Online algorithms for prefetching and caching on parallel disks

Lecture Notes in Computer Science, 1998

We address the problem of I O scheduling of read-once reference strings in a multiple-disk parallel I O system. We present a n o vel online algorithm, Red-Black Prefetching RBP, for parallel I O scheduling. In order to perform accurate prefetching RBP uses L-block l o o k ahead. The performance of RBP is analyzed in the standard parallel disk model with D independent disks and a shared I O bu er of size M. W e show that the number of parallel I Os performed by RBP is within a factot maxf p M D = L ; D 1=3 g of the number of I Os done by the optimal oline algorithm. This ratio is within a canstant factor of the best possible when L is L = OM D 1=3 .

2000

High performance applications involving large data sets require the e cient and exible use of multiple disks. In an external memory machine with D parallel, independent disks, only one block can be accessed on each disk in one I/O step. This restriction leads to a load balancing problem that is perhaps the main inhibitor for the e cient adaptation of single-disk external memory algorithms to multiple disks. We solve this problem for arbitrary access patterns by randomly mapping blocks of a logical address space to the disks.

Information Processing Letters, 2019

The distributed multi-level multi-server paging problem (DMLMSP) defined in this paper extends and generalizes the classical distributed paging problem [3] to a distributed concurrent multi-level setting, in which multiple servers share caches at multiple levels. The DMLMSP can be used for modeling algorithms for efficient distributed storage systems, in which multiple servers use caches for accelerating access to a centralized storage, maintaining cache coherency across multiple nodes while minimizing access latency and optimizing cache-hit ratio. The DMLMSP model fits basic principles of Non-Uniform Cache Architectures (NUCAs) and can be used for analyzing multiple-level centralized storage. We present an optimal offline algorithm for the DMLMSP model, with minimum number of page faults and minimum makespan, whose time complexity is polynomial in the length of the servers' page request sequences. The new algorithm generalizes and simplifies the state of the art algorithms [3,1].

Parallel Computing, 2002

For the design and analysis of algorithms that process huge data sets, a machine model is needed that handles parallel disks. There seems to be a dilemma between simple and flexible use of such a model and accurate modeling of details of the hardware. This paper explains how many aspects of this problem can be resolved. The programming model implements one large logical disk allowing concurrent access to arbitrary sets of variable size blocks. This model can be implemented efficiently on multiple independent disks even if zones with different speed, communication bottlenecks and failed disks are allowed. These results not only provide useful algorithmic tools but also imply a theoretical justification for studying external memory algorithms using simple abstract models. The algorithmic approach is random redundant placement of data and optimal scheduling of accesses. The analysis generalizes a previous analysis for simple abstract external memory models in several ways (higher efficiency, variable block sizes, more detailed disk model).

1996

AbstractÐThe I/O performance of applications in multiple-disk systems can be improved by overlapping disk accesses. This requires the use of appropriate prefetching and buffer management algorithms that ensure the most useful blocks are accessed and retained in the buffer. In this paper, we answer several fundamental questions on prefetching and buffer management for distributed-buffer parallel I/O systems. First, we derive and prove the optimality of an algorithm, P-min, that minimizes the number of parallel I/Os. Second, we analyze P-con, an algorithm that always matches its replacement decisions with those of the well-known demand-paged MIN algorithm. We show that P-con can become fully sequential in the worst case. Third, we investigate the behavior of on-line algorithms for multiple-disk prefetching and buffer management. We define and analyze P-lru, a parallel version of the traditional LRU buffer management algorithm. Unexpectedly, we find that the competitive ratio of P-lru ...

ACM Transactions on Algorithms, 2009

We study an optimization problem that arises in the context of data placement in multimedia storage systems. We are given a collection of M multimedia data objects that need to be assigned to a storage system consisting of N disks d 1 ,d 2 ,...,d N. We are also given sets U 1 ,U 2 ,...,U M such that U i is the set of clients requesting the ith data object. Each disk d j is characterized by two parameters, namely, its storage capacity C j which indicates the maximum number of data objects that may be assigned to it, and a load capacity L j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data objects on disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system. We study this data placement problem for two natural classes of storage systems, namely, homogeneous and uniform ratio. Our first main result is a tight upper and lower bound on the number of items that can always be packed for any input instance to homogeneous as well as uniform ratio storage systems. We show that an algorithm given in [11] for data placement, achieves this bound. Our second main result is a polynomial time approximation scheme for the data placement problem in homogeneous and uniform ratio storage systems, answering an open question of [11]. Finally, we also study the problem from an empirical perspective. Comments Comments Postprint version.

