On the worst-case ratio of a compound multiprocessor scheduling algorithm

The basic problem of nonpreemptive scheduling of independent tasks on identical processors is studied. The well-known heuristics LPT and Multifit are combined to an algorithm Mix which has a better worst-case ratio than each of its components. Exact ratios for the case of two and three processors are given.     

Robust performance with fixed and worst-case signals for uncertain time-varying systems

In this paper we focus our attention on the determination of upper bounds of the l^∞ norm of the output of a linear discrete-time dynamic system driven by a step input, in the presence of both persistent unknown, but, l^∞ bounded disturbances and memoryless time-varying model uncertainty. For the same type of systems we also analyze the transient behavior of the step response in terms of its overshoot. The problem is solved in a constructive way by determining appropriate invariant sets contained in a given convex region. Finally, we show how to extend these results to continuous-time systems.     

Tight performance bounds in the worst-case analysis of feed-forward networks

Network Calculus theory aims at evaluating worst-case performances in communication networks. It provides methods to analyze models where the traffic and the services are constrained by some minimum and/or maximum envelopes (arrival/service curves). While new applications come forward, a challenging and inescapable issue remains open: achieving tight analyzes of networks with aggregate multiplexing. The theory offers efficient methods to bound maximum end-to-end delays or local backlogs. However as shown in a recent breakthrough paper (Schmitt et al. 2008), those bounds can be arbitrarily far from the exact worst-case values, even in seemingly simple feed-forward networks (two flows and two servers), under blind multiplexing (i.e. no information about the scheduling policies, except FIFO per flow). For now, only a network with three flows and three servers, as well as a tandem network called sink tree, have been analyzed tightly.We describe the first algorithm which computes the maximum end-to-end delay for a given flow, as well as the maximum backlog at a server, for any feed-forward network under blind multiplexing, with piecewise affine concave arrival curves and piecewise affine convex service curves. Its computational complexity may look expensive (possibly super-exponential), but we show that the problem is intrinsically difficult (NP-hard). Fortunately we show that in some cases, like tandem networks with cross-traffic interfering along intervals of servers, the complexity becomes polynomial. We also compare ourselves to the previous approaches and discuss the problems left open.     

On upper bounds on worst-case H 2 performance obtained with dynamic multipliers

In this note, an iterative procedure is presented for obtaining a decreasing sequence of upper bounds on the worst-case H ₂ performance of a given stabilizing controller in the presence of normalized coprime-factor perturbations. To obtain such bounds, a descent procedure is introduced for a dual Lagrangean functional which gives upper bounds on the worst-case H ₂ performance index and is defined on the set of real-rational and non-negative functions (dynamic multipliers). Specific ways are presented for selecting feasible and descent directions in this set and lower bounds are derived for the corresponding decreases on the dual functional. At any step, the dynamics of the current multiplier gives rise to a linear class over which the optimization of the dual functional is shown to be equivalent to linear optimization subject to linear matrix inequalities (LMI). This allows for a combination of function space and LMI techniques in the process of obtaining increasingly tighter upper bounds on worst-case H ₂ performance, as illustrated in a numerical example.     

Projecting on-time performance for deterministic schedules in dynamic environments

Manufacturing in a world class environment demands a high level of customer service. The production control department is responsible for achieving this high level of service through accurate planning and scheduling. The ability to achieve such a high level of customer service is limited by the scheduling tools currently available. Production planning is typically performed using MRP infinite capacity, fixed lead-time, backward scheduling. The work in each MRP time-bucket is then sequenced to develop a schedule. The production floor however, is not a static environment. Dynamic events, that cannot be scheduled, degrade production performance relative to the projected schedule. In this paper the relationship between dynamic events and schedule degradation is examined. Common approaches to production scheduling underestimate the effect of capacity loading relative to unplanned events and schedule achievability. These dynamic events exhaust capacity previously allocated to production orders. To hedge against such known, but unscheduled events, production control can schedule resources to a level less than full capacity. The size of the capacity hedge and the duration of the unplanned event dictate the time to recover from the backlog created by these dynamic events. A performance metric is developed to measure the ability to achieve customer promise dates. A machine loading policy is also presented to achieve the optimal capacity hedge point that will maximize this performance measure. The results are compared to simulated failures to examine the accuracy of the predicted performance degradation. The results suggest a trade-off of throughput for improved performance to customer promise date.     

