Paging Algorithms Research Articles

Distributed Paging for General Networks

Distributed pagingdeals with the dynamic allocation of copies of files in a distributed network as to minimize the total communication cost over a sequence of read and write requests.Most previous work deals with thefile allocationproblem, where infinite nodal memory capacity is assumed. In contrast the distributed paging problem makes the more realistic assumption that nodal memory capacity is limited. Former work on distributed paging deals with the problem only in the case of a uniform network topology.This paper gives the first distributed paging algorithm forgeneralnetworks. The algorithm is competitive in storage and communication. The competitive rates are poly-logarithmic in the total number of network nodes and the diameter of the network.

On paged distributed virtual memory algorithms in a broadcasting environment

Advances in network and processor technology have improved and increased the performance of distributed virtual memory systems in recent years. Remote memory access is considered as a faster-than-disk memory level and has strongly influenced research in distributed virtual memory management. Moreover, the broadcasting transmission nature commonly used in todays LAN provides a simplified environment for paging purposes. In this paper, we show that remote memory paging in distributed virtual memory systems are significantly faster than traditional disk paging. Then through simulation, we compare the performance of two different systems, distributed virtual memory and dedicated memory systems. Distributed virtual memory systems provide significant performance improvement with relatively less cost and no extra hardware than dedicated memory systems. Also, we describe and evaluate several remote memory paging algorithms, the best of which is called the class priority algorithm.

A simple analytical framework for location management in personal communication systems

Efficient mobility management for portable stations (PS's)-handoff, channel assignment and locating-will play an important role in future personal communication systems (PCS's). Among these tasks, location management plays a critical role for wide-area roaming. The key elements of locating are location registration/updating and paging. Due to the smaller cell size in PCS, the high boundary crossing rate of PS will result in more frequent location area (LA) updating. This, in turn, will result in more interrogations with location registers, which will generate a higher volume of access and signaling traffic (SS7 traffic). One solution to this problem is to increase the size of LA, which, unfortunately, also increases paging traffic. Efficient paging algorithms may generate relatively less paging traffic such that larger LA's may become plausible. Depending on the call-arrival rate to the cell, boundary crossing rate, optimum size of LA, and paging technique used, the overall cost could vary substantially. The paging techniques considered in this paper are simultaneous paging and sequential paging. The two schemes are studied in detail in order to understand the problems associated with location management in the PCS environment. In the authors' opinion, this paper provides, for the first time, a simple yet powerful analytical framework which can be used to analyze intelligent paging schemes as well as simultaneous and sequential paging.

On the Influence of Lookahead in Competitive Paging Algorithms

We introduce a new model of lookahead for on-line paging algorithms and study several algorithms using this model. A paging algorithm is n-line with strong lookahead l if it sees the present request and a sequence of future requests that contains l pairwise distinct pages. We show that strong lookahead has practical as well as theoretical importance and improves the competitive factors of on-line paging algorithms. This is the first model of lookahead having such properties. In addition to lower bounds we present a number of deterministic and randomized on-line paging algorithms with strong lookahead which are optimal or nearly optimal.

Out-of-core streamline visualization on large unstructured meshes

This paper presents an out-of-core approach for interactive streamline construction on large unstructured tetrahedral meshes containing millions of elements. The out-of-core algorithm uses an octree to partition and restructure the raw data into subsets stored into disk files for fast data retrieval. A memory management policy tailored to the streamline calculations is used such that, during the streamline construction, only a very small amount of data are brought into the main memory on demand. By carefully scheduling computation and data fetching, the overhead of reading data from the disk is significantly reduced and good memory performance results. This out-of-core algorithm makes possible interactive streamline visualization of large unstructured-grid data sets on a single mid-range workstation with relatively low main-memory capacity: 5-15 megabytes. We also demonstrate that this approach is much more efficient than relying on virtual memory and operating system's paging algorithms.

Strongly Competitive Algorithms for Paging with Locality of Reference

What is the best paging algorithm if one has partial information about the possible sequences of page requests? We give a partial answer to this question by presenting the analysis of strongly competitive paging algorithms in the access graph model. This model restricts page requests so that they conform to a notion of locality of reference given by an arbitrary access graph We first consider optimal algorithms for undirected access graphs. Borodin et al. [Proc. 23rd ACM Symposium on Theory of Computing, 1991, pp. 249–259] define an algorithm, called FAR, and prove that it is within a logarithmic factor of the optimal online algorithm. We prove that FAR is in fact strongly competitive, i.e, within a constant factor of the optimum. For directed access graphs, we present an algorithm that is strongly competitive on structured program graphs—graphs that model a subset of the request sequences of structured programs.

