IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 11, November

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1 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. ISSN Matematical Model of Urban Taxi Subsidy Sceme Xiao Tong 1,Wang Zuo,Yang Liucong 3,Cen Cai 1, Yang Yanmei * 1 Arcitectural Engineering Institute, Nort Cina Uniersity of Science and Tecnology, Tangsan,Hebei,063000,Cina College of Science, Nort Cina Uniersity of Science and Tecnology, Tangsan,Hebei,063000,Cina 3 College of Information Engineering, Nort Cina Uniersity of Science and Tecnology, Tangsan,Hebei,063000,Cina yangyanmei@euu.edu.cn Abstract Te problem of aing difficulty to take a taxi is a ot issue in modern society. Te current researc on reasonable planning of urban taxi layout are mostly based on traditional way, Howeer tere are few researces related to te tird party platform. In order to effectiely improe te efficiency of waiting for a taxi, te subsidy sceme matematical model is studied in tis paper. Used two indicators of eicle mileage utilization and load factor to measure weter te balance of supply and demand determines taxi introduced balance correction coefficient, te degree "matcing supply and demand" is discussed. And analysis of te balance between supply and demand of taxi and taxi operators establis regional balance model based on te companys. Te study sows tat te existing taxi subsidy programs can alleiate te current situation to a certain extent. Finally, we use te eolutionary game model, and determine te weigts for eac part, ten get te new subsidy program tat cooperates wit te taxi company. Subsidies will be part of te profits to te taxi company. Te subsidy sceme elps taxi companies adocate te implementation of reasonable sceme. Keywords: Balance of te supply and demand; Reasonable scale; Subsidy sceme; eolutionary game model 1. Introduction According to some inestigations on te traffic status, urban traffic problems become increasingly serious. Especially te problems of aing difficulty take a taxi urgently need to sole. As te coming of Internet age, tere are lots of companies set up te software serice platforms of taking a taxi relying on te mobile Internet, wic aciees te information excanging between te passengers and te taxi drier. Te preious studies about a reasonable taxi plan are most based on te traditional taxi ways, oweer tere s few researc on te way in wic using te tird party platform to take a taxi. In order to elp te taxi firms propose reasonable plans and increase te efficiency tat people take a taxi, tis paper mainly study on te matcing degree of supply and demand of taxi resources among different time and space in te Internet age, and explores weter te taxi software and subsidy programs of tose taxi companies are elpful to ease te problem of Haing difficulty to take a taxi, wic can proide a reference for urban traffic management departments.. Te matcing model of supply and demand Tere are tree relationsips between supply and demand of taxi: basic balance of supply and demand, supply exceeding demand or demand exceeding supply. So to tell weter tere is a balance between supply and demand of taxi, we can measure mainly troug te mileage utilization ratio and te eicle load ratio[1] two indicators..1 Te reasonable scale model based on te balance between supply and demand By coosing model parameters from te aboe supply and demand angle, we can find tat te total effectie mileage of a taxi as a direct influence on taxi passenger demand and taxi supply. Terefore we can coose te total effectie mileage of a taxi as a model ariable [] wic tells weter tere is a balance between supply and demand of taxi, so tat we can set up te urban taxi s reasonable scale model based on te balance between supply and demand..1.1 Measurement and calculation of te total effectie traeling mileage of a taxi from a demand angle ( 1 ) Measurement and calculation of te traeling turnoer wic taxi undertakes Te traeling turnoer of urban residents and floating population wic taxi undertakes are partly expressed by formula (4)and formula (5). Q1 = P1 λ 1 pro( Taxi) 1D1 (4) Q = P λ pro( Taxi) D (5) In te two formulas: Q1, Q Respectiely represents te traeling turnoer of urban residents and floating population wic taxi undertakes; P1, P Respectiely represents te urban resident population and te total floating population; λ1, λ Respectiely represents te per capita daily trael times of urban resident and floating population; 597

