A wireless sensor network can be used to track an object. Every sensor has limited energy and detecting range. In order to conserve energy, sensors may be put into sleeping mode. A sensor in the sleeping mode can not communicate with other sensors or detect objects. When the object moves to the sensing range of a sleeping sensor, a tracking error occurs. To minimize the tracking error subject to an constraint on energy consumption, we should determine the sleeping schedules of sensors based on the mobility pattern of the object. We propose determining the sleeping schedules based on the observation history of the moving object. We use computer simulation to justify the usage of the proposed approach.

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The aim of this thesis is to first give a brief review of waiting line problems which often is a subject related to queueing theory. Simple counting processes such as the Poisson process and the duration of service time of each customer being exponentially distributed are often taught in a undergraduate or graduate stochastic process course. In this thesis, we will continue discussing such waiting line problems with priority assignment on each customer. This type of queueing processes are called priority queueing models. Patients requiring ER service are triaged and the order of providing service to patients more than often reflects early symptoms and complaints than final diagnoses. Triage systems used in hospitals vary from country to country and region to region. However, the goal of using a triage system is to ensure that the sickest patients are seen first. Such wait line system is much comparable to a priority queueing system in our study. The finite Markov chain imbedding technique is very effective in obtaining the waiting time distribution of runs and patterns. Applying this technique, we are able to obtain the probability distribution of customer wait time of priority queues. The results of this research can be applied directly when studying patient wait time of emergency medical service. Lengthy ER wait time issue often is studied from the view of limited spacing and complications in hospital administration and allocation of resources. In this thesis, we would like to study priority queueing systems by mathematical and probabilistic modeling.

An optimal stochastic multi-crop irrigation scheduling algorithm was developed which was able to incorporate complex farm system models, and constraints on daily and seasonal water use, with the objective of maximising farm profit. This scheduling method included a complex farm simulation model in the objective function, used decision variables to describe general management decisions, and used a custom heuristic method for optimisation. Existing optimal schedulers generally use stochastic dynamic programming which relies on time independence of all parameters except state variables, thereby requiring over-simplistic crop models. An alternative scheduling method was therefore proposed which allows for the inclusion of complex farm system models. Climate stochastic properties are modelled within the objective function through the simulation of several years of historical data. The decoupling of the optimiser from the objective function allows easy interchanging of farm model components. The custom heuristic method, definition of decision variables, and use of the Markov chain equation (relating an irrigation management strategy to mean water use) considerably increases optimisation efficiency. The custom heuristic method used simulated annealing with continuous variables. Two extensions to this method were the efficient incorporation of equality constraints and utilisation of population information. A case study comparison between the simulated annealing scheduler and scheduling using stochastic dynamic programming, using a simplistic crop model, showed that the two methods resulted in similar performance. This demonstrates the ability of the simulated annealing scheduler to produce close to optimal schedules. A second case study demonstrates the ability of the simulated annealing scheduler to incorporate complex farm system models by including the FarmWi$e model by CSIRO in the objective function. This case study indicates that under conditions of limited seasonal water, the simulated annealing scheduler increases pasture yield returns by an average of 10%, compared with scheduling irrigation using best management practice. Alternatively expressed, this corresponds to a 20-25% reduction in seasonal water use (given no change in yield return).

The aim of this thesis is to first give a brief review of waiting line problems which often is a subject related to queueing theory. Simple counting processes such as the Poisson process and the duration of service time of each customer being exponentially distributed are often taught in a undergraduate or graduate stochastic process course. In this thesis, we will continue discussing such waiting line problems with priority assignment on each customer. This type of queueing processes are called priority queueing models. Patients requiring ER service are triaged and the order of providing service to patients more than often reflects early symptoms and complaints than final diagnoses. Triage systems used in hospitals vary from country to country and region to region. However, the goal of using a triage system is to ensure that the sickest patients are seen first. Such wait line system is much comparable to a priority queueing system in our study. The finite Markov chain imbedding technique is very effective in obtaining the waiting time distribution of runs and patterns. Applying this technique, we are able to obtain the probability distribution of customer wait time of priority queues. The results of this research can be applied directly when studying patient wait time of emergency medical service. Lengthy ER wait time issue often is studied from the view of limited spacing and complications in hospital administration and allocation of resources. In this thesis, we would like to study priority queueing systems by mathematical and probabilistic modeling.

