## 4 Discussion  
The analysis model of traffic flow theory [15; 16; 17; 18; 19; 20] focused on describing the evolutionary behavior of traffic variables temporally and spatially. In historical studies [5; 21], the statistics of traffic variables were collected and counted in aggregate based on a single detector observation. In modern traffic systems, or the so called intelligent transportation systems, vehicle detections are accomplished automatically via the transaction data of electronic devices of, which vehicle identification is widely  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Extracting Significant Travel Time Patterns** & **Processes** & **Computational Time (hmin:s)** \\ \hline Pass One & Determining Right Boundary & 13:21:01 \\ Pass Two & Determining Left Boundary Verification & 12:56:47 \\  & Boundary Verification & 0:18:21 \\  & Total & 26:36:09 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Computational time via a Hadoop cluster with two name nodes and six computing nodes.  
Figure 15: The average of travel time of vehicles in the northern (N) direction vs. “24 h per day” and “seven days per week”.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hardware/Software** & **Specifications** \\ \hline CPU & Intel® Xeon® Processor E5-2630 v3 (8 cores) \\ RAM & 128 GB (16G**B**8, ECC/REG DDR4 2133 ) \\ Hard Disk & 6 TB (SATA 2 TB*3, 7200 rpm 3.5 inch) \\ Network Card & Intel Ethernet X540 10 GBASE-T RJ45 DualPort *4 \\ OS & CentOS 6.7 \\ Hadoop & Hadoop 2.6 (“Cloudera Express 5.4.5”) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Specifications of hardware and software within one computing node.  
available. With these records collected and the novel approach proposed in this paper, one can not only analyze the characteristics of traffic flow but also study the traffic congestion problem about the upstream propagation phenomenon such that he/she can have more precise observation about traffic flow from a microscopic point of view.  
Due to the scalability of the previous work [7], it is believed that our approach can handle a larger amount of timestamp gantry sequences collected from a longer time period, e.g., several years. With these long-term and fine-grain statistics of travel time patterns of vehicles, the domain expects to have precise observation of vehicle behavior such that they can trace back to analyzing why these historical events resulted in traffic jam or congestion. Therefore, they can provide a new approach or police to avoid such a situation happening again in the future.  
Indeed, there is still a lot of room for improving this study. First of all, an interactive data visualization interface, especially integrated with geographical map, is needed to promote the usage of these statistics as well as to stimulate users' comprehension sensitively. Instead of \"Hadoop\" based on an external-memory method, on the other hand, \"Spark\", an in-memory distributed computing, is expected to run 100\(\times\) faster than Hadoop MapReduce.With the aid of cloud computing for sharing these statistics of travel time patterns in times, if possible, that are computed consistently via \"Spark\", it may be attractive and expected to have this work as a software package, for providing current traffic information, integrated with IoT (Internet of Things) to make smart or driverless cars with more intelligence in the future.