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

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.