Research Article Route Choice Model Considering ...downloads.hindawi.com/journals/mpe/2013/464038.pdfRoute Choice Model Considering Generalized Travel Cost Based on Game Theory FengYu-qin,

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 464038 5 pageshttpdxdoiorg1011552013464038

Research ArticleRoute Choice Model Considering Generalized Travel Cost Basedon Game Theory

Feng Yu-qin1 Leng Jun-qiang23 Xie Zhong-Yu1 Zhang Gui-e3 and He Yi3

1 School of Automobile Engineering Heilongjiang Institute of Technology Harbin 150050 China2 School of Management Harbin Institute of Technology Harbin 150001 China3 School of Automobile Engineering Harbin Institute of Technology Weihai 264209 China

Correspondence should be addressed to Leng Jun-qiang lengjunqtomcom

Received 31 October 2012 Accepted 3 January 2013

Academic Editor Matjaz Perc

Copyright copy 2013 Feng Yu-qin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper aims at testing the influence of emission factors on travelersrsquo behavior of route choice The generalized travel cost isdefined as the linear weighted sum of emission factors travel time and travel time reliability The relational model of exhaustvolume and traffic volume is established using the BPR (Bureau of Public Road) function to calculate the cost of travel regardingemissionTheBPR function is used tomeasure the road segment travel time while the reliability is used to quantify the cost of traveltime fluctuation At last the route choice model considering the generalized travel cost is established based on the game theoryThe calculating and analyzing of results under a miniature road network show that the weight coefficient of travel cost influencesthe travelersrsquo behavior of route choice remarkably and the route choice model which takes emission into account can reduce theexhaust of road network effectively approximately 114 in this case

1 Introduction

How to reduce exhaust emission has become a very urgentsubject as the number of automobile grows rapidly in ChinaAt the moment research on energy saving and emissionreduction about the vehicle itself has been relatively maturewhile few studies were conducted concerning this problemfrom the perspective of traffic management The influence ofemission factors on travelersrsquo behavior of route choice will bestudied in this paper from the aspect of traffic managementwhich can provide information about vehicle emission fortrafficmanagers in order to decrease energy consumption andemission to some extent

Travel time cost and fuel consumption are usually con-sidered in travel cost estimation [1ndash3] However in generalformer route choice models only took travel time cost intoconsideration The researches on the relationship betweenroute choice model and exhaust emission are few [4 5] Andthere is only information about route length and travel time inthe traffic guidance system and no other valuable informationconcerning emission Travel cost was usually described usingtravel time which was presented by the BPR function

There are some route choice models of travelers suchas stochastic user equilibrium model and elastic demandequilibriummodel [6] As the prisonerrsquos dilemma games andits extensions have been studied frequently [7ndash10] the palygame is also used in the traffic distribution [11] Howevertheir BPR functions do not well reflect different demands oftravelers in choosing routes because emission has graduallybecome a factor affecting route choice And trip demandobjectives are not single and are often mutually contradic-tory for example shorter travel time higher reliability andsecurity [12 13] Hence generalized travel cost which tookemission into consideration was studied in the paper basedon the emission model for road segment Then the effectof route choice behavior and cost factors on route choice oftravelers was discussed

2 Generalized Travel CostConsidering Emission

Travelers are paying more attention to the emission problemin route choice besides the consideration of travel time andits fluctuation because of the aggravation of the energy crisis

2 Mathematical Problems in Engineering

and the pressing need of environmental protection It is theideal goal of travelers to reduce emission decrease travel timeincrease reliability and so forth [14] However these goalsoften lead to contradiction and conflicts Travelers are alwaysseeking compromise in pursuing them Therefore this paperis based on the generalized travel cost of the above factorsThegeneralized travel cost is defined as the linear weighted sumof travelersrsquo exhaust emission factor travel time and traveltime reliability So the generalized travel cost function maybe represented as

119888119886= 1199081119897119886119891119886(sdot) + 119908

2119879119886+ 1199083120574 (119879119886) (1)

where 119888119886is the generalized travel cost in road segment 119886 119891

119886(sdot)

represents the emission factor on road segment 119886 (gkm) 119897119886

is the length of road segment 119886 (km) 119879119886is the travel time of

road segment 119886 (s) 120574(119879119886) is the travel time fluctuation of road

segment 11988611990811199082 and119908

3are the weight of exhaust emission

travel time and travel time reliability in the generalizedtravel cost respectively These three weight coefficients mayreflect travelersrsquo attitude towards hazardsThe larger119908

