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Workload of Queueing Systems with Autocorrelated Service Times.

Andrzej Chydzinski1

  • 1Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.

Entropy (Basel, Switzerland)
|March 28, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces new formulas for calculating workload in queuing systems with autocorrelated service times. Results show average workload can significantly exceed predictions based on average queue size and service time.

Keywords:
autocorrelated service timesaverage workloadperformance evaluationqueueing systemssteady-state characteristictime-dependent characteristicworkload distributionworkload entropy

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Area of Science:

  • Operations Research
  • Applied Probability
  • Queueing Theory

Background:

  • Queuing systems are fundamental in operations research, modeling waiting lines in various service industries.
  • Understanding system workload is crucial for resource allocation and performance evaluation.
  • Autocorrelation in service times, where service duration depends on previous services, presents a complex challenge in traditional queuing analysis.

Purpose of the Study:

  • To develop novel analytical formulas for characterizing the workload in queuing systems with autocorrelated service times.
  • To investigate both time-dependent and steady-state behaviors of the system workload.
  • To provide a deeper understanding of workload dynamics, including its probability density, tail behavior, average value, and entropy.

Main Methods:

  • Derivation of new mathematical formulas for workload probability density and its related metrics.
  • Analysis of time-dependent and steady-state queuing system conditions.
  • Numerical examples to illustrate the derived formulas and validate theoretical findings.

Main Results:

  • New formulas for workload probability density, tail, average value, and entropy are derived.
  • Numerical illustrations demonstrate the application and implications of these formulas.
  • The study reveals that average workload can be substantially larger than commonly estimated, exceeding several times the product of average queue size and average service time.

Conclusions:

  • The derived formulas offer a more accurate method for workload assessment in queuing systems with service time autocorrelation.
  • The findings highlight the potential for underestimation of system workload and resource requirements in such systems.
  • This research provides valuable insights for optimizing resource management and service level agreements in complex queuing environments.