On Competitive On-Line Paging with Lookahead

This paper studies two methods for improving the competitive efficiency <br />of on-line paging algorithms: in the first, the on-line algorithm can<br />use more pages; in the second, it is allowed to have a look-ahead, or in<br />other words, some partial knowledge of the future. The paper considers a<br />new measure for the look-ahead size as well as Young's resource-bounded<br />look-ahead and proves that both measures have the attractive property<br />that the competitive efficiency of an on-line algorithm with k extra pages<br />and look-ahead l depends on k+l. Hence, under these measures, an on-line<br />algorithm has the same benefit from using an extra page or knowing an<br />extra bit of the future.

A proof of the optimality of the MIN paging algorithm using linear programming duality

A linear programming formulation of the page replacement problem is used for proving the optimality of the MIN algorithm in a novel way. We describe an algorithm for constructing a solution for the dual problem such that the cost of this solution equals the cost of the MIN solution for the primal problem, thus proving the optimality of the MIN solution for paging, and the optimality of our algorithm for the paging dual (which is a special case of the assignment dual).

Competitive Paging with Locality of Reference

The Sleator-Tarjan competitive analysis of paging (Comm. ACM28 (1985), 202-208) gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical comptitiveness of LRU is much larger than observed in practice, In addition, we would like to address the following important question: given some knowledge of a program′s reference pattern, can we use it to improve paging performance on that program? We address these concerns by introducing an important practical element that underlies the philosophy behind paging: locality of reference. We devise a graph-theoretical model, the access graph, for studying locality of reference. We use it to prove results that address the practical concerns mentioned above, In addition, we use our model to address the following questions: How well is LRU likely to perform on a given program? Is there a universal paging algorithm that achieves (nearly) the best possible paging performance on every program? We do so without compromising the benefits of the Sleator-Tarjan model, while bringing it closer to practice.

Thek-server dual and loose competitiveness for paging

This paper has two results. The first is based on the surprising observation that the well-known ``least-recently-used'' paging algorithm and the ``balance'' algorithm for weighted caching are linear-programming primal-dual algorithms. This observation leads to a strategy (called ``Greedy-Dual'') that generalizes them both and has an optimal performance guarantee for weighted caching. For the second result, the paper presents empirical studies of paging algorithms, documenting that in practice, on ``typical'' cache sizes and sequences, the performance of paging strategies are much better than their worst-case analyses in the standard model suggest. The paper then presents theoretical results that support and explain this. For example: on any input sequence, with almost all cache sizes, either the performance guarantee of least-recently-used is O(log k) or the fault rate (in an absolute sense) is insignificant. Both of these results are strengthened and generalized in``On-line File Caching'' (1998).

A transform from absorption to Raman excitation profile. A time-dependent approach

An alternative time-frame approach, which is canonically conjugate to the energy-frame approach, for implementing the transform relations for calculating Raman excitation profiles directly from the optical absorption spectrum is presented. Practical and efficient fast Fourier transformation in the time frame replaces the widely used Chan and Page algorithm for evaluating the Hilbert transform in the energy frame. The time-frame approach is applied to: (a) a two-mode model which illustrates the missing mode effect in both absorption and Raman excitation profiles, (b) carotene, in which both the absorption spectrum and the Raman excitation profile show vibrational structure and (c) hexamethylbenzene: TCNE electron donor—acceptor complex where the same spectra are structureless and the Raman excitation profile for the 168 cm −1 mode poses a problem for the energy-frame approach. A similar time-frame approach can be used for the inverse transform from the Raman excitation profile to the optical absorption spectrum.

Competitive paging algorithms

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2 H k of optimum. (Where H k is the kth harmonic number, which is roughly ln k.) The best such factor that can be achieved is H k . This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an on-line algorithm with the optimum off-line algorithm is the idea of comparing it to several other on-line algorithms. We have obtained results along these lines for the paging problem. Given a set of on-line algorithms and a set of appropriate constants, we describe a way of constructing another on-line algorithm whose performance is within the appropriate constant factor of each algorithm in the set.

A strongly competitive randomized paging algorithm

Thepaging problem is that of deciding which pages to keep in a memory ofk pages in order to minimize the number of page faults. We develop thepartitioning algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor ofH k of optimum. (H k is thekth harmonic number, which is about ln(k).) No on-line algorithm can perform better by this measure. Our result improves by a factor of two the best previous algorithm.

