A winter index for benchmarking winter road maintenance operations on Ontario highways

Canada is one of the snowiest countries in the world, and winter road maintenance activities cost in the order of a billion dollars a year. These activities vary considerably over both space and time, partly due to differences in winter weather, but also because of differences in road and traffic mix, terrain and other factors. The thesis explores the association between winter road maintenance activities and winter weather. The first objective is to characterize the spatial and temporal variation in severe winter weather in Ontario. The second objective is to identify a winter weather index that is sensitive to road maintenance activities in Ontario. The third objective is to modify the identified winter index based on Ontario’s climate and road maintenance situations. To account for the variation in winter weather from year to year and across the Province, three winter weather indices were applied to Ontario data. Monthly index values were correlated with monthly salt usage, on a maintenance district level, for the recent five winters. One of these indices was then modified to better reflect the Ontario situation. Road information was also considered. The main results include: the spatial and temporal variation of winter weather severity in Ontario is quite large. Among the winter indices concerned, the SHRP winter index is most suitable for Ontario winter road maintenance. After assigning particular weights on certain climate variables and adding a freezing precipitation variable, the modified SHRP index correlated better with salt usage than the original SHRP index did in most MT O districts. Salt usage regression models with temperature and precipitation as the explanatory variables performed similarly to the SHRP index at the district level, but the model coefficients varied considerably from one district to another indicating that there are substantial place differences in how road maintenance authorities respond to winter weather. The significance of the results is realized when applied to winter road maintenance management procedures. The SHRP index can be used at the district level to interpret temporal differences in regional salt usage and winter severity. This index can also be used to indicate the spatial distribution of winter severity and road salt usage across the province, aiding in the allocation of maintenance resources to different regions based on winter weather

An Iterative Scheme for Leverage-based Approximate Aggregation

The current data explosion poses great challenges to the approximate aggregation with an efficiency and accuracy. To address this problem, we propose a novel approach to calculate the aggregation answers with a high accuracy using only a small portion of the data. We introduce leverages to reflect individual differences in the samples from a statistical perspective. Two kinds of estimators, the leverage-based estimator, and the sketch estimator (a "rough picture" of the aggregation answer), are in constraint relations and iteratively improved according to the actual conditions until their difference is below a threshold. Due to the iteration mechanism and the leverages, our approach achieves a high accuracy. Moreover, some features, such as not requiring recording the sampled data and easy to extend to various execution modes (e.g., the online mode), make our approach well suited to deal with big data. Experiments show that our approach has an extraordinary performance, and when compared with the uniform sampling, our approach can achieve high-quality answers with only 1/3 of the same sample size.Comment: 17 pages, 9 figure