1is the

smaller 1199082and 119908

3will be which means travelers pay more

attention to emission tending to consider emission as a routechoice criterion Each weight can be determined on the basisof SP (stated preference) survey

The generalized travel cost of travelers can be representedas

119888119908

119896= sum

119886isin119860

119888119886120575119908

119886119896 (2)

where 119888119908119896is the generalized travel cost of route 119896 in OD pair

119908 120575119908119886119896is a 0-1 variable if road segment 119886 lies in the route 119896 of

the OD pair 119908 then 120575119908119886119896= 1 otherwise 120575119908

119886119896= 0

21 Quantification of Travel Cost Index

211 Travel Time The BPR (Bureau of Public Roads) traveltime function proposed by theUnited States FederalHighwayAdministration is the most representative achievement in theresearch of travel time model The most significant influenceof the model is on the field of traffic planning and it is mostwidely used in this field It was initially used in the highwaynetwork planning later in urban road network planning [15]The mathematical expression is

119879119886= 119905119886[1 + 120573(

119909119886

119862119886

)

119899

] (3)

where 119879119886is the travel time of road segment 119886 (s) 119905

119886is the

free flow travel time of road segment 119886 (s) 119909119886is the traffic

flow of road segment 119886 (pcuh) 119862119886is the traffic capacity

of road segment 119886 (pcuh) 120573 119899 are the model parametersthe recommended values are 120573 = 015 119899 = 4 in highwaynetwork application

212 Travel Time Fluctuation In 1991 Asakura and Kashi-wadani [16] presented the travel time reliability concept toreflect travel time fluctuation Travel time reliability is defined

as the probability that a trip may be completed within a spec-ified time under a certain LOS (level of service) demandwhich is ameasure of travel time stability index and describesthe flexibility of road network in stochastic traffic conditionsIn this paper the travel time reliability is defined as

119877 (119879119886) = 119875 (119879

119886le 119905119886+ Δ1015840

) (4)

where Δ1015840 is the acceptable threshold of buffer time it usuallytakes 5 10 15 or 20 of the free travel time For thesimple reason that people have different tolerance degreesin various traffic congestions in different areas Δ1015840 may bedetermined through the SP investigation other parametershave the same meanings as previously mentioned Substitute(3) into (4)

119877119886(119879119886) = 119875[119862

119886ge 119909119886(

119905119886120573

Δ1015840)

1119899

] (5)

Due to the capacity 119862119886is a random variable the distribution

function 119865119862119886

(119909) can be obtained by field observation it maybe written as

119877119886(119879119886) = 1 minus 119865

119862119886

(119909119886(

119905119886120573

Δ1015840)

1119899

)

119903 (119879119886) = 1 minus 119877

119886(119879119886) = 119865119862119886

((

119905119886120573

Δ1015840)

1119899

119909119886)

(6)

In the formula 119903(119879119886) is the probability of road segment 119886 not

meeting the requirement of travel time reliability it is deemedthat 119903(119879

119886) is the negative utility of travel time fluctuation

213 Exhaust Emission Model Average speed of vehicles isone of the most important factors that affect the exhaustemission Margiotta [17] believed that emission factors weresensitive to speed and put forward the relational modelbetween them Wang et al [18] calculated emission factorsof vehicles under different average speeds using the modifiedMOBILE model based on the field data in Nanjing and thencarried out a curve fitting taking emission factors as thedependent variable and the average speed of motor vehicleas the independent variable The polynomial computationalmodel for traffic exhaust emission can be written as follows

119891119886= 1198870+ 1198871119907119886+ 11988721199072

119886+ 11988731199073

119886 (7)

where 119891119886represents emission factor of passenger car on road

segment 119886 (gkm) 119907119886is the average speed of vehicles on

road segment 119886 (kmh) 0 le 119907119886le 90 119887

0 1198871 1198872 and 119887

3are

regression coefficientsAverage speed of vehicles on a road segment can be

calculated by travel time as follows for the average speed ofthe vehicle equals road length divided by average travel time

