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UBC Theses and Dissertations

An investigation into a two stage tandem queue for an optimum sawmill design Zwick, Robert Lewis


The applicability of queueing theory as an operations research tool for modelling sawmills is described. The model selected is a two-stage tandem queue with two stations in the second stage. Each of the stations has general service times and finite buffer storage capacities which create the possibility of blocking pieces coming out of the first stage. A three-variable service time distribution is proposed to model sawmill machinery processing the pieces. This distribution creates the potential to functionally describe the sawmilling process, in contrast to the traditional method of using empirical distributions gathered at an existing sawmill. The literature in tandem queues reveals the lack of work done and the degree of difficulty in this field of study. Analytical solutions do not exist for the queue system studied. Numerical approximation techniques were not used to model the queue system, but they have good potential for being utilized. A simulation study was performed on the queue system. A computer program was written with the intention of obtaining results anticipated in a mathematical analysis. Two separate queue disciplines were studied: saturated and unsaturated first-stage queues. The unsaturated queue investigated the dependency of system performance on the arrival rates. It also examined the operation of the queue under different second-stage arrival intensities. The saturated queue analysis focused on the phenomenon of piece blocking in the first stage. Some conclusions could be made from the simulation study with regards to design procedures for a sawmill. The study showed that in certain cases, improvement to system production by increasing a second-stage machine rate can be comparable to increasing the headrig rate. In addition, two stations in the second stage can complicate the analysis significantly. The simulation study also examined the possibility of utilizing tandem queue analysis to provide solutions for optimum second-stage buffer capacities. The feasibility of modelling sawmills by tandem queues exists, but the designer must choose the appropriate analytical method to use. Numerical approximation techniques would likely prove to be the most successful method. Machine service times should also be studied in a sawmill to establish the statistical nature of the sawmilling process. This will improve the solutions provided by queueing theory analysis.

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