Queueing theory as a subject of research started at the beginning of this century, when A. K. Erlang conducted his pioneering studies on individual queues, in the context of telephone switching. Since the 1950's, this area of study has experienced a rapid development and has found enormous amounts of application in industry and business. Today, more general queueing systems or queueing networks, rather than individual queues, have become a fashion as people have studied various types of interrelated service systems in real life. The rapidly developing of computer and communication technology has been a major factor in solving and creating many new problems;This research addresses both of these types of problems. The first one, consisting of chapter two only, is of classic queueing theory fashion, and investigates the moment convergence of the M/G/1 model and establishes its normalized moment convergence under heavy traffic. The second one, which consists of chapters three and four, addresses lineal and confluent production systems. Steady state performance measures of such systems are discussed under various disciplines and service time distributions. Some design issues also are discussed, with emphasis on the comparison of two-level confluent systems with their lineal counterparts, a topic apparently not discussed heretofore in the literatures.