Vlasiou, Maria; Zwart, Bert Time-dependent behaviour of an alternating service queue. (English) Zbl 1135.90327 Stoch. Models 23, No. 2, 235-263 (2007). Summary: We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit expressions for its time-dependent waiting-time distribution, the correlation between waiting times, and the distribution of the cycle length. As our model is closely related to Lindley’s recursion, we compare our results to those derived for Lindley’s recursion. Cited in 6 Documents MSC: 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory) Keywords:Busy period; covariance function; \(G/M/1\) queue; generalized Wiener-Hopf equation; Lindley’s recursion; phase-type distributions; waiting time PDFBibTeX XMLCite \textit{M. Vlasiou} and \textit{B. Zwart}, Stoch. Models 23, No. 2, 235--263 (2007; Zbl 1135.90327) Full Text: DOI arXiv References: [1] DOI: 10.1137/S003614459529298X · Zbl 0880.60089 · doi:10.1137/S003614459529298X [2] Asmussen S., Applied Probability and Queues (2003) · Zbl 1029.60001 [3] Blanc J.P.C., Operations Research Proceedings 2004 pp 297– (2004) [4] Blomqvist N., Skandinavisk Aktuarietidskrift 50 pp 157– (1967) [5] Blomqvist N., Skandinavisk Aktuarietidskrift 51 pp 178– (1968) [6] Blomqvist N., Skandinavisk Aktuarietidskrift 52 pp 125– (1969) [7] Cohen J.W., The Single Server Queue (1982) · Zbl 0481.60003 [8] DOI: 10.1017/S1446788700006509 · Zbl 0164.47802 · doi:10.1017/S1446788700006509 [9] Koenigsberg E., Proceedings of the 7th International Conference on Automation in Warehousing pp 173– (1986) [10] Noble B., Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (1958) · Zbl 0082.32101 [11] DOI: 10.1214/aoms/1177693171 · Zbl 0278.60077 · doi:10.1214/aoms/1177693171 [12] DOI: 10.1239/jap/1059060890 · Zbl 1140.90359 · doi:10.1239/jap/1059060890 [13] Vlasiou , M. A non-increasing Lindley-type equation . (Technical Report 2005-015) , Eurandom , Eindhoven , The Netherlands , 2005 . Available atwww.eurandom.nl . · Zbl 1165.90411 [14] DOI: 10.1017/S0269964805050254 · Zbl 1336.60180 · doi:10.1017/S0269964805050254 [15] DOI: 10.1016/j.orl.2005.12.004 · Zbl 1120.60093 · doi:10.1016/j.orl.2005.12.004 [16] DOI: 10.1239/jap/1101840561 · Zbl 1062.60095 · doi:10.1239/jap/1101840561 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.