In the present paper we present a mathematical theory for the transient analysis of probabilistic models relevant to communication networks. First we review the z-transform method, the matrix method, and the Laplace transform, as applied to a class of birth-and-death process model that is relevant to characterize network traffic sources. We then show how to develop transient solutions in terms of the eigenvalues and spectral expansions. In the latter half the paper we develop a general theory to solve dynamic behavior of statistical multiplexer for multiple types of traffic sources, which will arise in the B-ISDN environment. We transform the partial differential equation that governs the system into a concise form by using the theory of linear operator. We present a closed form expression (in the Laplace transform domain) for transient solutions of the joint probability distribution of the number of on sources and buffer content for an arbitrary initial condition. Both finite and infinite buffer capacity cases are solved exactly. The essence of this general result is based on the unique determination of unknown boundary conditions of the probability distributions. Other possible applications of this general theory are discussed, and several problems for future investigations are identified.

A new algorithm for timing driven placement based on the fuzzy theory is proposed. In this method, the signal delay on the longest path, the chip area and the total wire length can be simultaneously minimized. Introducing the probability measures of fuzzy events, falling down into the local optimal solutions can be avoided. At first, we define the fuzzy placement relation using the graph distance matrix and fuzzy distance relation matrix, and we give a new placement method based on the fuzzy placement relation and the probability measures of fuzzy events. Secondly, we extend this placement method so as to apply to the timing driven placement problem by introducing a fuzzy membership functions which represent the signal delay on the longest path and the chip area. Finally, experimental results are shown to compare our method with one of the previous methods.

A new timing driven placement method based on the fuzzy theory is proposed. In this method, the longest path delay, the chip area and the wire length can be simultaneously minimized. Introducing the probability measures of fuzzy events, falling down into the optimal solutions can be avoided.

A layout system for mixed analog/digital standard cell LSI's is described. The system includes interactive floorplan and placement features and automatic global and channel router. In mixed analog/digital circuits, crosstalk noise causes chip performance degradation. Thus, the proposed global routing algorithm routes analog nets in areas that are free of digital nets as much as possible. The number of line crossovers, especially for analog nets, is minimized by both global and detailed routers, because these crossovers are the dominant factors in the crosstalk noise. Double width lines can be used to avoid unexpected voltage drops caused by parasitic resistances. A postprocess automatically puts up shield lines for very noise sensitive wirings to improve the S/N ratio. Experimental results show that the proposed algorithms are effective in reducing the number of crossovers and redundant vias.

In this paper, we propose a new algorithm for the problem of floorplanning of the mixed design of macro and standard cells. The proposed algorithm which is based on partitioning and slicing approach, uses a modified min-cut bipartitioning heuristic. The heuristic bipartitions a block of a mixture of macro and standard cells to minimize the netcut, which are the number of nets connecting both sub-blocks, with size constraints. A sub-block is a resulting descendant block. Before starting the bipartitioning of the block, the macro cell with the longest side in the block is selected first. Using edges of the selected macro cell, bipartitionings are performed twice fixing the location of the macro cell on one of 4 corners of the block with its rotation and reflection. Bipartitioning of blocks is repeated until each block has either a macro cell or standard cells without macro cells. As a result of bipartitioning, a slicing tree is constructed. Using the proposed floorplan algorithm, we developed an automatic placement and routing tool, Cell Designer, for the mixed design of macro and standard cells. According to the floorplanner, macro cells are placed and standard cells are grouped into standard cell blocks. Standard cells are placed and routed within estimated area of block using conventional tools. They form a fixed-shaped block like a macro cell. Interconnections between the two adjacent blocks are performed with a conventional channel router. The channels and the order of channel routing are determined following the hierarchy of the slicing tree. Cell Designer has a dedicated graphics editor to provide interactive services to users. Experimental results on well-known benchmark data are shown.

We studied transient fields on a perfectly conducting sphere excited by a half sine pulse wave and examined the Poynting vectors, the energy densities and the energy velocities of the creeping waves. We used FILT (Fast Inversion of Laplace Transform) method for transient analysis. We compared the amplitudes of the creeping wave with that of steady state high frequency approximation obtained by the Watson transformation. The main results are: (1) We confirmed in the transient response that the pulse propagates clockwise and counterclockwise along the geodesic circumference. (2) In the transient electromagnetic field observed in the E-plane we can recognize creeping waves clearly. (3) The existence of creeping waves is not clear in the H-plane. (4) The pulse wave propagation on the sphere is seen more clearly from the Poynting vectors and the energy densities than the field components. (5) The energy velocity of the wave front is equal to the light velocity as should be. The energy velocity of the wave body becomes smaller with the passage of time. (6) The amplitude of the creeping wave for a beat pulse and the amplitude obtained by the Watson transform for mono spectrum agree in the order of relative error below 25%.