Expected and worst-case storage requirements for quadtrees

The expected and worst-case numbers of nodes required for the quadtree representation of curves or regions are investigated. It is shown that in both cases the numbers are roughly proportional to the number of pixels in the curve or the boundary of the region, but that the worst case-storage requirements are at least 2 √2 times the size of the expected storage requirements, provided some reasonable assumptions are made.     

Minimizing worst-case and average-case makespan over scenarios

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all scenarios in an explicitly given set. Each scenario is a subset of jobs that must be executed in that scenario. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. We also consider some (easier) special cases. Combinatorial optimization problems under scenarios in general, and scheduling problems under scenarios in particular, have seen only limited research attention so far. With this paper, we make a step in this interesting research direction.     

On the structure and complexity of worst-case equilibria

In the resource allocation game introduced by Koutsoupias and Papadimitriou, n$n$ jobs of different weights are assigned to m$m$ identical machines by selfish agents. For this game, it has been conjectured by several authors that the fully mixed Nash equilibrium (FMNE) is the worst possible w.r.t. the expected maximum load over all machines. Assuming the validity of this conjecture, computing a worst-case Nash equilibrium for a given instance was trivial, and approximating the Price of Anarchy for this instance would be possible by approximating the expected social cost of the FMNE by applying a known FPRAS.     

Combining static worst-case timing analysis and program proof

This paper describes SPATS—a new toolset for the development of safety-critical and hard real-time systems. SPATS integrates the analysis traditionally offered by program proof and static timing analysis tools through analysis of program basic-path graphs. This paper concentrates on SPATS' facilities for high-level static timing analysis and analysis of worst-case stack usage. The integration of timing analysis and program proof allows timing analysis to be performed where worst-case execution time (WCET) depends on a program's input data, and allows timing annotations to be formally verified. The approach is developed and illustrated with a worked example. The implementation and experimental application of SPATS to realistic industrial case-studies are also described. We conclude that SPATS offers a novel new approach to static timing analysis, offers several new analyses not seen in previous systems, and can be implemented in a useful and efficient toolset.This work was completed while Rod Chapman was with the Dependable Computing Systems Centre at the University of York.     

Improving the worst-case performance of the Hunt-Szymanski strategy for the longest common subsequence of two strings

Among the algorithms set up to date for finding the longest common subsequence of two strings, the one by Hunt and Szymanski exhibits the best known performance in favorable cases, but can be worse than any straightforward algorithm for a large variety of inputs. The new algorithm presented here pursues a schedule of primitive operations quite close to the one inherent to the Hunt-Szymanski strategy, but with substantially enhanced efficiency. In fact, the new algorithm improves on the former in two important respects. First, its worst case is never worse than linear in the product nm of the lengths of the two input strings. Second, its time bound does not always grow with the cardinality r of the set R of all pairs of matching positions of the input strings. Rather, it depends on the cardinality d of a specific subset of R, whose elements are called here dominant matches, and are elsewhere referred to as minimal candidates. This second improvement also appears of significance, since it seems that whenever r gets too close to mn, this forces d to be linear in m. The new algorithm requires standard preprocessing, and makes use of finger-trees. In a forthcoming paper, it will be shown among other things that the same performance can be achieved with simpler and handier auxiliary data structures.     

Generalized worst-case bounds for an homogeneous multiprocessor model with independent memories—Completion time performance criterion

This paper deals with the performance of the Priority-Driven scheduling algorithm, under various preset ordering rules, on a homogeneous multiprocessor computing model with independent memories. The performance criterion used is the completion time of the schedules. For each ordering rule we prove informative worst-case bounds that generalize the ones derived earlier by D.G. Kafura and V.Y. Shen.     

