38 11Results and Discussion•TheunknownparametersoftheGaussianmixturedistributionwereestimatedbyusingtheExpectation–MaximizationAlgorithm.•Traveltimeofnon-workingdays(peak)andthatofnon-workingdays(off-peak)bothindicatethatamixtureoftwoGaussiandistributionisbimodal(Schillingetal.,2002).•Theestimatedresultscanillustratethecongestedstatewithalargermeanandstandarddeviation,andtheuncongestedstatewithasmallermeanandstandarddeviation,respectively.GroupsCongested stateUncongested state(mixture)(mean)(SD)(mean)(SD)Working days (peak)615.22 229.00 311.44 98.48 0.33 Working days (off-peak)379.30 123.53 236.42 56.47 0.05 Non-working days (peak)*465.14 98.99 275.47 62.29 0.43 Non-working days (off-peak)*390.65 54.87232.00 49.22 0.08 Note: 1) SD is the acronym of standard deviation.2) * indicates a bimodal mixture of two Gaussian distributions .11221212()12Results and Discussion•Agraphicalillustrationoftraveltimefittingresults(fourgroups)isshownasfollows.•TheGaussianmixturedistributionhasahighervalueofthedecimallogarithmoflikelihoodwithrespecttosampledata.0.000.040.080.120.160.200.240501001502002503003504004505005506006507007508008509009501000Probability DensityTravel time (Unit: second)histogramGaussianmixture0.000.040.080.120.160.200.240501001502002503003504004505005506006507007508008509009501000Probability DensityTravel time (Unit: second)histogramGaussianmixture(a) Working days (peak)(a) Non-working days (peak)0.000.040.080.120.160.200.240501001502002503003504004505005506006507007508008509009501000Probability DensityTravel time (Unit: second)histogramGaussianmixture0.000.040.080.120.160.200.240501001502002503003504004505005506006507007508008509009501000Probability DensityTravel time (Unit: second)histogramGaussianmixture(a) Working days (off-peak)(a) Non-working days (off-peak)
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