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Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns.

Messaoud Bounkhel¹, Lotfi Tadj², Ramdane Hedjar³

¹Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This study introduces a flexible queueing system where a single server switches between single-customer and bulk-customer service based on system size. The model incorporates server breakdowns and repairs, analyzing steady-state probabilities for queueing optimization.

Keywords:

Markovian queue flexible server linear operator steady-state distribution unreliable server

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Area of Science:

Operations Research
Applied Probability
Queueing Theory

Background:

Queueing systems are fundamental to resource allocation and performance analysis.
Flexible service strategies can enhance efficiency in dynamic environments.
Server reliability and repair dynamics significantly impact system performance.

Purpose of the Study:

To analyze a single-server queueing system with a size-dependent service strategy.
To model and evaluate the impact of server breakdowns and repairs on system performance.
To derive steady-state probabilities for system size in a flexible queueing model.

Main Methods:

Development of a flexible single-server queueing model with a threshold-based service strategy (single vs. bulk).
Incorporation of exponential service times and Poisson breakdowns with distinct rates for single and bulk service.
Application of probability generating functions and linear operator approaches to determine steady-state probabilities.

Main Results:

The study derives system size steady-state probabilities for the flexible queueing system.
Analysis quantifies the impact of the service threshold 'c' on system behavior.
The model accounts for differing breakdown and repair rates during single and bulk service phases.

Conclusions:

The flexible queueing system demonstrates adaptability to varying customer loads.
Server breakdowns and repairs introduce complexities that are successfully modeled.
The derived steady-state probabilities provide insights for optimizing queueing system design and management.