A Markov process methodology for modeling machine interactions in timber harvesting systems

Recent advancements in timber harvesting systems analysis have been almost exclusively simulation based. A similar degree of effort in developing analytic models has been conspicuously absent.

That part of timber harvesting analysis where simulation plays its most vital role is the study of machine interactions. The importance of machine interactions lies in determining the proportions of delay, idle and productive time for the interacting machines. This in turn, is important for balancing productivity so that no single component of the interaction is accumulating excessive amounts of delay or idle time.

The objective of this study was to determine the feasibility of applying Markov process theory to the analysis of timber harvesting systems and components. Through modeling the interaction between a fixed location slasher and a grapple skidder, it is shown how a Markov model can be used to obtain proportions of delay, idle and productive time. Unlike the statistical solutions derived from simulation models, the Markov model improves upon this by providing an analytic solution. The Markov model also avoids the problems of correlated output data from simulations by explicitly recognizing that any possible future state is dependent only on the current state of the system and is conditionally independent of the past history of the system.

The methodology for building a Markov model requires dealing with only two probability distributions, the Erlang and mixed Erlang, for modeling time based activities (such as cycle times) of the interacting machines. These probability distributions in turn, provide the necessary data for developing a system of algebraic equations for solving the Markov process model.

While this is the first step in applying stochastic process theory to timber harvesting analysis, the results of this study indicate that the technique has considerable potential for application in timber harvesting system modeling.