119907119886=

119897119886

119879119886

=

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

(8)

where 119897119886is the length of road segment (km) other parameters

are of the samemeaning asmentioned previouslyThe volume

Mathematical Problems in Engineering 3

of exhaust emission can be expressed as the function of thelength of road segment traffic volume and its capacity

Pluging (8) into (7) we can get the followingmodel of thetraffic volume and exhaust emission

119891119886= 1198870+ 1198871(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

+ 1198872(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

2

+ 1198873(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

3

(9)

22 Weight of Cost Index Weight of different cost index maybe determined on the basis of SP data using the relativecomparison method First make all indexes a square matrixSecond compare every two indexes and score them using[0 1] scoring method Third sum up each index score anddo the normalizationThe weight of index 119894may be expressedas

119908119894=

sum119899

119895=1119886119894119895

sum119899

119894=1sum119899

119895=1119886119894119895

(10)

where 119886119894119895is the importance of index 119894 relative to index 119895 Other

parameters have the samemeanings asmentioned previously

23 Nondimensionalization of Indexes To make differentdimensional evaluation index comparable and additive themethod of mathematical transformation was used to elimi-nate the influence of index dimension in generalized travelcost This paper uses linear proportion method to processnondimensionalization The formula is

119910119894=

119909119894

1199091015840

119894

(11)

where 119909119894is the sample value 119910

119894is the dimensionless results of

119909119894 and 1199091015840

119894is the minimum maximum or average value of the

sample value

3 Game Theory Model

The theory of games is a study about the interaction betweenrational decision makers Each player has a number ofstrategies (feasible actions) which determines the outcomeof the game and the payment to each player In this game anetwork user looks for a route tominimize the expected travelcost while an ldquoevil entityrdquo imposes road segment costs on theuser so as to maximize the expected trip costThis is assumedto be a two-player noncooperative and zero-sum game Theuser guesses what road segment costs will be imposed andthe evil entity guesses which route will be chosen The mixedstrategy that the Nash equilibrium proposed offers a usefulmeasure for network reliability since it yields the expectedtrip costwhen the user is extremely pessimistic about the stateof the network [19 20]

We assume that situation 119895 implies performance degra-dation failure or attack on road segment 119894 The problem is tosolve the following maximization and minimization model

min119901119894

max119902119895

119862 = sum

119894119895

119901119894119888119894119895119902119895= sum

119894119895

sum

119896

120575119894119896ℎ119896119888119894119895119902119895

= sum

119896

ℎ119896sum

119895

119892119896119895119902119895

St sum119895

119902119895= 1

119902119895ge 0

sum

119896

120575119894119896ℎ119896= 119901119894

sum

119896

ℎ119896= 1

ℎ119896ge 0

(12)

where 119901119894is the probability that road segment 119894 is chosen 119902

119895

is the probability of situation 119895 119888119894119895is the travel cost of road

segment 119894 under situation 119895 119892119894119895is the travel cost of path 119896

under situation 119895 ℎ119896is the probability path 119896 is chosen 120575

119894119896

equals 1 if road segment 119894 is on path 119896 0 otherwiseTo facilitate the application of the route choice model the

method of successive average (MSA) scheme is used and itcan be described as follows

Step 1 Initialize 119902119895for all situations 119895 and 119899 larr 1

Step 2 Set expected road segment costs tosum119895119888119894119895119901119895for all road

segments 119894

Step 3 Build the least expected cost path 119909119894larr 1 if road

segment 119894 is on this path and 0 otherwise

Step 4 119901119894larr (1119899)119909

119894+ (1 minus 1119899)119901

119894for all road segments 119894

Step 5 Find the 119895 which maximizes sum119894119888119894119895119901119894 119910119895larr 1 for all

situations 119896 = 119895 119910119896larr 0

Step 6 119902119895larr (1119899)119910

119894+ (1 minus 1119899)119902

119895for all situations 119895

Step 7 119899 larr 119899 + 1 and return to Step 2 until a satisfactoryconvergence is achieved

4 Numerical Example

A numerical example was chosen to verify the applicabilityof the model proposed in this paper As shown in Figure 1it includes 4 nodes 5 road segments and 1 OD pair (1 rarr

4) The value of OD pair is 2600 pcuh In BPR functionparameters 120573 = 015 119899 = 4 road segments length free traveltime capacity and emission parameters and so forth areshown in Table 1 In the numerical example Δ1015840 takes 15 ofthe free travel time 119905

