modeling technique introduced in this paper.

This paper presents an analysis of closed, balanced, fork-join queueing networks with exponential service time distributions. The fork-join queue is mapped onto two non-parallel networks, namely, a serial-join model and a state-dependent model. Using these models, it is proven that the proportion of the number of jobs in the different subsystems of the fork-join queueing network remains constant, irrespective of the multiprogramming level. This property of balanced fork-join networks is used to compute quick, inexpensive bounds for arbitrary fork-join networks.

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