IEEE Transactions on Computers, 2003

Random redundant data storage strategies have proven to be a good choice for efficient data storage in multimedia servers. These strategies lead to a retrieval problem in which it is decided for each requested data block which disk to use for its retrieval. In this paper, we give a complexity classification of retrieval problems for random redundant storage. Index Terms-Random redundant storage, load balancing, video servers, complexity analysis. ae 1 INTRODUCTION A multimedia server [13] offers continuous streams of multimedia data to multiple users. In a multimedia server, one can generally distinguish three parts: an array of hard disks to store the data, an internal network, and fast memory used for buffering. The latter is usually implemented in random access memory (RAM). The multimedia data is stored on the hard disks in blocks such that a data stream is realized by periodically reading a block from disk and storing it in the buffer, from which the stream can be consumed in a continuous way. A block generally contains a couple of hundred milliseconds of video data. The total buffer space is split up into a number of buffers, one for each user. A user consumes, possibly at a variable bit rate, from his/her buffer and the buffer is repeatedly refilled with blocks from the hard disks. A buffer generates a request for a new block as soon as the amount of data in the buffer becomes smaller than a certain threshold. We assume that requests are handled periodically in batches, in a way that the requests that arrive in one period are serviced in the next one [16]. In the server, we need a cost-efficient storage and retrieval strategy that guarantees, either deterministically or probabilistically, that the buffers do not underflow or overflow. Load balancing is very important within a multimedia server, as efficient usage of the available bandwidth of the disk array increases the maximum number of users that can be serviced simultaneously, which results in lower cost per user. Random redundant storage strategies have proven to enable a good load balancing performance [1], [3], [15], [23]. In these storage strategies, each data block is stored more than once, on different, randomly chosen disks. This data redundancy gives the freedom to obtain a balanced load with high probability. To exploit this freedom, an algorithm is needed to solve, in each period, a retrieval problem, i.e., we have to decide, for each data block, from which disk(s) to retrieve it in such a way that the load is balanced.

IEEE Transactions on Computers, 1991

Disk interleaving, or disk striping, distributes a data block across a group of disks and allows parallel transfer of data. Disk interleaving is achieved by dividing a data block into a number of subblocks and placing each subblock on a separate disk. A subblock can be stored on an interleaved disk at a predetermined location (relative to the adjacent subblocks), or it can be stored at any location on the disk. We consider a system where adjacent subblocks are placed independently of each other, we call it an asynchronous disk interleaving system, and analyze its performance implications. Since each of the disks in such a system is treated independently while being accessed as a group, the access delay of a request for a data block in an n-disk system is the maximum of n access delays. Using approximate analysis, we obtain a simple expression for the expected value of such a maximum delay. The analytic approximation is verified by simulation using trace data, the relative error is found to be at most 6%.

1997

We consider the problem of sorting a file of N records on the D-disk model of parallel I/O in which there are two sources of parallelism. Records are transferred to and from disk concurrently in blocks of B contiguous records. In each I/O operation, up to one block can be transferred to or from each of the D disks in parallel. We propose a simple, efficient, randomized mergesort algorithm called SRM that uses a forecast-and-flush approach to overcome the inherent difficulties of simple merging on parallel disks. SRM exhibits a limited use of randomization and also has a useful deterministic version. Generalizing the technique of forecasting, our algorithm is able to read in, at any time, the "right" block from any disk, and using the technique of flushing, our algorithm evicts, without any I/O overhead, just the "right" blocks from memory to make space for new ones to be read in. The disk layout of SRM is such that it enjoys perfect write parallelism, avoiding fundamental inefficiencies of previous mergesort algorithms. By analysis of generalized maximum occupancy problems we are able to derive an analytical upper bound on SRM's expected overhead valid for arbitrary inputs. The upper bound derived on expected I/O performance of SRM indicates that SRM is provably better than disk-striped mergesort (DSM) for realistic parameter values D, M , and B. Average-case simulations show further improvement on the analytical upper bound. Unlike previously proposed optimal sorting algorithms, SRM outperforms DSM even when the number D of parallel disks is small.

Computing, 1978

A Performance Model for Preplanned Disk Sorting. The idea of preplanning strings on disks which are merged together is investigated from a performance point of view. Schemes of internal buffer allocation, initial string creation by an internal sort, and string distribution on disks are evaluated. An algorithm is given for the construction of suboptimal merge trees called plannable merge trees. A cost model is presented for accurate preplanning which consists of detailed assumptions on disk allocation for k input disks and r-way merge planning. Timing considerations for sort and merge including hardware characteristics of moveable head disks show a significant gain of time compared to widely used sort/merge applications. Leistungsanalyse beim vorgeplanten Sortieren auf Magnctplatten. Der Ansatz, Strings, die zusammengemischt werden, auf Magnetplatten vorzuplanen, wird unter Leistungsgesichtspunkten untersucht. Konzepte far die interne Pufferzuordnung, fiir die Erzeugung der anf'finglichen Strings dutch ein internes Sortierveffahren, und ffir die Stringverteilung auf Magnetplatten werden ansgewertet. Ein Algorithmns besehreibt die Konstruktion yon suboptimalen Mischb/iumen, die planbare Mischbgiume genannt werden. Ein Kostenmodell, das auf detaillierte Annahmen der Zuordnung yon k Eingabeplatten und der Planung eines r-Wege-Misehens beruht, wird far das exakte Vorplanen aufgestellt. Zeitbetrachtungen for Sortieren und Mischen, die Hardware-Eigenschaften yon Magnetplatten einschlieBen, zeigen signifikante Zeitgewinne verglichen mit weitverbreiteten Sortier-and Mischverfabren.