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On the ordering of tandem queues with exponential servers. (English) Zbl 0591.60089
Summary: We consider tandem queues which have a general arrival process. The queueing system consists of s (s$$\geq 2)$$ single-server service stations and the servers have exponential service-time distributions. Firstly we give a new proof for the fact that the departure process does not depend on the particular allocation of the servers to the stations.
Secondly, considering the service rates, we prove that the departure process becomes stochastically faster as the homogeneity of the servers increases in the sense of a given condition. It turns out that, given the sum of the service rates, the departure process is stochastically fastest in the case where the servers are homogeneous.

MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research
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