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Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance.
Srinivas R Chakravarthy1, Shruti2, Alexander Rumyantsev3,4
1Departments of Industrial and Manufacturing Engineering, Mathematics, Kettering University, Flint, MI 48504 USA.
Methodology and Computing in Applied Probability
|October 26, 2020
Summary
This study analyzes a single-server queueing system with a "group clearance" bulk service rule. The research provides a steady-state analysis for batch Markovian arrivals and general service times using Markov renewal processes and matrix-analytic methods.
Area of Science:
- Operations Research
- Applied Probability
- Queueing Theory
Background:
- Queueing models are fundamental to understanding system performance in various applications.
- Bulk service queueing systems, where a server handles multiple customers simultaneously, present unique analytical challenges.
- The 'group clearance' rule, allowing infinite batch sizes, requires specialized modeling techniques.
Purpose of the Study:
- To analyze a single-server queueing model with a general bulk service rule termed 'group clearance'.
- To investigate the steady-state behavior of the system under batch Markovian point process arrivals and general service distributions.
- To develop analytical methods for performance evaluation of this specific queueing system.
Main Methods:
- Employed the embedded Markov renewal process approach for general service time distributions.
- Utilized continuous-time Markov chain analysis with a special generator structure for phase-type service times.
- Applied matrix-analytic methods for steady-state analysis and explored special cases.
Main Results:
- Developed analytical frameworks to study the 'group clearance' queueing model.
- Obtained steady-state results using advanced queueing theory techniques.
- Demonstrated the model's applicability across diverse service time distributions (constant, uniform, Weibull, phase-type).
Conclusions:
- The study successfully analyzes a complex bulk service queueing system.
- The matrix-analytic approach provides a robust method for performance evaluation.
- Findings are applicable to systems requiring batch service with potentially large group sizes.
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