On the performance of transputer arrays for dense linear systems

In this paper, computation and communication performance is evaluated for single and multitransputer arrays. Performance models are proposed for Occam program execution, under Transputer Development System TDS2. The performance features of normalised arithmetic, concurrent floating and integer arithmetic, logarithmic array indexing, and on-chip/off-chip RAM are studied. The startup time, byte transfer rate, asymptotic link bandwidth, and half performance message length are estimated for simultaneous operation of one, two, three, and four links at 10/20 MHz clock in unidirectional/bidirectional modes. The impact of various performance maximisation techniques on execution time is also addressed.

The matrix factorisation algorithms for dense linear systems are chosen as the focus for this study. The implementations include LUD, Householder, Gauss-Jordan, Choleski, and Givens methods. Floating point operations count alone is inadequate to estimate computation time; many other factors such as array indexing, load/store overhead, and loop overhead play a significant role in the transouter performance for the dense linear systems. The reduction in array indexing overheads in multitransputer arrays may result in superlinear speedups.     

密集WiFi网络环境网络分配矢量优化与性能分析

IEEE 802.11协议利用RTS/CTS帧交换来设置设备的网络分配矢量(NAV)。现有NAV方案未考虑密集部署场景,可能存在误清除的情况。提出一种简便可行的可计数NAV(C-NAV)设置方案,通过统计NAV设置信息的个数并进行实时更新以防止误清除,从而更有效地利用传输机会。对所提C-NAV方案进行了理论分析和仿真验证,证明在密集部署WiFi场景中,该方案能有效避免现有设置方案NAV时长浪费和错误清除等问题,提升网络的整体吞吐量。     

A measure of worst-case H∞ performance and of largest acceptable uncertainty

The structured singular value (SSV or μ) is known to be an effective tool for assessing robust performance of linear time-invariant models subject to structured uncertainty. Yet all single μ analysis provides is a bound β on the uncertainty under which stability as well as H_∞ performance level of κ/β are guaranteed, where κ is preselectable. In this paper, we introduce a related quantity ν which provides answers for the following questions: (i) given β, determine the smallest with the property that, for any uncertainty bounded by β, an H∞ performance level of is guaranteed; (ii) conversely, given , determined the largest β with the property that, again, for any uncertainty bounded by β, an H_∞ performance level of is guaranteed. Properties of this quantity are established and approaches to its computation are investigated. Both unstructured uncertainty and structured uncertainty are considered.     

Automatic performance tuning using the ATMathCoreLib tool: Two experimental studies related to dense symmetric eigensolvers

We consider automatic performance tuning of dense symmetric eigenvalue problems using ATMathCoreLib, which is a library to assist automatic tuning. We deal with two problems, namely, automatic code selection for the symmetric generalized eigenvalue problem in distributed-memory parallel environments and automatic parameter tuning in tridiagonalization of dense symmetric matrices on multicore processors. As for the first problem, numerical experiments show that ATMathCoreLib can choose the fastest solver for a given computing environment and problem size quickly even if the fluctuation in the execution time is as high as 40%. As for the second problem, ATMathCoreLib was able to select nearly optimal combinations of the algorithm and its parameter reliably and efficiently for various computing environments and matrix sizes. The performance of auto-tuning was further enhanced by incorporating a user-provided execution-time model into ATMathCoreLib.     

State-based scheduling with tree schedules: analysis and evaluation

Distributed real-time systems require bounded communication delays and achieve them by means of a predictable and verifiable control mechanism for the communication medium. Real-time bus arbitration mechanisms control access to the medium and guarantee bounded communication delays. These arbitration mechanisms can be static dispatch tables or dynamic, algorithmic approaches. In this work, we introduce a real-time bus arbitration mechanism called tree schedules that takes the best parts of both sides: It can be analyzed like static dispatch tables, and it provides a certain degree of flexibility similar to algorithmic approaches. We present tree schedules as a framework to specify real-time traffic and introduce mechanisms to analyze it. We discuss how tree schedules can capture application-specific behavior in a time-triggered state-based supply model by means of conditional branching built into the model. We present analysis results for this model specifically aiming at schedulability in fixed and dynamic priority schemes and waiting time analysis. Finally, we demonstrate the advantages of state-based supply over stateless supply by means of two case studies.