We consider a queuing network with M exponential service stations and with N customers. We study the behavior of a subsystem u, which has a single node as input and a single node as output, when the subsystem parameters are varied. An "equivalent" network is constructed in which all queues except those in subsystem u are replaced by a single composite queue. We show that for certain classes of system parameters, the behavior of subsystem u in the equivalent network is the same as in the given network. The analogy to Norton's theorem in electrical circuit theory is demonstrated. In addition, the equivalent network analysis can be applied to open exponential networks.
An approximate iterative technique for the analysis of complex queuing networks with general service times is presented. The technique is based on an application of Norton's theorem from electrical circuit theory to queuing networks which obey local balance. The technique determines approximations of the queue length and waiting time distributions for each queue in the network. Comparison of results obtained by the approximate method with simulated and exact results shows that the approximate method has reasonable accuracy.
The type synthesis of plane linkages can be formulated as a systematic enumeration of linear graphs. In this study, the concepts of a “contraction map” of a graph and of enumeration technique by permutation group are introduced in order to enumerate plane kinematic chains having 13 turning joints and 10 links. In addition, an algorithm for deriving all plane kinematic chains from those of a lower number of links is introduced.
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