Quantitative Methods in Parallel Systems


The Basic Research project QMIPS (Quantitative Methods In Parallel Systems) involves eight leading research groups from France, Germany, Italy, The Netherlands, Spain and the U.K. This book contains a selection of papers produced by the project during the last 3 years, on a variety of topics concerned with the specification, modelling, evaluation and optimization of parallel and distributed computer systems. The contributions are divided into three broad categories: Formalisms, Solution Methods and Applications. ...
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The Basic Research project QMIPS (Quantitative Methods In Parallel Systems) involves eight leading research groups from France, Germany, Italy, The Netherlands, Spain and the U.K. This book contains a selection of papers produced by the project during the last 3 years, on a variety of topics concerned with the specification, modelling, evaluation and optimization of parallel and distributed computer systems. The contributions are divided into three broad categories: Formalisms, Solution Methods and Applications. The spectrum of methodologies that are covered includes process algebras, Petri nets, multidimensional Markov processes and G-nets.
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Product Details

  • ISBN-13: 9783642799198
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/8/2011
  • Series: ESPRIT Basic Research Series
  • Edition description: Softcover reprint of the original 1st ed. 1995
  • Edition number: 1
  • Pages: 298
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.67 (d)

Table of Contents

I Formalisms.- Shastic Process Algebras.- 1. Introduction. The Indivisibility of Functional and Temporal Behaviour.- 2. The Roots of Shastic Process Algebra.- 3. The Shastic Process Algebra TIPP.- 3.1 Syntax.- 3.2 Semantics.- 3.3 Equivalences.- 3.4 Axiomatisation.- 4. Example. A Multiprocessor with MMPP Arrival Stream.- 4.1 Load modelling.- 4.2 The machine model.- 4.3 Model simplification.- 4.4 Numerical results.- 5. Case Studies.- 6. Tool Support.- 7. Recent Extensions.- 8. Summary and Outlook.- Shastic Process Algebra for Discrete Event Simulation.- 1. Introduction.- 2. Language.- 3. Semantics.- 4. Strong bisimulation.- 5. Weak bisimulation.- 6. Examples and speculations.- 6.1 Generalised Semi-Markov Processes (GSMP).- 6.2 Two processor queue.- 6.3 Equivalence.- 7. Conclusions.- GSPN and SPA Compared in Practice.- 1. Introduction.- 2. Comparison between GSPN and SPA.- 2.1 Notational level.- 2.2 State versus Action.- 2.3 Compositionality and Equivalences.- 2.4 Abstraction Mechanism.- 2.5 Analysis Techniques.- 2.6 Tool Support.- 2.7 Translation from SPA to GSPN.- 3. A Distributed Electronic Mail System.- 4. Modelling the system.- 4.1 GSPN model.- 4.2 SPA Specification.- 5. Comparing the developed models.- 6. Transforming SPA to GSPN.- 7. Conclusion.- Functional and Performance Analysis of Cooperating Sequential Processes.- 1. Introduction.- 2. Deterministic Systems of Sequential Processes.- 2.1 Basic Definitions and Notations of Petri Nets.- 2.2 Deterministic Systems of Sequential Processes, and Other Subclasses.- 2.3 Time Representation.- 3. Functional Analysis of DSSP’s.- 3.1 The Coarse net of a DSSP.- 3.2 Well-Formedness and Liveness.- 4. Performance Analysis of DSSP’s.- 4.1 Home States and Ergodicity.- 4.2 Computation of Visit Ratios.- 4.3 Performance Bounds.- II Techniques.- Analysis of Parallel Processing Systems via the (max,+) Algebra.- 1. Introduction.- 2. The Basic Problem.- 3. Modeling via (max, +)-Linear Recurrence Equations.- 3.1 Algebraic Framework.- 3.2 Recurrence Equations.- 3.3 Variations.- 3.4 Canonical Recurrence Equations.- 3.5 Response Times.- 4. Stability.- 4.1 First Order Limits.- 4.2 Second Order Limits.- 4.3 Multiple Stationary Regimes for Closed Systems.- 5. Analytical Results.- 5.1 Markovian Analysis.- 5.2 Taylor Expansions for the M/G Case.- 5.3 Transient and Stationary Distributions for the M/D Case.- 6. Parallel Simulation Issues.- 6.1 Parallel Simulation Algorithms.- 6.2 Minimal Standard Representations.- TIPP and the Spectral Expansion Method.- 1. Introduction.- 2. The Spectral Expansion solution method.- 3. SE-TIPP.- 3.1 Syntax.- 3.2 Semantic model.- 3.3 Construction schema.- 4. Application example.