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A Quantitative Fitness Analysis Workflow

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An M/PH/1 queue with workload-dependent processing speed and vacations.

Yutaka Sakuma¹, Onno Boxma², Tuan Phung-Duc^3,4

¹Department of Computer Science, National Defense Academy of Japan, Yokosuka, Japan.

Queueing Systems

|March 31, 2021

Summary

This study optimizes computer system performance by balancing delay and energy use. It introduces a model where a server powers down and reactivates based on workload, minimizing system costs.

Keywords:

Autoscaling Matrix exponential solution Phase-type demand Workload-dependent service

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Area of Science:

Computer Science
Operations Research
Queueing Theory

Background:

Modern systems face a trade-off between processing speed (delay) and energy consumption.
Existing queueing models often do not account for dynamic server states or workload-dependent service rates.

Purpose of the Study:

To analyze a single-server queue with workload-dependent service speed and intermittent server activity.
To derive the steady-state workload distribution and its moments for this system.
To determine an optimal server activation threshold that minimizes a defined cost function.

Main Methods:

Modeling a single-server queue with phase-type service requirements.
Implementing a piecewise constant service speed function based on workload.
Incorporating server switch-off and reactivation logic based on workload thresholds.
Deriving steady-state distributions and moments analytically.

Main Results:

The steady-state workload distribution and its moments of any order were successfully obtained.
A method to select the optimal activation threshold was established.
The model provides a framework for minimizing a cost function balancing processing, activation, and workload costs.

Conclusions:

The developed queueing model effectively addresses the delay-energy trade-off in computer systems.
The derived results enable optimization of server activation policies for energy efficiency and performance.
This research offers practical insights for designing energy-aware computing and communication systems.