The authors describe a computational approach for modeling and analyzing modern communication systems based on numerical methods for Markov chains. Advanced direct and iterative procedures for the calculation of the stationary distribution of a homogeneous discrete- or continuous-time Markov chain with finite state space are presented. They are implemented in a convenient software tool called MACOM for interactive modeling and performance evaluation of communication systems. MACOM provides the user with a predefined markovian model world describing modern telecommunication networks with adaptive routing schemes and advanced congestion-control mechanisms. The versatility of these algorithms is illustrated by their application to Markovian queuing models derived from telecommunications networks.>