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In equations describing switched-capacitor (SC) circuits, the switching equation of some switching instant is represented by Vc+ = F · Vc- + G · u+. Historically, the transformation matrices F and G have been obtained by the limiting method, in which each switching resistance approaches infinity or zero. This method derives the transformation matrices F and G directly. But it has numerical instability for large-scale SC circuits, because Frame's method is used. In this paper, we propose two methods to obtain the transformation matrix F from a characteristic matrix C. The first method is the Danielevsky's method, and the second is the backward Euler method. We also propose another method to transform F to G by means of characteristic matrices given by circuit topology, by relation of zero input and the zero state responses. The results of the simulation are represented by a simulator. [ABSTRACT FROM AUTHOR]

This paper considers the primary distributed-type switching network which serves as the prototype for the distributed switching network. A method is shown to determine the route with the minimum number of tandem stages from the originator to the destination nodes in the network (called shortest route). The shortest route is given either by the straight path directly connecting the originator and the destination switching nodes, or, if such does not exist, by the following path. Consider the parallelogram that directly connects the originator and the destination switching nodes. Then the route is obtained from the originator switching node to the destination switching node by connecting arbitrarily the unit links on the border and the inside of the parallelogram, in the same direction as that of the edges of the parallelogram from the originator switching node to the destination switching node. The number of shortest routes between the originator and the destination switching nodes increases following the exponential function of the distance between the originator and the destination switching nodes. The number of tandem stages in the shortest route increases linearly with the distance. If a honeycomb-type network is employed, the number of tandem stages in the shortest mute can be reduced by approximately 15 percent at the maximum, compared to the grid-type network. When a failure such as blocking is produced between the originator and the destination, there exist three kinds of shortest mutes depending on the point of generation. [ABSTRACT FROM AUTHOR]

An end-to-end error recovery scheme is a promising way to obtain low end-to-end delays in packet switching networks. However, a too-short timeout interval may cause unnecessary packet retransmissions even when a packet is transmitted successfully to the receiver. On the other hand, a longer timeout interval may introduce large end-to-end delay when a packet is actually lost. Thus, it becomes important to determine an appropriate timeout period in the scheme. This paper analyzes a tandem queueing network system with blocking due to finite capacity in intermediate nodes and investigates the effect of the timeout period on the end-to-end delay performance. It is found that there exists the timeout period minimizing the mean packet transmission delay in the end-to-end error recovery scheme. The delay performance between end-to-end and link-by-link error recovery schemes also is compared and it is found that the delay performances of these schemes are influenced significantly by the node-to-node delay. [ABSTRACT FROM AUTHOR]