2 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. pro( Taxi) 1, pro( Taxi ) Respectiely represents te proportion of taking a taxi for traeling in all traffic modes among urban resident population and floating population; D1, D Respectiely represents te aerage trael distance of urban resident and floating population wen traeling by a taxi. ()Measurement and calculation of te total effectie traeling mileage of a taxi from a demand angle Wen a taxi is in te operation process, te number of passengers is not te same eac time. From demand angle, te total traeling mileage of a taxi is equal to te traeling turnoer wic te taxi undertakes diided by te aerage effectie number of passengers per traeling of a taxi[3]. Ten te total effectie traeling mileage of a taxi measured and calculated from a demand angle can be expressed by formula (6). Q1 Q L = S + 1 S (6) In te formula: L te total effectie traeling mileage of a taxi measured and calculated from a demand angle; S1, S Respectiely represents te aerage effectie number of passengers per traeling of urban resident and floating population wen taking a taxi..1.. Measurement and calculation of te total effectie traeling mileage of a taxi from a supply angle Te empty driing rate of a taxi is an important parameter wit wic goernments can adjust te supply of taxis, besides, tere is a direct correlation between te total effectie traeling mileage of a taxi and its empty driing rate[4].and te empty driing rate of a taxi can be expressed by formula (7). L K = 1 (7) T n In te formula: L te total effectie traeling mileage of a taxi measured and calculated from a supply angle; n te total supply quantities of urban taxis; T te aerage operation time of taxis; te aerage operation speed of taxis; K te aerage empty driing rate of taxis. From tis we can see tat te computational formula of a taxi s total effectie traeling mileage measured and calculated from a supply angle is L = n (1 K) T (8) ISSN According to te balance of a taxi s supply and demand, wen te supply and demand of a taxi come to balance, it s te best state of urban taxi scales. Here we regard te total effectie traeling mileage as a equilibrium point, tat is to say wen te total effectie traeling mileage of a taxi measured and calculated from a demand angle L is equal to te total effectie traeling mileage of a taxi measured and calculated from a supply angle L, te passenger transport demand and supply of taxis come to a relatie equilibrium. Q1 Q + n (1 K) T S1 S = (9) Wen deformed we can get Q1 / S1 + Q / S n = T (1 K) (10). Te correction of urban taxi s reasonable scale model based on te balance between supply and demand Actually tere are many factors wic can influence te reasonable scale of taxis. But in te modeling, only te strongly related factors tat can be operated and can be easily acquired from te data are considered, so tere are certain limitations. So we need to make some proper corrections to te model, and ten te reliability and practicability of our model can be improed. In tis paper, we draw into an equilibrium coefficient η to correct te model. Its purpose is to make taxis fully meet people s trael needs as well as to meet te profits of te taxi business. Te alue of η sould be a alue more tan 1,and te larger its alue adjusts to, te more tat taxi s supply will be able to adapt to te passenger traffic demand of taxis under an emergency. But in te oter and, te alue can t be too large, or tere will be a ig empty driing rate of a taxi, wic will finally bring pressure to urban traffics. In tis paper, we take η from 1.1 to 1.5, so te urban taxi s reasonable scale model is η β L N = (11) T (1 K ) α In te formula: N te reasonable scale of a taxi; β te proportion of trael amount matced te taxi s main operation period in te total daily trael amount; T te wole time matced te taxi s main operation period in a day; α te taxi driing rate, in tis paper, we take it as 90%. 598

