A Discrete State, Continuous Parameter Markov Process Approach to Timber Harvesting Systems Analysis

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The introduction of simulation into timber harvesting systems analysis has spawned a proliferation of such models. As a result, the potential for applying stochastic process theory has been largely overlooked. This paper develops the theoretical aspects of a discrete state, continuous parameter Markov process model for application to timber harvesting systems analysis. Erlang and mixed Erlang probability distributions are introduced as models for time-based timber harvesting activities. These families of distributions are used because they offer flexibility in modeling the variety of distributions encountered in the field, yet maintain the integrity of the Markov assumptions. General formulation and solution of the Markov process model is discussed. An application of the theory to the analysis of timber harvesting system interaction is presented. The interaction between a grapple skidder and a mechanical slasher is formulated and solved as a discrete state, continuous parameter Markov process. The analytic solution showed that the system was severely unbalanced, with the skidder delayed 84.5% of the time, the slasher never idle, and both simultaneously performing productive work 15.5% of the time. For. Sci. 34(2):276-291.

Keywords: State space; random variable; rate matrix; steady-state

Document Type: Journal Article

Affiliations: Associate Professor, Department of Forest Products, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

Publication date: June 1, 1988

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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