Relative Interval Analysis of Paging Algorithms on Access Graphs

Access graphs, which have been used previously in connection with competitive analysis and relative worst order analysis to model locality of reference in paging, are considered in connection with relative interval analysis. The algorithms LRU, FIFO, FWF, and FAR are compared using the path, star, and cycle access graphs. In this model, some of the expected results are obtained. However, although LRU is found to be strictly better than FIFO on paths, it has worse performance on stars, cycles, and complete graphs, in this model. We solve an open question from [Dorrigiv, Lopez-Ortiz, Munro, 2009], obtaining tight bounds on the relationship between LRU and FIFO with relative interval analysis.Comment: IMADA-preprint-c

Distributed Selfish Coaching

Although cooperation generally increases the amount of resources available to a community of nodes, thus improving individual and collective performance, it also allows for the appearance of potential mistreatment problems through the exposition of one node's resources to others. We study such concerns by considering a group of independent, rational, self-aware nodes that cooperate using on-line caching algorithms, where the exposed resource is the storage at each node. Motivated by content networking applications -- including web caching, CDNs, and P2P -- this paper extends our previous work on the on-line version of the problem, which was conducted under a game-theoretic framework, and limited to object replication. We identify and investigate two causes of mistreatment: (1) cache state interactions (due to the cooperative servicing of requests) and (2) the adoption of a common scheme for cache management policies. Using analytic models, numerical solutions of these models, as well as simulation experiments, we show that on-line cooperation schemes using caching are fairly robust to mistreatment caused by state interactions. To appear in a substantial manner, the interaction through the exchange of miss-streams has to be very intense, making it feasible for the mistreated nodes to detect and react to exploitation. This robustness ceases to exist when nodes fetch and store objects in response to remote requests, i.e., when they operate as Level-2 caches (or proxies) for other nodes. Regarding mistreatment due to a common scheme, we show that this can easily take place when the "outlier" characteristics of some of the nodes get overlooked. This finding underscores the importance of allowing cooperative caching nodes the flexibility of choosing from a diverse set of schemes to fit the peculiarities of individual nodes. To that end, we outline an emulation-based framework for the development of mistreatment-resilient distributed selfish caching schemes. Our framework utilizes a simple control-theoretic approach to dynamically parameterize the cache management scheme. We show performance evaluation results that quantify the benefits from instantiating such a framework, which could be substantial under skewed demand profiles.National Science Foundation (CNS Cybertrust 0524477, CNS NeTS 0520166, CNS ITR 0205294, EIA RI 0202067); EU IST (CASCADAS and E-NEXT); Marie Curie Outgoing International Fellowship of the EU (MOIF-CT-2005-007230

Effective And Efficient Preemption Placement For Cache Overhead Minimization In Hard Real-Time Systems

Schedulability analysis for real-time systems has been the subject of prominent research over the past several decades. One of the key foundations of schedulability analysis is an accurate worst case execution time (WCET) for each task. In preemption based real-time systems, the CRPD can represent a significant component (up to 44% as documented in research literature) of variability to overall task WCET. Several methods have been employed to calculate CRPD with significant levels of pessimism that may result in a task set erroneously declared as non-schedulable. Furthermore, they do not take into account that CRPD cost is inherently a function of where preemptions actually occur. Our approach for computing CRPD via loaded cache blocks (LCBs) is more accurate in the sense that cache state reflects which cache blocks and the specific program locations where they are reloaded. Limited preemption models attempt to minimize preemption overhead (CRPD) by reducing the number of allowed preemptions and/or allowing preemption at program locations where the CRPD effect is minimized. These algorithms rely heavily on accurate CRPD measurements or estimation models in order to identify an optimal set of preemption points. Our approach improves the effectiveness of limited optimal preemption point placement algorithms by calculating the LCBs for each pair of adjacent preemptions to more accurately model task WCET and maximize schedulability as compared to existing preemption point placement approaches. We utilize dynamic programming technique to develop an optimal preemption point placement algorithm. Lastly, we will demonstrate, using a case study, improved task set schedulability and optimal preemption point placement via our new LCB characterization. We propose a new CRPD metric, called loaded cache blocks (LCB) which accurately characterizes the CRPD a real-time task may be subjected to due to the preemptive execution of higher priority tasks. We show how to integrate our new LCB metric into our newly developed algorithms that automatically place preemption points supporting linear control flow graphs (CFGs) for limited preemption scheduling applications. We extend the derivation of loaded cache blocks (LCB), that was proposed for linear control flow graphs (CFGs) to conditional CFGs. We show how to integrate our revised LCB metric into our newly developed algorithms that automatically place preemption points supporting conditional control flow graphs (CFGs) for limited preemption scheduling applications. For future work, we will verify the correctness of our framework through other measurable physical and hardware constraints. Also, we plan to complete our work on developing a generalized framework that can be seamlessly integrated into real-time schedulability analysis

