Busy periods of two-stage tandem service systems and their algorithmic implementation

Busy periods of finite buffer tandem service systems have not been addressed in the available literature. This paper defines the stage-I and stage-II busy periods of a two-stage tandem service system M^(x)/M/c → /PH^(r)/1/K, analytically obtains their distributions, and presents efficient algorithms for the distributions with uniform error in time. The detailed analysis and algorithmic implementation for the two-stage tandem service system are completed, and the theoretical basis for its potential practical applications is provided.