Abstract

This paper is motivated by the problem of capturing and releasing the CPU by a routine software application in order to accommodate other non-routine requests that need the CPU. Specifically, we consider a network of distributed software agents where each agent is assigned with routine tasks that need to be processed by a CPU. The CPU also receives requests from other processes running on the machine. The problem is to select an optimal threshold on the workload of the agent so that the agent releases the CPU and recaptures it from time-to-time based on its workload.

In order to do that, we use a stochastic fluid-flow model with two buffers, one for the agent that runs the routine tasks and the other for the remaining non-routine jobs at the CPU. Input to the two buffers are from on-off sources and the processor switches between the two buffers using a threshold-based policy. We develop analytical approximations for the buffer content distribution and determine the Quality of Service (QoS) experienced by the two sources of traffic. We use the QoS performance measures to formulate and solve an optimization problem to design an optimal threshold value.

Keywords: Quality of service; Multi-class traffic; Fluid queues; Multi-agent systems

Article Outline

1. Introduction

2. Problem description

2.1. Scenario

2.2. Modeling traffic as on-off fluids

2.3. Model: two-buffer fluid-flow model of the system

2.4. Objective

3. Preliminaries

3.1. Effective bandwidths

3.2. Bounds on limiting distribution of buffer content

3.3. First passage times in fluid flow models

3.4. Steady state distribution for fluid flow models

4. Analysis: zero switch-over times

4.1. Time between switching

4.1.1. Distribution of time spent on buffer 1

4.1.2. Distribution of time spent on buffer 2

4.1.3. Average time between switching

4.2. Buffer 2 analysis

4.2.1. Compensating source

4.2.2. Limiting distribution of buffer contents

4.3. Buffer 1 analysis

4.3.1. SMP model

4.3.2. Approximate model

5. Approximations: positive switch-over times

5.1. Necessary condition for existence of distributions

5.2. Buffer 2 approximations

5.3. Buffer 1 approximations

6. Results

6.1. Buffer content distribution

6.2. Optimization results

7. Generalization: N general input sources for buffer 2

8. Conclusions and extensions

Acknowledgements

Appendix A. Joint distribution of buffer contents

Appendix B. Random switch-over times analysis

Appendix B.1. Buffer 2 approximations

Appendix B.2. Buffer 1 approximations

References

Vitae