Forecast of Freight Volume in Xi’an Based on Gray GM (1, 1) Model and Markov Forecasting Model

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Year</td><td class="align_center">Freight volume (<span class="nowrap"><svg height="11.7978pt" id="M27" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 22.0225 11.7978" width="22.0225pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.527,-5.741)"><path d="M253 635C142 635 71 555 71 471C71 401 113 353 178 316C144 294 106 267 91 252C70 231 46 202 46 157C46 51 132 -12 241 -12C328 -12 442 52 442 168C442 257 379 305 311 343C354 373 380 398 388 407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.473,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g></svg>)</span></td><td class="align_center">Predicted value (<span class="nowrap"><svg height="11.7978pt" id="M28" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 22.0225 11.7978" width="22.0225pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.527,-5.741)"><path d="M253 635C142 635 71 555 71 471C71 401 113 353 178 316C144 294 106 267 91 252C70 231 46 202 46 157C46 51 132 -12 241 -12C328 -12 442 52 442 168C442 257 379 305 311 343C354 373 380 398 388 407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.473,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g></svg>)</span></td><td class="align_center">Relative error (%)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">2009</td><td class="align_center">3.0606</td><td class="align_center">2.6050</td><td class="align_center">−14.87</td></tr><tr><td class="align_left">2010</td><td class="align_center">3.4323</td><td class="align_center">3.0894</td><td class="align_center">9.99</td></tr><tr><td class="align_left">2011</td><td class="align_center">3.9239</td><td class="align_center">3.6325</td><td class="align_center">−7.43</td></tr><tr><td class="align_left">2012</td><td class="align_center">4.4924</td><td class="align_center">4.3272</td><td class="align_center">−3.68</td></tr><tr><td class="align_left">2013</td><td class="align_center">5.0119</td><td class="align_center">5.1615</td><td class="align_center">2.98</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Xi’an’s predicted freight volume from 2009 to 2013 based on the Gray GM (1, 1) model.</div>

Journal of Mathematics

tab2

Table 2

Table 2: Forecast of Freight Volume in Xi’an Based on Gray GM (1, 1) Model and Markov Forecasting Model 