119886 Matlab 70 was used in the calculations

The results show that the different attitudes of travelerstowards travel cost have obvious effects on road network


Table 1 Attribute data of road network unit

Road segment Road segment 1 Road segment 2 Road segment 3 Road segment 4 Road segment 5Free travel time 119905

119886s 76 70 49 76 49

Capacity 119862119886(pcuh) 119873 (1400 70) 119873 (1100 90) 119873 (1000 120) 119873 (1400 70) 119873 (1000 120)

Length lm 1600 1900 1200 1600 1200Parameters of emission model1198870

168351 157483 168351 168351 1683511198871

minus53423 minus56240 minus53423 minus53423 minus534231198872

00674 00609 00674 00674 006741198873


Table 2 Volume under different weight coefficient (pcuh)

1199081

1199082

1199083

Road segment 1 Road segment 2 Road segment 3 Road segment 4 Road segment 50 10 0 662 1062 906 662 9060 0 10 843 962 795 843 79502 02 06 739 971 890 739 89002 04 04 641 1071 888 641 88802 06 02 767 1054 779 767 77902 08 0 705 994 901 705 90104 02 04 737 1083 781 737 78104 04 02 831 1031 738 831 73804 06 0 735 1004 861 735 86106 02 02 702 1044 854 702 85406 04 0 712 1030 857 712 85708 02 0 685 1076 840 685 84010 0 0 653 1043 904 653 904

1 4

2

3

D

1

2

3

4

5O

Figure 1 Test road network

traffic assignment From the results of Table 2 it can befound that when119908

1is gradually increasing until it approaches

1 which means gradually increase the weight of emissionfactor in travel cost the travelers tend to select emission as acriterion of route choice Meanwhile the travelers will selectthe low emission route as their priority selection Becauseroute 1ndash4 is the longest it is 168 times as long as route 2and 133 times as long as route 3ndash5 and it has the largestemission in terms of unit distance so the emission cost ofroute 1ndash4 is the highest When 119908

1is 1 the distributed traffic

capacity on route 1ndash4 is the lowest it is only 653 pcuhbut the traffic assignments on other routes are 1043 pcuhand 904 pcuh As a result the emission of the whole localroad network can be reduced by 114 When 119908

2increases

and approaches 1 it indicates that travelers tend to selecttravel time as a criterion of route choice and travelers tend

to select the lower time-consuming route Due to the factthat route 2 takes the shortest travel time route 3ndash5 thenext and then route 1ndash4 when 119908

2is 1 the distribution of

traffic on route 2 is the highest which is 1062 pcuh route3ndash5 is 906 pcuh and route 1ndash4 is the lowest which is only662 pcuh When 119908

3gradually approaches 1 it indicates that

the travelers tend to treat reliability as a criterion They willselect the high-capacity and low-fluctuation route and route3ndash5 has the lowest capacity and highest fluctuationThereforethe assignment on route 3ndash5 is the smallest which is only795 pcuh

5 Conclusions

On the basis of the research carried out on emission modelroad segment travel time travel reliability and generalizedtravel cost are defined and quantified Meanwhile the trafficdistributionmodel that considers emission is proposed basedon game theory By means of the calculation examples itis proved that travelersrsquo different attitudes towards emissionhave obvious effects on route choice The route choice modelconsidering emission can distinctly reduce road networkemission in the example it reduced by 114 With thepopularized application of ITS further researches about theeffects of information and other factors on route choicebehavior should be carried out


Acknowledgments

This research was supported by China Postdoctoral Sci-ence Foundation 2011M500676 National EducationMinistryHumanities and Social Sciences Foundation 12YJCZH097Heilongjiang Institute of Technology Doctoral Science Foun-dation 2011BJ05 Technology Research and DevelopmentProgram of Shandong 2012G0020129 and Natural ScienceFoundation of Heilongjiang Province QC2011C060 Theauthors are also grateful to the anonymous referees for theirhelpful comments and constructive suggestions on an earlierversion of the paper

References

[1] S Ghufran S Khowaja and M J Ahsan ldquoOptimummultivari-ate stratified sampling designs with travel cost a multiobjectiveinteger nonlinear programming approachrdquo Communications inStatistics vol 41 no 5 pp 598ndash610 2012