We present a Markov chain analysis for studying the performance of wireless ad hoc networks. The models presented in this dissertation support an arbitrary backoff strategy. We found that the most important parameter affecting the performance of binary exponential backoff is the initial backoff window size. Our experimental results show that the probability of collision can be reduced when the initial backoff window size equals the number of terminals. Thus, the throughput of the system increases and, at the same time, the delay to transmit the frame is reduced. In our second contribution, we present a new analytical model of a Medium Access Control (MAC) layer for wireless ad hoc networks that takes into account frame retry limits for a four-way handshaking mechanism. This model offers flexibility to address some design issues such as the effects of traffic parameters as well as possible improvements for wireless ad hoc networks. It effectively captures important network performance characteristics such as throughput, channel utilization, delay, and average energy. Under this analytical framework, we evaluate the effect of the Request-to-Send (RTS) state on unsuccessful transmission probability and its effect on performance particularly when the hidden terminal problem is dominant, the traffic is heavy, or the data frame length is very large. By using our proposed model, we show that the probability of collision can be reduced when using a Request-to-Send/Clear- to-Send (RTS/CTS) mechanism. Thus, the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. In our third contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account channel bit errors and frame retry limits for a two-way handshaking mechanism. This model offers flexibility to address design issues such as the effects of traffic parameters and possible improvements for wireless ad hoc networks. We illustrate that an important parameter affecting the performance of binary exponential backoff is the initial backoff window size. We show that for a low bit error rate (BER) the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. Results show also that the negative acknowledgment-based (NAK-based) model proves more useful for a high BER. In our fourth contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account Quality of Service (QoS) of the MAC layer for a two-way handshaking mechanism. The model includes a high priority traffic class (class 1) and a low priority traffic class (class 2). Extension of the model to more QoS levels is easily accomplished. We illustrate an important parameter affecting the performance of an Arbitration InterFrame Space (AIFS) and small backoff window size limits. They cause the frame to start contending the channel earlier and to complete the backoff sooner. As a result, the probability of sending the frame increases. Under this analytical framework, we evaluate the effect of QoS on successful transmission probability and its effect on performance, particularly when high priority traffic is dominant. / Graduate

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This study tests the size effect in the London Stock Exchange, using data for all nonfinancial listed firms from January 1985 to December 1995. The initial tests indicate that average stock returns are negatively related to firm size and that small firm portfolios earn returns in excess of the market risk. Further, the study tests whether the size effect is a proxy for variables such as the Book-to- Market Value and the Borrowing Ratio, as well as the impact of the dividend and the Bid- Ask spread on the return of the extreme size portfolios. The originality of this study is in the application of the Markov Chain Model to testing the Random Walk and Bubbles hypotheses, and the Vector Autoregression (VAR) framework for testing the relationship of macroeconomic variables with size portfolio returns.

Master of Science / Department of Agricultural Economics / Terry Griffin / Farmers and agricultural lenders often seek the ability to identify positive or negative characteristics to improve farm operations. Determining these characteristics has been the goal of many research studies. More often than not, a unique set of uncontrollable events was credited for contributing the majority of one farm’s success relative to their peers. The goal of this study was to evaluate the assumption that farmers can control their financial persistence defined as remaining in their current financial category, based upon a farm’s debt to asset ratio (D/A), and net farm income per acre (NFI acre⁻¹). Financial categories give agricultural producers a concrete answer to the question of one farm’s ability to maintain their financial persistence during market downturns and poor growing conditions and include Favorable, Marginal Income, Marginal Solvency, and Vulnerable. Farmers across the United States are subject to many uncontrollable variables (temperature, precipitation, market volatility, land value fluctuations, interest rates) leaving them vulnerable to agricultural market downturns, such as the one that began in 2014. Seasonal cash inflows and outflows of farms and their profitability create a difficult situation for farmers and agricultural lenders alike to predict the future. Identifying and estimating the likelihood of financial persistence has become an area of interest for farmers, their advisors, and their financial lenders. Currently, agricultural lenders rely on loan assessment techniques, such as net present values and loss-based methods. These techniques fail to account for the unique and often long-term investment nature of farming. If an additional method for identifying at-risk farms or at least understanding the likelihood of persistence in farms could be found, it would provide an insight into the riskiness of lending to a farm and provide agricultural lenders with an additional analysis tool. The dynamic nature of farm financials and the ever-changing variables of farming limit traditional statistical methods. Considering the difficulty associated with predicting farm default rates due to the complexity of the question, a secondary approach is possible. This study utilized an approach in determining farm financial persistence by estimating the Markov Chain probabilities of four financial categories ranging from Favorable, solvent with positive income to Vulnerable, an insolvent and negative income financial position. Kansas Farm Management Association (KFMA) data from 1993 to 2014 were used to estimate the probability of transitioning between financial categories. This thesis combines transition probabilities of Kanas farms and a multinomial logit model (MNL) to identify farm characteristics of significance. The matrix of probabilities generated, when interpreted, provide information about Kansas farms and their probability of financial persistence, and the MNL model allows for insights into favorable or un-favorable farm characteristics. Farms were found to transition easily between financial categories that had the same debt to asset ratio (D/A), but different net farm income per acre (NFI acre⁻¹, positive or negative) indicating that farm income is more easily changed than farm D/A ratios. Farms in the Favorable category (D/A < 0.4, + NFI acre⁻¹) had the largest probability of financial persistence at 0.83, whereas Vulnerable farms (D/A > 0.4, - NFI acre⁻¹) were most likely to transition to the Marginal Solvency category (D/A > 0.4, + NFI acre⁻¹) with a probability of transitioning of 0.55 versus the probability of remaining in the Vulnerable category of 0.33. It was also found that crop mixture and age were not statistically significant in the MNL model, but gross profit margin and a farm’s percentage of owned land out of total crop acres were statistically significant in explaining why farms were in each category.