Page placement policies for NUMA multiprocessors

In many parallel applications, the size of the program's data exceeds even the very large amount of main memory available on large-scale multiprocessors. Virtual memory, in the sense of a transparent management of the main/secondary memory hierarchy, is a natural solution. The replacement, fetch, and placement policies used in uniprocessor paging systems need to be reexamined in light of the differences in the behavior of parallel computations and in the memory architectures of multiprocessors. In particular, we investigate the impact of page placement in nonuniform memory access time (NUMA) shared memory MIMD machines. We experimentally evaluate several paging algorithms that incorporate different approaches to the placement issue. Under certain workload assumptions, our results show that placement algorithms that are strongly biased toward local frame allocation but are able to borrow remote frames can reduce the number of page faults over strictly local allocation. The increased cost of memory operations due to the extra remote accesses is more than compensated for by the savings resulting from the reduction in demand fetches, effectively reducing the computation completion time for these programs without having adverse effects on the performance of “typical” NUMA programs. We also discuss some early results obtained from an actual kernel implementation of one of our page placement algorithms.

Optimal Concurrency Control Schedulers in Terms of Secondary Storage Access

AbstractConventional concurrency control schedulers are used to increase concurrency to avoid transaction rollbacks, and it is widely accepted that a scheduler is effective if it can provide more concurrency. However, transaction rollbacks seldom occur in a practical transaction processing system. The performance of a scheduler should be evaluated by how efficient a schedule it can generate in such a situation. We select the number of secondary storage accesses to process a given schedule as such an efficient criterion.A schedule is regarded as a page reference string and the memory cost of the schedule is defined by the cost to process the schedule by an optimal paging algorithm. Then we consider the minimum memory cost scheduling problem for a given set of transactions. The problem is shown to be NP hard in the general case. Thus we turn our attention to: (1) a restriction of the transaction model to construct an optimal schedule in a linear time; and (2) a nearly optimal solution to the given problem under a general transaction model. The nearly optimal scheduling problem is shown to be rather difficult.

Transience des chaines de Markov lineaires sur les permutations

Computer scientists have introduced ‘paging algorithms' which are a special class of Markov chains on permutations known, in probability theory, as ‘libraries': books being placed on a shelf T (T is an infinite interval of the set Z of the integers) and a policy ρ : T → T such that ρ (t) < t being chosen, a book b placed at t ∊ T is selected with probability pb, it is removed and replaced at ρ (t) prior to next removal. The different arrangements of books on the shelf are the states of the Markov chain. In this paper we prove that, if the shelf is not bounded on the left, any library (i.e. for any policy ρ and any probability ρ on the books) is transient.

Transience des chaines de Markov lineaires sur les permutations

Computer scientists have introduced ‘paging algorithms' which are a special class of Markov chains on permutations known, in probability theory, as ‘libraries': books being placed on a shelf T (T is an infinite interval of the set Z of the integers) and a policy ρ : T → T such that ρ (t) < t being chosen, a book b placed at t ∊ T is selected with probability pb , it is removed and replaced at ρ (t) prior to next removal. The different arrangements of books on the shelf are the states of the Markov chain. In this paper we prove that, if the shelf is not bounded on the left, any library (i.e. for any policy ρ and any probability ρ on the books) is transient.

Amortized efficiency of list update and paging rules

In this article we study the amortized efficiency of the “move-to-front” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the ith element from the front of the list takes θ(i) time, we show that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules. Other natural heuristics, such as the transpose and frequency count rules, do not share this property. We generalize our results to show that move-to-front is within a constant factor of optimum as long as the access cost is a convex function. We also study paging, a setting in which the access cost is not convex. The paging rule corresponding to move-to-front is the “least recently used” (LRU) replacement rule. We analyze the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule (Belady's MIN algorithm) by a factor that depends on the size of fast memory. No on-line paging algorithm has better amortized performance.

An application of a grouping procedure to a multi-item production system

Abstract In this paper a problem of multi-item production on a single facility is being dealt with. The facility is an electrochemical machining (ECM) system and the products are impact sockets of various sizes for power wrenches. Sequencing production lots in a certain order minimizes set-up time for each new production lot. However, as demand differs from item to item, it is not essential to produce each item in every production cycle. A grouping procedure of the various items is adopted. A modified version of the Page and Paul algorithm is then applied to insure production cycle times which are multiples of the shortest production cycle time. Application of a sequencing policy based on this modified algorithm led to considerable savings

Program behavior prediction and prepaging

The design and evaluation of a prepaging technique is presented. It consists in the preloading, at instants at which page-faults occur, of those pages whose use in the future is the most likely. These pages are determined as a function of an a-priori knowledge of program behavior. We shall first present two tools for predicting that behavior. The first is based on a Markov memory reference transition model, the second on a semi-Markov model of page-fault transitions. Both methods are successively experimented by a paging algorithm allowing prepaging. Experimentation shows that prepaging can significantly improve the performance of the paging algorithm, especially when the prediction is based on the transitions between page-faults. The sensitivity of prepaging performance to various working conditions is tested. Implementation of prepaging is examined and is shown to be feasible without the use of special hardware devices. The study is completed by an evaluation of the influence of prepaging on global system performance. Some common cases of system architecture experimentation show a non-negligible increase in CPU utilization.