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Server pooling models for separate and bounded queues.

Hila Hindy Ling1,2, Ran Etgar2, Hillel Bar-Gera1

  • 1Ben-Gurion University of the Negev, Department of Industrial Engineering and Management, Israel.

Heliyon
|March 4, 2024
PubMed
Summary
This summary is machine-generated.

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Pooling separate finite waiting spaces in queueing models improves efficiency. This study analyzes the benefits of pooling, especially when arrival rates differ, using a Quasi-Birth-and-Death model.

Area of Science:

  • Operations Research
  • Applied Probability
  • Queueing Theory

Background:

  • Existing queueing models often assume shared waiting spaces or unlimited capacity.
  • Finite, separate waiting spaces present unique challenges in analyzing pooling benefits.
  • Container terminal operations highlight the need for efficient resource allocation in queueing systems.

Purpose of the Study:

  • To investigate the advantages of pooling finite, separate waiting spaces in multi-source queueing systems.
  • To develop and analyze a queueing model applicable to practical scenarios like container terminals.
  • To quantify the inefficiency introduced by stochastic interactions and the impact of pooling.

Main Methods:

  • Development of a Quasi-Birth-Death (QBD) model for the general case of separate finite queues.
Keywords:
Arrival ratesContainer terminalsPoolingQBDSeparate waiting queuesService rates

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  • Analytical derivation of the relative interaction delay (RID) for a single waiting space scenario.
  • Numerical evaluations to assess pooling benefits under varying arrival rate conditions.

    • Main Results:

    • Analytical proof that relative interaction delay (RID) is inversely proportional to the number of pooled queues in the base model.
    • Numerical evidence demonstrating significant added benefits of pooling when arrival rates are unequal.
    • Observed a pronounced, linear enhancement in efficiency due to pooling with differing arrival rates.

    Conclusions:

    • Pooling separate finite waiting spaces is beneficial, particularly when arrival rates vary across sources.
    • The proposed QBD model provides a framework for analyzing such systems and quantifying inefficiencies.
    • The findings have direct implications for optimizing resource management in systems like container terminals.