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Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns.

Messaoud Bounkhel¹, Lotfi Tadj², Ramdane Hedjar³

¹Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This study introduces a novel Markovian queueing system with a threshold-dependent batch service. The entropy principle accurately approximates queueing system performance, aligning well with analytical methods.

Keywords:

Markovian queue flexible server maximum entropy principle steady-state distribution unreliable server

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Area of Science:

Operations Research
Applied Probability
Queueing Theory

Background:

Queueing systems are fundamental in performance analysis.
Server failures and batch services introduce complexities.
Existing models may not capture threshold-dependent behaviors effectively.

Purpose of the Study:

To analyze a versatile Markovian queueing system with a threshold-dependent batch service.
To investigate the impact of server failures on system performance.
To apply the entropy principle for approximating queueing system probabilities.

Main Methods:

Modeling a Markovian queue with a threshold 'c' for single or batch service.
Incorporating server failures with state-dependent rates.
Utilizing analytical methods and the entropy principle to derive probability vectors.

Main Results:

The system exhibits distinct behaviors for queue lengths below and above the threshold 'c'.
Server failure and repair rates are dependent on service mode (single or batch).
Entropy principle provides accurate approximations for initial and tail probabilities, closely matching analytical results.

Conclusions:

The proposed queueing model effectively captures complex service dynamics.
The entropy principle offers a viable and accurate approximation method for such systems.
The findings are valuable for optimizing systems with threshold-based batching and server unreliability.