Exact Analysis of Discrete Part Production Lines: The Markovian Queueing Network and the Stochastic Automata Networks Formalisms

Abstract

Manufacturing systems are quite complex and many research works have been devoted to their analysis, modeling, design and operation. This work is concerned with the exact analysis of discrete part production lines. More specifically, two formalisms are provided: (a) the Markovian Queueing Network and (b) the Stochastic Automata Network (SAN). These two methods are described explicitly via the use of an example of a production line consisting of three stations. SAN methodology utilizes both classical and generalized tensor algebra. The tensor or Kronecker representation of the SAN three-station example is given and comparisons are made between these two exact methods. Their limitations are also examined regarding the numerical results concerned with throughput of discrete part production lines. It is seen that with the SAN formalism one may solve exactly much larger production line configurations than those traditional Markovian formalism can handle.