3 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. Taking in consideration tat tere are different taxi situation in different leel cities and in different time period, we coose te representatie first-tier city Sangai and te representatie second-tier city Harbin as our researc subjects, respectiely discussing te different time period. For te sake of te fact tat tird and four-tier cities ae relatiely small population simple traffic situation and isn t representatie, ere we don t discuss tem. Finally we reflect te taxi supply and demand penomenon among our wole nation.. 3Analysis of first-tier cities ISSN (3)te time distribution of residents trael mode Residents rely on public transits and walking as te main trael mode, wose proportion respectiely is 3.46% and 6.4% in all daily trael modes. And among tose trael modes, te proportion of residents wo coose a taxi is 6.6%.Te proportion of residents trael mode in Sangai is expressed as Cart. Te problem of Haing difficulty to take a taxi is particularly acute in te first-tier cities. In order to explore te matcing degree of supply and demand in tose firsttier cities, we first coose Sangai as te researc subject to discuss wit. Te data is cosen from te fift surey report about residents trael in Sangai, referring to te results of te fift compreensie traffic surey in Sangai at te same time. Te trael intensity and aerage daily trael times of residents in Sangai From te surey report we can see, te total amount of residents daily trael times in downtown Sangai is times, and per capita daily trael times come to.37 times. Te distribution of residents trael time From te results of te fift compreensie traffic surey in Sangai: te difference between te flat peak and te ig peak as srunk. Te trael amount of morning ig peak continues to grow, and te trael amount increases by 10%.Te eening ig peak as an adanced trend, and its trael amount increases by 5%.Te rising range of te flat peak s trael amount is a bit large. Te trael amount increases by 11% from 10:00 to 15:00.Bot te trael amount of te afternoon flat peak (from 15:00 to 17:00) and te flat peak after te eening ig peak(from 19:00 to 1:00) increase by 15%. Te rising range of te flat peak s trael amount is large, wic srinks te gap between it and te ig peak. Te distribution of daily trael time of residents in Sangai is expressed as Cart1. (4) te aerage trael distance Te aerage trael distance of urban residents population and floating population wen traeling by a taxi is 6.9 kilometers. (5) te aerage empty driing rate of taxis From te statistics, te aerage empty driing rate of taxis is K=0.3. Calculation of related basic data Measurement and calculation of taxis passenger transport turnoer: From formula (6) and te surey data in te year of 015, we can acquire te taxis passenger transport turnoer in te downtown Sangai is 4 Qt = % 69 = 57.47(10 person km) In te downtown Sangai in 015, te aerage number of passengers per taxi is 1.78.From formula (6) we acquire tat te total effectie traeling mileage of a taxi in downtown Sangai is: Q t (10 4 L ) = = = km S 1.78 Measurement and calculation of te reasonable taxi number: Since Sangai is te economy center of our country and a ery big city, so tere are many floating people and all kinds of public transits in te city, and tere is a big elastic demand of taxis. So we sould take η as a bigger alue and ere we take it as η=1.55. As te result of te fact tat bot residents ae different demand of taxis and road conditions are not te same in different time periods. Following we will discuss on morning and eening ig peak togeter wit leisure time separately: 599

4 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. (1)Te time period of morning and eening ig peak From 7:00am to 9:00am and from 16:00 to 18:00 are te two main time periods wen residents trael out, te proportion of wic respectiely comes to 6.3% and 17.9%.During tis time period, te demand of taxis is pretty large, and at te same time, because te pressure of road traffic increases, te aerage speed of a taxi runs down. According to te results of te fift compreensie traffic surey in Sangai, te aerage speed of a taxi during te ig peak period is 1=0km/. From formula (11), ten te taxi s reasonable scale during morning and eening ig peak period in downtown Sangai in 015 is: η β1 L N1 = = = 77555e T (1 K) α At present, te number of taxis operating among te wole Sangai is 5.06 ten tousand.because now we are considering a center city and te fact tat taxi can t operate all day, te actual number of taxis operating during te ig peak period is far less tan te supply of taxis we calculate during te ig peak period. Tere is a ery large breac of taxi supply. At tis time, passengers will ae worse trael experience, for example, aing difficulty in taking a taxi, waiting for a long time, or een coming across a penomenon in wic te taxi drier refuses to