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Finite Buffer GI/M(n)/1 Queue with Bernoulli-Schedule Vacation Interruption under N-Policy.

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This study analyzes a finite buffer queueing system with a special vacation policy. The research provides steady-state distributions and performance insights for optimizing queue management.

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Area of Science:

  • Operations Research
  • Applied Probability
  • Queueing Theory

Background:

  • Queueing systems are fundamental in performance analysis.
  • Understanding server vacation policies is crucial for efficiency.
  • Finite buffer systems present unique challenges in managing congestion.

Purpose of the Study:

  • To analyze a finite buffer GI/M(n)/1 queue with a Bernoulli-scheduled vacation interruption policy.
  • To derive steady-state system length distributions under specific conditions.
  • To investigate the impact of system parameters on performance measures.

Main Methods:

  • Application of the supplementary variable technique.
  • Utilization of a recursive method for analysis.
  • Derivation of steady-state distributions at prearrival and arbitrary epochs.

Main Results:

  • Obtained steady-state system length distributions for the analyzed queue.
  • Identified conditions for vacation interruption based on queue length.
  • Presented numerical computations demonstrating parameter effects on performance.

Conclusions:

  • The study provides a comprehensive analysis of a complex queueing model.
  • The derived performance measures can inform system design and resource allocation.
  • The findings offer valuable insights for optimizing queueing systems with server vacations.