In: Jacyno, Z.: Proceedings of the IASTED International Symposium on Modelling, Simulation and Optimization, 1990, Montreal, Que., Canada, pages 83-86. Calgary, Alta., Canada: Acta Press, 1990.
Abstract: For marked graphs the ratio of the total execution time to the number of tokens in a cycle gives a lower bound for the cycle time of the system, and the maximum of these ratios over all cycles determines the overall system performance. Carrying out this evaluation for an actual system is often impractical, since the number of cycles in a graph usually grows exponentially. The authors give a linear algebraic characterization for directed cycles, and based on this result, transform the problem of performance evaluation into a simple linear programming problem.
Keywords: performance evaluation (of) marked graph (by) linear programming; cycle time; directed cycle; job shop system.