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<p>In this paper, we analyze a single-server Markovian queue with customer abandonment. We use confluent hypergeometric functions to derive <i>exact</i> expressions for the probability mass function (pmf), cumulative distribution function (cdf), probability generating function, and moments of the queue length. We also derive the Laplace-Stieltjes transform (LST) of the steady-state queue length and waiting time distributions and show how to compute all moments as simple integrals. Finally, we derive new formulas for the conditional and unconditional probability of abandonment. Thus, our work provides a complete analysis of the single-server Markovian queue with customer abandonment.</p>

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The \(M_{\lambda }/M_{\mu }/1+M_{\theta }\) queue via hypergeometric functions

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • Jamol Pender

摘要

In this paper, we analyze a single-server Markovian queue with customer abandonment. We use confluent hypergeometric functions to derive exact expressions for the probability mass function (pmf), cumulative distribution function (cdf), probability generating function, and moments of the queue length. We also derive the Laplace-Stieltjes transform (LST) of the steady-state queue length and waiting time distributions and show how to compute all moments as simple integrals. Finally, we derive new formulas for the conditional and unconditional probability of abandonment. Thus, our work provides a complete analysis of the single-server Markovian queue with customer abandonment.