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Bayesian analysis on single server Markovian queueing model with impatient customers.

Gulab Singh Bura1, Himanshi Sharma2

  • 1Department of Statistics, University of Delhi, Delhi, India.

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Summary
This summary is machine-generated.

This study analyzes customer queue behavior using Bayesian inference for M/M/1 models. It found customer impatience significantly impacts balking probability, affecting queue dynamics and traffic intensity estimates.

Keywords:
Bayesian estimationM/M/1 queuebalkingcredible intervalssampling importance resamplingtraffic intensity

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Area of Science:

  • Operations Research
  • Applied Probability
  • Statistical Modeling

Background:

  • Queuing theory models real-world waiting lines.
  • Balking, where customers avoid queues, is influenced by waiting time and impatience.
  • Understanding balking is crucial for optimizing service systems.

Purpose of the Study:

  • To perform Bayesian inference on an M/M/1 queuing model incorporating balking.
  • To analyze how customer impatience levels affect balking probability.
  • To provide Bayesian estimates for traffic intensity (ρ) using diverse prior distributions.

Main Methods:

  • Developed an M/M/1 queuing model where balking probability is a function of queue length and customer impatience.
  • Employed Bayesian inference with beta, truncated gamma, and uniform prior distributions.
  • Utilized the Sampling Importance Re-sampling (SIR) technique for posterior estimation.

Main Results:

  • Bayesian estimates for traffic intensity (ρ) were derived.
  • Posterior estimates, risk, and credible intervals were obtained via SIR.
  • Simulation studies confirmed the convergence of estimators.

Conclusions:

  • Customer impatience is a critical factor influencing balking behavior.
  • The proposed Bayesian methodology effectively estimates queuing model parameters.
  • Findings were validated using real-world data analysis.