Considerations on M|G|∞ Queue Busy Period Variance

2022/10/10 by Manuel Ferreira, Ferreira, Manuel Alberto M.
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Reliability and Maintenance Optimization #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2210.04931

openalex publication_date 2022/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some important results on the variance of the M|G|∞ queue busy period are presented. Often, this parameter depends on the whole structure of the service time distribution. So, the importance of the bounds presented, depending only on some parameters. Also, some bounds for service time distributions important in reliability theory, with technological and financial applications, are presented and a particular stochastic ordination is explored to explain those results. Finally, an interesting result about the exponentiality of the MGInf queue busy period, resulting from the coefficient of variation study is shown.

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