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System of two servers in bi-series with a serial service channel and phase type service

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Summary

The paper studies the time independent solution of a queueing system wherein units demanding one, two or three service phases arrive at the three service channels. It is assumed that first two channels are bi-serial to each other and both are separately in series with a common server. Poisson arrivals and exponential service times are assumed at all the three service channels of the system. Mean queue length of the system for infinite number of input sources has been obtained. Also, mean queue length of the system for finite number of input sources has been found out. Some particular cases of importance are given in the end.

Zusammenfassung

Der Aufsatz behandelt die zeitunabhängige Lösung eines Warteschlangenproblems, dessen Elemente ein, zwei oder drei Bedienungsphasen erfordern. Das System besteht aus drei Stationen. Die ersten beiden sind bi-seriell zueinander und jede für sich in Reihe zur dritten Station angeordnet (vgl. Abb. 1). An allen Stationen werden poissonverteilte Ankünfte und exponentiell verteilte Bedienzeiten vorausgesetzt. Es wird die mittlere Warteschlangenlänge sowohl für offene als auch für geschlossene Systeme angegeben. Einige wichtige Spezialfälle bilden den Schlu\.

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References

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Arya, K.L. System of two servers in bi-series with a serial service channel and phase type service. Zeitschrift für Operations Research 16, B115–B122 (1972). https://doi.org/10.1007/BF01959719

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  • DOI: https://doi.org/10.1007/BF01959719

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