Output stream analysis in a queueing model with working vacation mechanism as a power reduction strategy

Area of Science:

• Operations Research
• Applied Probability
• Queueing Theory

Background:

• Queueing models are essential for analyzing waiting lines in various systems.
• Working vacation models introduce periods where servers operate at a reduced capacity or are idle.
• Understanding departure processes is crucial for system efficiency and performance evaluation.

Purpose of the Study:

• To analyze the departure process of a queueing system with a working vacation mechanism.
• To derive the explicit solution for the Laplace transform of the generating function of the departure process.
• To compute the time-dependent mean number of jobs served.

Main Methods:

• Utilizing a queueing model with a general independent input stream and exponential service times.
• Deriving the explicit solution for the Laplace transform of the generating function.
• Employing numerical Laplace transform inversion for time-dependent analysis.

Main Results:

• An explicit solution for the Laplace transform of the generating function of the departure process was determined.
• The time-dependent mean number of jobs served was computed using numerical inversion.
• Numerical examples illustrated the output stream's behavior concerning various model parameters.

Conclusions:

• The departure process is significantly influenced by interarrival distribution and working vacation parameters.
• The study provides a framework for analyzing queueing systems with server vacations.
• Results offer valuable insights for optimizing system performance in scenarios with intermittent service availability.