Fluid Net Models: From Behavioral Properties to Structural Objects

Abstract

Increasing the production in manufacturing systems is one of the main demands in modern systems. The naive approach that this goal can be achieved when more or faster resources are used is not always valid. In fact, the complex interactions among system’s elements may lead to paradoxical behaviors; for example, using faster machines could reduce the equilibrium throughput (number of part fabricated per unit time in steady state) of the system, or even worse, block all system activities, reducing it to zero. This work leverages the concepts about fluidization and analysis techniques used in Timed Continuous Petri nets (TCPN) presented in earlier works to study the behavior of the equilibrium throughput when more/faster machines are used. Herein, we illustrate how discontinuities induced bifurcations of the equilibrium throughput are due to the existence of paths that can increase/decrease the marking of certain subnets. In particular, if paths gaining/losing tokens are fired without a particular balance, then the equilibrium throughput exhibits discontinuities since the equilibrium marking loses hyperbolicity. Moreover, these discontinuities imply other undesired throughput behaviors; for example, the existence of non-monotonicities of the equilibrium throughput (when more/faster resources are used in the system, its equilibrium throughput is reduced). The discontinuities together with a homothecy property are used to explain non-monotonicities in the equilibrium throughput. A relevant aspect is that these undesired system behaviors appear when the net has structural objects named problematic configurations that are associated with certain subnets in which there are no P-semiflows. Although the number of these configurations increase exponentially in the size of the net, some reduction rules are introduced to remove configurations, while the problematic ones are kept (or can be recovered) in the reduced net. This saves computation time in the analysis and, more importantly, provides useful insights about the root of undesired behaviors. This work focus on systems that can be modeled with fluid (or continuous) mono T-semiflow Timed Continuous Petri nets. Even if under certain constraints, they are capable of capturing many characteristics of modern systems, such as interleaving of cooperation and competition.