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The Mλ/Mμ/1+Mθ queue via hypergeometric functions
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DOI：10.1007/s11134-025-09965-y.png)
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Abstract
En 中文
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.
Keywords:
Queues
Abandonment
Special functions
Hypergeometric functions
Single server
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