[2] G Erdogan M Battarra G Laporte and D Vigo ldquoMetaheuris-tics for the traveling salesman problem with pickups deliveriesand handling costsrdquo Computers and Operations Research vol39 no 5 pp 1074ndash1086 2012

[3] V Ovaskainen M Neuvonen and E Pouta ldquoModelling recre-ation demandwith respondent-reported driving cost and statedcost of travel time a finnish caserdquo Journal of Forest Economicsvol 18 no 4 pp 303ndash317 2012

[4] S Sugawara and D A Niemeier ldquoHow much can vehicle emis-sions be reduced Exploratory analysis of an upper boundaryusing an emissions-optimized trip assignmentrdquo TransportationResearch Record no 1815 pp 29ndash37 2002

[5] E Ericsson H Larsson and K Brundell-Freij ldquoOptimizingroute choice for lowest fuel consumptionmdashpotential effects of anew driver support toolrdquo Transportation Research C vol 14 no6 pp 369ndash383 2006

[6] C M Benedek and L R Rilett ldquoEquitable traffic assignmentwith environmental cost functionsrdquo Journal of TransportationEngineering vol 124 no 1 pp 16ndash22 1998

[7] Z Wang and M Perc ldquoAspiring to the fittest and promotion ofcooperation in the prisonerrsquos dilemma gamerdquo Physical ReviewE vol 82 no 2 Article ID 021115 2010

[8] M Perc and Z Wang ldquoHeterogeneous aspirations promotecooperation in the prisonerrsquos dilemma gamerdquo PLoS ONE vol5 no 12 Article ID e15117 2010

[9] Z Wang A Murks W B Du Z H Rong andM Perc ldquoCovet-ing thy neighbors fitness as ameans to resolve social dilemmasrdquoJournal of Theoretical Biology vol 277 no 1 pp 19ndash26 2011

[10] Z Wang S Attila and M Perc ldquoEvolution of public coopera-tion on interdependent networks the impact of biased utilityfunctionsrdquo Europhysics Letters vol 97 no 4 Article ID 480012012

[11] U Naohiro and T Eiichi ldquoA study of dispatcherrsquos route choicemodel based on evolutionary game theoryrdquo Procedia vol 39 pp495ndash509 2012

[12] K Ahn and H Rakha ldquoThe effects of route choice decisionson vehicle energy consumption and emissionsrdquo TransportationResearch D vol 13 no 3 pp 151ndash167 2008

[13] G H Tzeng and C H Chen ldquoMultiobjective decision makingfor traffic assignmentrdquo IEEE Transactions on Engineering Man-agement vol 40 no 2 pp 180ndash187 1993

[14] S Zerguini N Khademi and J Shahi ldquoVariability of travel timeusersrsquo uncertainty and trip information new approach to cost-benefit analysisrdquo Transportation Research Record no 2254 pp160ndash169 2011

[15] L Engelson ldquoProperties of expected travel cost function withuncertain travel timerdquo Transportation Research Record no2254 pp 151ndash159 2011

[16] Y Asakura and M Kashiwadani ldquoRoad network reliabilitycaused by daily fluctuation of traffic flowrdquo in Proceedings of the19th PTRC Summer Annual Meeting pp 73ndash84 Brighton UKSeptember 1991

[17] R A Margiotta Improved Vehicle Speed Estimation Proceduresfor Air Quality and Planning Application The University ofTennessee Knoxville Tenn USA 1996

[18] W Wang Q J Xiang and T Z Li Urban Transport SystemEnergy Consumption and Environmental Impact Analysis Sci-ence Press Beijing China 2003

[19] V Bioglio R Gaeta M Grangetto M Sereno and S Spoto ldquoAgame theory framework for ISP streaming trafficmanagementrdquoPerformance Evaluation vol 68 pp 1162ndash1174 2011

[20] L J Sun and Z Y Gao ldquoAn equilibrium model for urbantransit assignment based on game theoryrdquo European Journal ofOperational Research vol 181 no 1 pp 305ndash314 2007

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and the pressing need of environmental protection It is theideal goal of travelers to reduce emission decrease travel timeincrease reliability and so forth [14] However these goalsoften lead to contradiction and conflicts Travelers are alwaysseeking compromise in pursuing them Therefore this paperis based on the generalized travel cost of the above factorsThegeneralized travel cost is defined as the linear weighted sumof travelersrsquo exhaust emission factor travel time and traveltime reliability So the generalized travel cost function maybe represented as

