A new algorithm based on binary decision diagram (BDD) for the analysis of a system with multistate components is proposed. Each state of a multistate component is represented by a boolean variable, and a multistate system is represented by a series of multistate fault trees. A Boolean algebra with restrictions on variables is used to address the dependence among these boolean variables that collectively represent the same component and a new BDD operation is proposed to realize this Boolean algebra. Due to the nature of the BDD, the sum of disjoint products (SDP) can be implicitly represented, which avoids huge storage and high computational complexity for large multistate systems. Some applications are given to illustrate the use of our new algorithm.

We develop performance models of the broadcast and unknown server (BUS) in the LANE. The traffic on the BUS is divided into two classes: the broadcast and multicast traffic, and the unicast relay flow. The broadcast and multicast traffic is assumed to form a Markov modulated Poisson process (MMPP). The traffic for a particular unicast relay flow is an MMPP as well. However, the number of active unicast relay flows sojourning on the BUS is determined by a tandem queueing system, where the flow arrival process is Poisson, the address resolution delay is exponentially distributed, and the connection setup delay is three-stage Erlang distributed. The size of data frames in traffic flows is a random variable with three possible values: short, medium, and large. In order to deal with the intractability (i.e., largeness and stiffness) of the underlying Markov chain, a hierarchical model is used to decompose the system. With the help of the Stochastic Petri Net Package (SPNP), a software package for the automated generation and solution of Markovian stochastic systems, and the decomposition method, we study the performance of the BUS module under different loads. We also investigate the effect of address resolution delay and connection setup delay on the performance of the BUS.