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<p>This paper focuses on analyzing a balking <i>M</i>/<i>G</i>/1 queue with general differentiated vacations. The server can take two types of vacations, each with a general distribution. We establish the stability condition for the model and employ the supplementary variable technique to derive the probability generating functions. Furthermore, we determine the distribution of the number of customers in the system, waiting time, and sojourn time. Additionally, we present the performance measures of the model. To examine customers’ behavior in the fully unobservable scenario, we conduct a game-theoretic analysis and derive optimal individual Nash equilibrium and socially optimal equilibrium strategies. Through numerical experiments, we investigate the impact of various system parameters on performance measures, individual and social optimal equilibrium mixed strategies, social benefit, throughput, and the price of anarchy. These experiments provide valuable insights into how different factors influence the system performance and efficiency.</p>

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On a Balking M/G/1 Queue with General Differentiated Vacations

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Abdoun Sylia,
  • Taleb Samira

摘要

This paper focuses on analyzing a balking M/G/1 queue with general differentiated vacations. The server can take two types of vacations, each with a general distribution. We establish the stability condition for the model and employ the supplementary variable technique to derive the probability generating functions. Furthermore, we determine the distribution of the number of customers in the system, waiting time, and sojourn time. Additionally, we present the performance measures of the model. To examine customers’ behavior in the fully unobservable scenario, we conduct a game-theoretic analysis and derive optimal individual Nash equilibrium and socially optimal equilibrium strategies. Through numerical experiments, we investigate the impact of various system parameters on performance measures, individual and social optimal equilibrium mixed strategies, social benefit, throughput, and the price of anarchy. These experiments provide valuable insights into how different factors influence the system performance and efficiency.