119888119886= 1199081119897119886119891119886(sdot) + 119908

2119879119886+ 1199083120574 (119879119886) (1)

where 119888119886is the generalized travel cost in road segment 119886 119891

119886(sdot)

represents the emission factor on road segment 119886 (gkm) 119897119886

is the length of road segment 119886 (km) 119879119886is the travel time of

road segment 119886 (s) 120574(119879119886) is the travel time fluctuation of road

segment 11988611990811199082 and119908

3are the weight of exhaust emission

travel time and travel time reliability in the generalizedtravel cost respectively These three weight coefficients mayreflect travelersrsquo attitude towards hazardsThe larger119908

1is the

smaller 1199082and 119908

3will be which means travelers pay more

attention to emission tending to consider emission as a routechoice criterion Each weight can be determined on the basisof SP (stated preference) survey

The generalized travel cost of travelers can be representedas

119888119908

119896= sum

119886isin119860

119888119886120575119908

119886119896 (2)

where 119888119908119896is the generalized travel cost of route 119896 in OD pair

119908 120575119908119886119896is a 0-1 variable if road segment 119886 lies in the route 119896 of

the OD pair 119908 then 120575119908119886119896= 1 otherwise 120575119908

119886119896= 0

21 Quantification of Travel Cost Index

211 Travel Time The BPR (Bureau of Public Roads) traveltime function proposed by theUnited States FederalHighwayAdministration is the most representative achievement in theresearch of travel time model The most significant influenceof the model is on the field of traffic planning and it is mostwidely used in this field It was initially used in the highwaynetwork planning later in urban road network planning [15]The mathematical expression is

119879119886= 119905119886[1 + 120573(

119909119886

119862119886

)

119899

] (3)

where 119879119886is the travel time of road segment 119886 (s) 119905

119886is the

free flow travel time of road segment 119886 (s) 119909119886is the traffic

flow of road segment 119886 (pcuh) 119862119886is the traffic capacity

of road segment 119886 (pcuh) 120573 119899 are the model parametersthe recommended values are 120573 = 015 119899 = 4 in highwaynetwork application

212 Travel Time Fluctuation In 1991 Asakura and Kashi-wadani [16] presented the travel time reliability concept toreflect travel time fluctuation Travel time reliability is defined

as the probability that a trip may be completed within a spec-ified time under a certain LOS (level of service) demandwhich is ameasure of travel time stability index and describesthe flexibility of road network in stochastic traffic conditionsIn this paper the travel time reliability is defined as

119877 (119879119886) = 119875 (119879

119886le 119905119886+ Δ1015840

) (4)

where Δ1015840 is the acceptable threshold of buffer time it usuallytakes 5 10 15 or 20 of the free travel time For thesimple reason that people have different tolerance degreesin various traffic congestions in different areas Δ1015840 may bedetermined through the SP investigation other parametershave the same meanings as previously mentioned Substitute(3) into (4)

119877119886(119879119886) = 119875[119862

119886ge 119909119886(

119905119886120573

Δ1015840)

1119899

] (5)

Due to the capacity 119862119886is a random variable the distribution

function 119865119862119886

(119909) can be obtained by field observation it maybe written as

119877119886(119879119886) = 1 minus 119865

119862119886

(119909119886(

119905119886120573

Δ1015840)

1119899

)

119903 (119879119886) = 1 minus 119877

119886(119879119886) = 119865119862119886

((

119905119886120573

Δ1015840)

1119899

119909119886)

(6)

In the formula 119903(119879119886) is the probability of road segment 119886 not

meeting the requirement of travel time reliability it is deemedthat 119903(119879

119886) is the negative utility of travel time fluctuation

213 Exhaust Emission Model Average speed of vehicles isone of the most important factors that affect the exhaustemission Margiotta [17] believed that emission factors weresensitive to speed and put forward the relational modelbetween them Wang et al [18] calculated emission factorsof vehicles under different average speeds using the modifiedMOBILE model based on the field data in Nanjing and thencarried out a curve fitting taking emission factors as thedependent variable and the average speed of motor vehicleas the independent variable The polynomial computationalmodel for traffic exhaust emission can be written as follows

