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31
RAID: HighPerformance, Reliable Secondary Storage
 ACM COMPUTING SURVEYS
, 1994
"... 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 o ..."
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Cited by 298 (6 self)
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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 06 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 arrayrelated literature.
The Stochastic Rendezvous Network Model for Performance of Synchronous ClientServerlike Distributed Software
 IEEE Transactions on Computers
, 1995
"... Distributed or parallel software with synchronous communication via rendezvous is found in clientserver systems and in proposed Open Distributed Systems, in implementation environments such as Ada, V, Remote Procedure Call systems, in Transputer systems, and in specification techniques such as CSP, ..."
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Cited by 98 (28 self)
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Distributed or parallel software with synchronous communication via rendezvous is found in clientserver systems and in proposed Open Distributed Systems, in implementation environments such as Ada, V, Remote Procedure Call systems, in Transputer systems, and in specification techniques such as CSP, CCS and LOTOS. The delays induced by rendezvous can cause serious performance problems, which are not easy to estimate using conventional models which focus on hardware contention, or on a restricted view of the parallelism which ignores implementation constraints. Stochastic Rendezvous Networks are queueing networks of a new type which have been proposed as a modelling framework for these systems. They incorporate the two key phenomena of included service and a second phase of service. This paper extends the model to also incorporate different services or entries associated with each task. Approximations to arrivalinstant probabilities are employed with a MeanValue Analysis framework, to...
Walks with small steps in the quarter plane
 Contemporary Mathematics
"... Abstract. Let S ⊂ {−1, 0,1} 2 \ {(0, 0)}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and always remain in the first quadrant {(i, j) : i ≥ 0, j ≥ 0}. A priori, there are 2 8 problems of this type, but some are trivial. Some others are equivalent to a mo ..."
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Cited by 26 (3 self)
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Abstract. Let S ⊂ {−1, 0,1} 2 \ {(0, 0)}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and always remain in the first quadrant {(i, j) : i ≥ 0, j ≥ 0}. A priori, there are 2 8 problems of this type, but some are trivial. Some others are equivalent to a model of walks confined to a halfplane: such models can be solved systematically using the kernel method, which leads to algebraic generating functions. We focus on the remaining cases, and show that there are 79 inherently different problems to study. To each of them, we associate a group G of birational transformations. We show that this group is finite (of order at most 8) in 23 cases, and infinite in the 56 other cases. We present a unified way of solving 22 of the 23 models associated with a finite group. For all of them, the generating function is found to be Dfinite. The 23rd model, known as Gessel’s walks, has recently been proved by Bostan et al. to have an algebraic (and hence Dfinite) solution. We conjecture that the remaining 56 models, associated with an infinite group, have a nonDfinite generating function. Our approach allows us to recover and refine some known results, and also to obtain new
Walks in the quarter plane: Kreweras’ algebraic model
, 2004
"... We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j ≥ 0, and are made of three types of steps: NorthEast, West and South. These walks are known to have remarkable enumerative and probabilistic properties: – they are counted by nice numbers (Kreweras 1965), – t ..."
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Cited by 22 (6 self)
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We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j ≥ 0, and are made of three types of steps: NorthEast, West and South. These walks are known to have remarkable enumerative and probabilistic properties: – they are counted by nice numbers (Kreweras 1965), – the generating function of these numbers is algebraic (Gessel 1986), – the stationary distribution of the corresponding Markov chain in the quadrant has an algebraic probability generating function (Flatto and Hahn 1984). These results are not well understood, and have been established via complicated proofs. Here we give a uniform derivation of all of them, which is more elementary that those previously published. We then go further by computing the full law of the Markov chain. This helps to delimit the border of algebraicity: the associated probability generating function is no longer algebraic, unless a diagonal symmetry holds. Our proofs are based on the solution of certain functional equations, which are very simple to establish. Finding purely combinatorial proofs remains an open problem.
Computing Performance Bounds of ForkJoin Parallel Programs Under a Multiprocessing Environment
 IEEE TRANS. ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1998
"... We study a multiprocessing computer system which accepts parallel programs that have a forkjoin computational paradigm. The multiprocessing computer system under study is modeled as K homogeneous servers, each with an infinite capacity queue. Parallel programs arrive at the multiprocessing system a ..."
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Cited by 13 (1 self)
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We study a multiprocessing computer system which accepts parallel programs that have a forkjoin computational paradigm. The multiprocessing computer system under study is modeled as K homogeneous servers, each with an infinite capacity queue. Parallel programs arrive at the multiprocessing system according to a seriesparallel phase type interarrival process with mean arrival rate of l. Upon the program arrival, it forks into K independent tasks and each task is assigned to an unique server. Each task's service time has a kstage Erlang distribution with mean service time of 1/m. A parallel program is completed upon the completion of its last task. This kind of queuing model has no known closed form solution in the general (K # 2) case. In this paper, we show that by carefully modifying the arrival and service distributions at some imbedded points in time, we can obtain tight performance bounds. We also provide a computational efficient algorithm for obtaining upper and lower bounds o...
On the holonomy or algebraicity of generating functions counting lattice walks
 in the quarterplane. Markov Process. Related Fields
"... Abstract. In two recent works [1, 2], it has been shown that the counting generating functions (CGF) for the 23 walks with small steps confined in a quarterplane and associated with a finite group of birational transformations are holonomic, and even algebraic in 4 cases — in particular for the so ..."
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Cited by 11 (8 self)
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Abstract. In two recent works [1, 2], it has been shown that the counting generating functions (CGF) for the 23 walks with small steps confined in a quarterplane and associated with a finite group of birational transformations are holonomic, and even algebraic in 4 cases — in particular for the socalled Gessel’s walk. It turns out that the type of functional equations satisfied by these CGF appeared in a probabilistic context almost 40 years ago. Then a method of resolution was proposed in [4], involving at once algebraic techniques and reduction to boundary value problems. Recently this method has been developed in a combinatorics framework in [11], where a thorough study of the explicit expressions for the CGF is proposed. The aim of this paper is to derive the nature of the bivariate CGF by a direct use of some general theorems given in [4].
An Analytic Performance Model of Disk Arrays and its Applications
, 1991
"... 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 be ..."
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Cited by 10 (6 self)
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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 forkjoin 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
Bridges and networks: Exact asymptotics
 Annals of Applied Probability
, 2005
"... 607] to obtain the sharp asymptotics of the steady state probability of a queueing network when one of the nodes gets large. We focus on a new phenomenon we call a bridge. The bridge cases occur when ..."
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Cited by 7 (1 self)
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607] to obtain the sharp asymptotics of the steady state probability of a queueing network when one of the nodes gets large. We focus on a new phenomenon we call a bridge. The bridge cases occur when
Queueingtheoretic solution methods for models of parallel and distributed systems
 Performance Evaluation of Parallel and Distributed Systems Solution Methods. CWI Tract 105 & 106
, 1994
"... 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 solutio ..."
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Cited by 4 (3 self)
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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.