Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.

Optimisation of the food dairy coop supply chain

In the European Union under the Common Agricultural Policy (CAP) milk production was restricted by milk quotas since 1984. However, due to recent changes in the Common Agricultural Policy (CAP), milk quotas will be abolished by 2015. Therefore, the European dairy sector will soon face an opportunity, for the first time in a generation, to expand. Numerous studies have shown that milk production in Ireland will increase significantly post quotas (Laepple and Hennessy (2010), Donnellan and Hennessy (2007) and Lips and Reider (2005)). The research in this thesis explored milk transport and dairy product processing in the Irish dairy processing sector in the context of milk quota removal and expansion by 2020. In this study a national milk transport model was developed for the Irish dairy industry, the model was used to examine different efficiency factors in milk transport and to estimate milk transport costs post milk quota abolition. Secondly, the impact of different milk supply profiles on milk transport costs was investigated using the milk transport model. Current processing capacity in Ireland was compared against future supply, it was concluded that additional milk processing capacity would not be sufficient to process the additional milk. Thirdly, the milk transport model was used to identify the least cost locations (based on transport costs) to process the additional milk supply in 2020. Finally, an optimisation model was developed to identify the optimum configuration for the Irish dairy processing sector in 2020 taking cognisance of increasing transport costs and decreasing processing costs.