- 4.1 System description.- 4.2 System semantics.- 4.3 System evaluation.- 5. Conclusion.- G-Networks: A Survey of Results, a Solver and an Application.- 1. Introduction.- 2. G-networks with positive and negative customers.- 3. G-networks with signals.- 4. G-networks with signals and batch removals.- 5. The solver tool.- 6. An example: Performance evaluation of receiver initiated load balancing.- 7. Conclusions.- Polling Models with Threshold Switching.- 1. Introduction.- 2. Analytic Solution for the preemptive model.- 3. Analytic Solution for the non-preemptive model.- 4. Power series algorithm.- Two-Dimensional Nearest-Neighbour Queueing Models.- 1. A review.- 2. The symmetrical shortest queueing model.- M/G/1 Queues with FCFS Negative Arrivals.- 1. Introduction.- 2. Derivation of equations defining the generating function.- 3. An iterative algorithm.- 4. Conclusion.- Operational Analysis of Timed Petri Nets and Application to the Computation of Performance Bounds.- 1. Introduction.- 2. Observable quantities and operational laws.- 2.1 Basic operational quantities.- 2.2 Conflict-free nets.- 2.3 General nets with conflicts.- 3. Performance bounds based on operational laws.- 3.1 Extension to TWN’s.- 3.2 LPP formulation.- 4. An example of application.- 5. Conclusions.- Approximate Throughput Computation of Shastic Marked Graphs.- 1. Introduction.- 2. Basics on shastic marked graphs.- 2.1 Basic notations.- 2.2 Implicit places and MG’s.- 3. Structural decomposition of MG’s.- 4. Approximate throughput computation.- 4.1 First approach: Ping-Pong algorithm.- 4.2 A solution: Pelota1 algorithm.- 5. Conclusions.- III Applications.- Allocation of Customer Types to Servers: Clustering is Optimal.- 1. Introduction.- 2. Model description.- 3. Finding an optimal allocation.- 4. The case of ordered customer types.- 5. Concluding remarks and suggestions for further research.- A. Proof of Lemma 3.1.- B. Proof of Lemma 3.2.- C. Proof of Lemma 3.3.- D. Proof of Lemma 3.4.- Majorization and Shastic Comparison Techniques for Scheduling of Parallel Systems.- 1. Introduction.- 2. Majorization and Shastic Orders.- 2.1 Comparison of Real Vectors.- 2.2 Comparison of Random Vectors.- 2.3 Relations Between Majorization and Shastic Orderings.- 2.4 Other shastic orderings.- 3. Scheduling of Monoprogrammed Systems.- 3.1 Introduction and Notation.- 3.2 Previous Results.- 3.3 Forest-Cut Graphs.- 3.4 Shastic Minimization of Makespan.- 4. Scheduling of Multiprogrammed Systems.- 4.1 Introduction.- 4.2 Problem Description.- 4.3 Extremal Policies.- 5. Concluding Remarks.- Dependability of Distributed Programs: Algorithms and Performance.- 1. Introduction.- 2. Detection and Recovery Algorithms.- 3. Approximate Analysis and Simulations.- 3.1 Approximate Analytical Results.- 3.2 Comparing Detection Algorithms.- 4. An Example: A Task-Graph for Matrix Multiplication.- 5. An Example: Dependable Execution of the Parallel FFT Algorithm.- 5.1 Detailed Algorithmics of Failure Detection and Recovery.- 5.2 Simulations for the Dependable Parallel FFT Algorithm.- A Fixed-Point Model of a Distributed Memory Consistency Prool.- 1. Introduction.- 1.1 Workload Assumptions.- 2. A New Model for SCI.- 2.1 Actions generated by a processor.- 2.2 The analytical model.- 2.3 Mean transmission Time.- 2.4 Cache/Memory Access Delay.- 3. Results and Validation.- Routing Among Different Nodes Where Servers Break Down Without Losing Jobs.- 1. Introduction.- 2. The model.- 3. Queue size distributions.- 4. Evaluation of scheduling strategies.- 5. Generalizations.- 6. Joint distribution for N = 2.- 7. Conclusions.- Modeling Symmetric Computer Architectures by SWNs.- 1. Introduction.- 2. Multilevel Fat Trees.- 3. Multidimensional Mesh interconnection.- 4. Conclusions.- Arrival Theorems for Product-Form Shastic Petri Nets.- 1. Introduction.- 2. Product-Form Shastic Petri Nets: Basic Definitions.- 2.1 Definition of Shastic Petri Nets.- 2.2 Definition of Product-Form Shastic Petri Nets.- 3. Arrival Theorems for PF-SPNs.- 3.1 What is an Intermediate Marking.- 3.2 Example: Illustration of Intermediate Markings.- 3.3 Global Arrival Theorem by Transition for a PF-SPN.- 3.4 Example: Illustration of Theorem.- 3.5 The Notion of Direction.- 3.6 Local Arrival Theorems.- 4. Mean Sojourn Time.- 5. Conclusion.
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