Boundedly Rational User Equilibrium with Restricted Unused Routes

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9848916/figures/9848916.fig.008a.svgz" name="9848916.fig.008a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>R-BRUE solution set with <svg height="8.55521pt" id="M391" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 26.6363 8.55521" width="26.6363pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.963,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.226,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9848916/figures/9848916.fig.008b.svgz" name="9848916.fig.008b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>R-BRUE solution set with <svg height="8.55521pt" id="M392" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 32.8997 8.55521" width="32.8997pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.963,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.226,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.466,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9848916/figures/9848916.fig.008c.svgz" name="9848916.fig.008c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>R-BRUE solution set with <svg height="8.55521pt" id="M393" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 32.8997 8.55521" width="32.8997pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.963,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.226,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.466,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></td></tr></table>

<div>R-BRUE solution sets illustration.</div>

Discrete Dynamics in Nature and Society

fig8

Figure 8

Figure 8: Boundedly Rational User Equilibrium with Restricted Unused Routes 