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Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation.

G K Tamrakar1, A Banerjee1

  • 1Indian Institute of Technology (BHU), Varanasi, India.

International Journal of Applied and Computational Mathematics
|November 29, 2021
PubMed
Summary
This summary is machine-generated.

This study analyzes a queueing system with batch services and server vacations. The research provides mathematical insights into queue length and batch size dynamics for improved system management.

Keywords:
Bivariate generating functionInfinite bufferNon Poisson queueSingle (Multiple) vacation

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Area of Science:

  • Operations Research
  • Applied Probability
  • Performance Modeling

Background:

  • Queueing models with server vacations are crucial for managing real-world congestion.
  • Existing models often simplify batch service or vacation policies.

Purpose of the Study:

  • To analyze an infinite buffer single-server batch service queue with queue-size-dependent vacations.
  • To investigate batch-size-dependent batch service rules.
  • To derive steady-state probabilities and performance measures.

Main Methods:

  • Utilized an embedded Markov chain technique with service/vacation completion epochs as embedded Markov points.
  • Derived bivariate generating functions for queue size, vacation type, and batch size.
  • Extracted steady-state joint probabilities.

Main Results:

  • Obtained generating functions for queue size and vacation type at vacation termination.
  • Derived generating function for queue size and batch size at service completion.
  • Successfully extracted steady-state joint probabilities for various system states.

Conclusions:

  • The study provides a comprehensive mathematical analysis of a complex queueing system.
  • Derived performance measures offer valuable insights for system optimization.
  • Graphical and tabular representations illustrate the model's behavior.