Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections

<div>The distance over time. (a) <span class="nowrap"><svg height="10.4342pt" id="M41" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -7.25272 28.8961 10.4342" width="28.8961pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.998,3.132)"><path d="M345 0V33C260 38 258 46 258 122V635C174 612 105 594 35 583V554L87 550C124 546 130 539 130 494V122C130 46 127 38 42 33V0H345Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.507,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.77,0)"><path d="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z"></path></g></svg>;</span> (b) <span class="nowrap"><svg height="10.9562pt" id="M42" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -7.77468 28.8961 10.9562" width="28.8961pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.998,3.132)"><path d="M345 0V33C260 38 258 46 258 122V635C174 612 105 594 35 583V554L87 550C124 546 130 539 130 494V122C130 46 127 38 42 33V0H345Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.507,0)"><path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.77,0)"><path d="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z"></path></g></svg>.</span></div>

Journal of Advanced Transportation

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Figure 3

Figure 3: Queue Length Estimation Based on Probe Vehicle Data at Signalized Intersections 