119891119886= 1198870+ 1198871119907119886+ 11988721199072

119886+ 11988731199073

119886 (7)

where 119891119886represents emission factor of passenger car on road

segment 119886 (gkm) 119907119886is the average speed of vehicles on

road segment 119886 (kmh) 0 le 119907119886le 90 119887

0 1198871 1198872 and 119887

3are

regression coefficientsAverage speed of vehicles on a road segment can be

calculated by travel time as follows for the average speed ofthe vehicle equals road length divided by average travel time

119907119886=

119897119886

119879119886

=

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

(8)

where 119897119886is the length of road segment (km) other parameters

are of the samemeaning asmentioned previouslyThe volume




119891119886= 1198870+ 1198871(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

+ 1198872(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

2

+ 1198873(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

3

(9)


119908119894=

sum119899

119895=1119886119894119895

sum119899

119894=1sum119899

119895=1119886119894119895

(10)




119910119894=

119909119894

1199091015840

119894

(11)



119909119894 and 1199091015840


sample value

3 Game Theory Model



min119901119894

max119902119895

119862 = sum

119894119895

119901119894119888119894119895119902119895= sum

119894119895

sum

119896

120575119894119896ℎ119896119888119894119895119902119895

= sum

119896

ℎ119896sum

119895

119892119896119895119902119895

St sum119895

119902119895= 1

119902119895ge 0

sum

119896

120575119894119896ℎ119896= 119901119894

sum

119896

ℎ119896= 1

ℎ119896ge 0

(12)


119895




119894119896





segments 119894



Step 4 119901119894larr (1119899)119909

119894+ (1 minus 1119899)119901



situations 119896 = 119895 119910119896larr 0

Step 6 119902119895larr (1119899)119910

119894+ (1 minus 1119899)119902



4 Numerical Example








119886s 76 70 49 76 49

Capacity 119862119886(pcuh) 119873 (1400 70) 119873 (1100 90) 119873 (1000 120) 119873 (1400 70) 119873 (1000 120)


168351 157483 168351 168351 1683511198871


00674 00609 00674 00674 006741198873



1199081

1199082

1199083


1 4

2

3

D

1

2

3

4

5O







2increases







5 Conclusions



Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119891119886= 1198870+ 1198871(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

+ 1198872(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

2

+ 1198873(

119897119886

119905119886[1 + 120573(119909

119886119862119886)119899

]

)

3

(9)


119908119894=

sum119899

119895=1119886119894119895

sum119899

119894=1sum119899

119895=1119886119894119895

(10)




119910119894=

119909119894

1199091015840

119894

(11)



119909119894 and 1199091015840


sample value

3 Game Theory Model



min119901119894

max119902119895

119862 = sum

119894119895

119901119894119888119894119895119902119895= sum

119894119895

sum

119896

120575119894119896ℎ119896119888119894119895119902119895

= sum

119896

ℎ119896sum

119895

119892119896119895119902119895

St sum119895

119902119895= 1

119902119895ge 0

sum

119896

120575119894119896ℎ119896= 119901119894

sum

119896

ℎ119896= 1

ℎ119896ge 0

(12)


119895




119894119896





segments 119894



Step 4 119901119894larr (1119899)119909

119894+ (1 minus 1119899)119901



situations 119896 = 119895 119910119896larr 0

Step 6 119902119895larr (1119899)119910

119894+ (1 minus 1119899)119902



4 Numerical Example








119886s 76 70 49 76 49

Capacity 119862119886(pcuh) 119873 (1400 70) 119873 (1100 90) 119873 (1000 120) 119873 (1400 70) 119873 (1000 120)


168351 157483 168351 168351 1683511198871


00674 00609 00674 00674 006741198873



1199081

1199082

1199083


1 4

2

3

D

1

2

3

4

5O







2increases







5 Conclusions



Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119886s 76 70 49 76 49

Capacity 119862119886(pcuh) 119873 (1400 70) 119873 (1100 90) 119873 (1000 120) 119873 (1400 70) 119873 (1000 120)


168351 157483 168351 168351 1683511198871


00674 00609 00674 00674 006741198873



1199081

1199082

1199083


1 4

2

3

D

1

2

3

4

5O







2increases







5 Conclusions



Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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