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dc.contributor.authorAbolnikov, Lev M.
dc.contributor.authorDshalalow, Jewgeni H
dc.contributor.authorDukhovny, Alexander M.
dc.identifier.citationAbolnikov, L., Dshalalow, J. H., & Dukhovny, A. M. (1994). 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.descriptionbusy period, continuous time parameter, process embedded, Markov chain, idle period modulated, random measure, output process, Queueing process, semi-Markov process, semi-regenerative process, service cycleen_US
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. © 1994, Hindawi Publishing Corporation. All rights reserved.en_US
dc.rights© 1994 the author(s)en_US
dc.titleFirst Passage Processes in Queuing System MX/GR/1 With Service Delay Disciplineen_US

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