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dc.contributor.authorAbolnikov, Lev M.
dc.contributor.authorDukhovny, Alexander M.
dc.contributor.authorDshalalow, Jewgeni H.
dc.date.accessioned2014-11-18T15:00:40Z
dc.date.available2014-11-18T15:00:40Z
dc.date.issued1992-02-01
dc.identifier.citationLev Abolnikov, Jewgeni H. Dshalalow, and Alexander M. Dukhovny. (1992) First passage processes in Queuing system MX/Gr/1 with service delay discipline. International Journal of Mathematics and Mathematical Sciences, 17(3), 571-586.en_US
dc.identifier.urihttp://hdl.handle.net/11141/413
dc.description.abstractThis article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time. The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. The authors use the recent results on the first excess level processes to explicitly find all characteristics of the named processes. Some characteristics of the input process, service cycle, intensity of the system, and both idle and busy periods are also found. The results obtained in the article are illustrated by numerous examples.en_US
dc.language.isoen_USen_US
dc.rightsThis published article is available in accordance with the publisher's policy. It may be subject to U.S. Copyright Law.en_US
dc.rights.urihttp://www.hindawi.com/journals/apm/apc/en_US
dc.titleFirst passage processes in Queuing system MX/Gr/1 with service delay disciplineen_US
dc.typeArticleen_US
dc.identifier.doi10.1155/S0161171294000827


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