Paging with Dynamic Memory Capacity

We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors. It turns out that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space and time, and suboptimality by an arbitrarily large factor. More precisely, adopting the competitive analysis framework, we show that some online paging algorithms, despite having an optimal (h,k)-competitive ratio when capacity remains constant, are not (3,k)-competitive for any arbitrarily large k in the presence of minimal capacity fluctuations. In this light it is surprising that several classic paging algorithms perform remarkably well even if memory capacity changes adversarially - in fact, even without taking those changes into explicit account! In particular, we prove that LFD still achieves the minimum number of faults, and that several classic online algorithms such as LRU have a "dynamic" (h,k)-competitive ratio that is the best one can achieve without knowledge of future page requests, even if one had perfect knowledge of future capacity fluctuations. Thus, with careful management, knowing/predicting future memory resources appears far less crucial to performance than knowing/predicting future data accesses. We characterize the optimal "dynamic" (h,k)-competitive ratio exactly, and show it has a somewhat complex expression that is almost but not quite equal to the "classic" ratio k/(k-h+1), thus proving a strict if minuscule separation between online paging performance achievable in the presence or absence of capacity fluctuations

Response-time analysis for fixed-priority systems with a write-back cache

This paper introduces analyses of write-back caches integrated into response-time analysis for fixed-priority preemptive and non-preemptive scheduling. For each scheduling paradigm, we derive four different approaches to computing the additional costs incurred due to write backs. We show the dominance relationships between these different approaches and note how they can be combined to form a single state-of-the-art approach in each case. The evaluation explores the relative performance of the different methods using a set of benchmarks, as well as making comparisons with no cache and a write-through cache. We also explore the effect of write buffers used to hide the latency of write-through caches. We show that depending upon the depth of the buffer used and the policies employed, such buffers can result in domino effects. Our evaluation shows that even ignoring domino effects, a substantial write buffer is needed to match the guaranteed performance of write-back caches

Alternative Measures for the Analysis of Online Algorithms

In this thesis we introduce and evaluate several new models for the analysis of online algorithms. In an online problem, the algorithm does not know the entire input from the beginning; the input is revealed in a sequence of steps. At each step the algorithm should make its decisions based on the past and without any knowledge about the future. Many important real-life problems such as paging and routing are intrinsically online and thus the design and analysis of online algorithms is one of the main research areas in theoretical computer science. Competitive analysis is the standard measure for analysis of online algorithms. It has been applied to many online problems in diverse areas ranging from robot navigation, to network routing, to scheduling, to online graph coloring. While in several instances competitive analysis gives satisfactory results, for certain problems it results in unrealistically pessimistic ratios and/or fails to distinguish between algorithms that have vastly differing performance under any practical characterization. Addressing these shortcomings has been the subject of intense research by many of the best minds in the field. In this thesis, building upon recent advances of others we introduce some new models for analysis of online algorithms, namely Bijective Analysis, Average Analysis, Parameterized Analysis, and Relative Interval Analysis. We show that they lead to good results when applied to paging and list update algorithms. Paging and list update are two well known online problems. Paging is one of the main examples of poor behavior of competitive analysis. We show that LRU is the unique optimal online paging algorithm according to Average Analysis on sequences with locality of reference. Recall that in practice input sequences for paging have high locality of reference. It has been empirically long established that LRU is the best paging algorithm. Yet, Average Analysis is the first model that gives strict separation of LRU from all other online paging algorithms, thus solving a long standing open problem. We prove a similar result for the optimality of MTF for list update on sequences with locality of reference. A technique for the analysis of online algorithms has to be effective to be useful in day-to-day analysis of algorithms. While Bijective and Average Analysis succeed at providing fine separation, their application can be, at times, cumbersome. Thus we apply a parameterized or adaptive analysis framework to online algorithms. We show that this framework is effective, can be applied more easily to a larger family of problems and leads to finer analysis than the competitive ratio. The conceptual innovation of parameterizing the performance of an algorithm by something other than the input size was first introduced over three decades ago [124, 125]. By now it has been extensively studied and understood in the context of adaptive analysis (for problems in P) and parameterized algorithms (for NP-hard problems), yet to our knowledge this thesis is the first systematic application of this technique to the study of online algorithms. Interestingly, competitive analysis can be recast as a particular form of parameterized analysis in which the performance of opt is the parameter. In general, for each problem we can choose the parameter/measure that best reflects the difficulty of the input. We show that in many instances the performance of opt on a sequence is a coarse approximation of the difficulty or complexity of a given input sequence. Using a finer, more natural measure we can separate paging and list update algorithms which were otherwise indistinguishable under the classical model. This creates a performance hierarchy of algorithms which better reflects the intuitive relative strengths between them. Lastly, we show that, surprisingly, certain randomized algorithms which are superior to MTF in the classical model are not so in the parameterized case, which matches experimental results. We test list update algorithms in the context of a data compression problem known to have locality of reference. Our experiments show MTF outperforms other list update algorithms in practice after BWT. This is consistent with the intuition that BWT increases locality of reference