Multiplexer design is a challenging task due to the high number of variables involved, raising the difficulty as the numbers of filters increase. Numerical computing tools provide a suitable environment to evaluate topologies and technologies before starting the long journey to the device. A direct scattering matrix solution for a star-junction multiplexer, based on the circuit theory, is presented in this work. The resulting star-junction matrix is introduced in a matrix system with the scattering matrix of each filter to evaluate the overall multiplexer response. This approach allows the acquisition of main multiplexer parameters like transmission, reflection, and cross-isolation response in a compact way, achieving a good starting point for the further full-wave optimization procedure. Furthermore, an approach for the design of a star-junction multiplexer is tackled based on the reflection coefficient phase. A triplexer under this interpretation is presented and evaluated using lumped elements.

We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process