Establishing Monitoring Programs for Travel Time Reliability (2014) / Chapter Skim
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51 C h a p t e r 5 Introduction Operating agencies have historically created monitoring systems that use sensors placed at strategic locations along their freeway networks. Figure 5.1 shows a section of freeway in California where there are 10 sensors in 5 miles, or a sensor about every 0.5 miles.
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52 Figure 5.1. Typical sensor spacing on a freeway.
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53 Approximating Temporal Patterns from Discrete Samples If traffic measurements (from a continuous traffic process) are available at some time interval (say, 30 seconds)
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54 Using the first three frequency components (up to a 6.7-hour wavelength, a frequency of 1/0.15 cycles/hour) , it is possible to capture the day-by-day trends, as seen in Figure 5.6.
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55 Nyquist–Shannon sampling theorem to determine the theoretical minimum sampling rate. That is, if a function xt contains no frequencies higher than B hertz, it is completely determined from a series of sample points spaced 1/2B seconds apart.
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56 find a spatial wavelength of about 0.3 miles (again stop to stop)
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57 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 5 10 15 20 25 30 35 40 Distance: ft Sp ee d: fe et /s ec (a) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 5 10 15 20 25 30 35 40 Distance: ft Sp ee d: ft /s ec (b)
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58 (c) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 5 10 15 20 25 30 35 40 Distance: ft Sp ee d: ft /s ec Figure 5.9.
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59 Figure 5.10. (continued)
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60 spectrum pattern still lacks a clear indication of what the cutoff frequency should be. In general, identifying the cutoff frequency is difficult in its own right and may require a large data set to uncover the inherent patterns.
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61 nonrecurring events occur, although 30 seconds is somewhat better. • Longer sampling intervals can be used when transients are not expected (e.g., off peak)
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