Dynamically Computing Approximate Frequency Counts in Sliding Window over Data Stream

This paper presents two one-pass algorithms for dynamically computing frequency counts in sliding window over a data stream-computing frequency counts exceeding user-specified threshold ε. The first algorithm constructs subwindows and deletes expired sub-windows periodically in sliding window, and each sub-window maintains a summary data structure. The first algorithm outputs at most 1/ε ＋ 1 elements for frequency queries over the most recent N elements. The second algorithm adapts multiple levels method to deal with data stream. Once the sketch of the most recent N elements has been constructed, the second algorithm can provides the answers to the frequency queries over the most recent n （ n≤N） elements. The second algorithm outputs at most 1/ε ＋ 2 elements. The analytical and experimental results show that our algorithms are accurate and effective.

Statistical modeling of total crash frequency at highway intersections

Intersection-related crashes are associated with high proportion of accidents involving drivers, occupants, pedestrians, and cyclists. In general, the purpose of intersection safety analysis is to determine the impact of safety-related variables on pedestrians, cyclists and vehicles, so as to facilitate the design of effective and efficient countermeasure strategies to improve safety at intersections. This study investigates the effects of traffic, environ- mental, intersection geometric and pavement-related characteristics on total crash fre- quencies at intersections. A random-parameter Poisson model was used with crash data from 357 signalized intersections in Chicago from 2004 to 2010. The results indicate that out of the identified factors, evening peak period traffic volume, pavement condition, and unlighted intersections have the greatest effects on crash frequencies. Overall, the results seek to suggest that, in order to improve effective highway-related safety countermeasures at intersections, significant attention must be focused on ensuring that pavements are adequately maintained and intersections should be well lighted. It needs to be mentioned that, projects could be implemented at and around the study intersections during the study period （7 years）, which could affect the crash frequency over the time. This is an important variable which could be a part of the future studies to investigate the impacts of safety related works at intersections and their marginal effects on crash frequency at signalized intersections.

THE POINT PROCESS OF STATETRANSITIONS IN AREGULAR MARKOV CHAIN

In this paper, we study the point process of state transitions in a regular Markov chain.Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution,the renewal distribution and the entering probability. As an applicstion, using these formulas we derive the LS transform of the busy period for the M/M/∞ queue.