Greenberg, Betsy S.; Wolff, Ronald W. An upper bound on the performance of queues with returning customers. (English) Zbl 0626.60092 J. Appl. Probab. 24, 466-475 (1987). The authors consider a stationary queueing system with Poisson arrival and exponential service time depending on the queue length. They discuss the following orbit system: Customers who cannot be served immediately join the queue once again with probability \(r_ 1\) for the first time and \(r_ 2\) for further times. They derive properties of the expected number of reentering customers and bounds on the performance of geometric \((r_ 2=r_ 1<1)\) and infinite \((r_ 2=1)\) orbit systems. Reviewer: W.Schlee-Kossler Cited in 15 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:orbit queueing system; Poisson arrival; exponential service time PDFBibTeX XMLCite \textit{B. S. Greenberg} and \textit{R. W. Wolff}, J. Appl. Probab. 24, 466--475 (1987; Zbl 0626.60092) Full Text: DOI