take you. Now tere is a sortage of demand. ()te leisure time period To remoe te morning and eening ig peak time one day, we get te leisure time period. During tis time period, te road conditions are preferable as well as te number of residents traeling out is less. According to te results of te fift compreensie traffic surey in Sangai, Te aerage speed of a taxi during te leisure time period is =30km/.From formula (11), and ten te taxi s reasonable scale model during te leisure time period in downtown Sangai in 015 is: η β L N1 = = = 34076e T (1 K) α During te leisure time period, te number of taxis operating among te wole Sangai is a little more tan te taxi demand. At tis time, te degree of supply and demand balance is basically reaced. So residents traeling out by taxi ae a iger degree of satisfaction, and at te same time, te empty driing rate of taxis is witin a reasonable range. In order to analyze taxi situations of different leel cities, we coose Harbin from second-tier cities as our researc subject. Te data is cosen from te surey report about residents trael and te road traffic olume in Harbin. Te researc metod is te same as te aboe. According to te surey report, we can acquire tat Harbin s total ISSN amount of residents daily trael out is Te proportion of residents wo coose a taxi traeling out is 5.59%. Te aerage trael distance of urban residents population and floating population by a taxi is 6. kilometers. Calculation of related basic data Measurement and calculation of taxis passenger transport turnoer: From formula (4) and te surey data in te year of 015, we can acquire te taxis passenger transport turnoer in Harbin is 4 Qt = % 6. = (10 person km) In Harbin in 015, te aerage number of passengers per taxi is 1.76.From formula (6) we acquire tat te total effectie traeling mileage of a taxi in Harbin is: Qt L = = = 03.(10 km) S Analysis of second-tier cities Harbin is a main city in te nort, and it s te representaties of second-tier cities. Altoug its public transits and urban population flows isn t as ig as tem of Sangai, tey are still relatiely ig in te wole country. So ere we take te equilibrium coefficient η as η =1.35.From formula (11), ten te taxi s reasonable scale in Harbin is: η β L N1 = = = 9491e T (1 K) α At present, te wole Harbin as te total amount of taxis as 1300, wic is more tan te reasonable scale. From te statistical data we can acquire tat Harbin s taxi ownersip amount is ranked nint among te wole nation. As we can see, Harbin is a city were it s not difficult to take a taxi. Howeer, tere is a sligt penomenon of supply exceeding demand in Harbin. Syntesize te soling results of te first and second tier representatie cities Sangai and Harbin, and we will acquire Table1. Table1 Te comparison table of te soling results of te first and te second tier cities City Te first-tier city Sangai Te secondtier city Time period Morning and eening ig peak period Leisure time period Te reasonable scale of taxis (e) Te amount of taxi operation (e) All day

5 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. Harbin From te table aboe we can acquire tat in tose domestic first cities taking Sangai as te representatie, during te morning and eening ig peak period, in oter words from 7:00 to 9:00 and from 16:00 to 18:00,tere is a large demand of taxis. So te number of taxis operating now can far from meet te demand, and te penomenon of demand exceeding supply arises. In te oter and, during te leisure time period, tere is a balance between supply and demand. Howeer, taking oerall consideration, now te amount of taxis in te first-tier cities in our country can ardly meet passengers demand, and te problem of Haing difficulty to taking a taxi is particularly seere. Comparing to first-tier cities, in tose second-tier cities, te total amount of taxis now can better satisfy te needs of passengers, and een te penomenon of supply exceeding demand arises. Te penomenon of Haing difficulty to taking a taxi seldom appears. In summary, measure weter taxis ae a supply and demand balance troug te mileage utilization ratio and te eicle load ratio two indicators, draw into a equilibrium coefficient η to correct te model, set up te urban taxi s reasonable scale model based on te balance between supply and demand, and ten researc and analyze te specific city Sangai te representatie of te first-tier cities, Harbin te representatie of te second cities in real life. Finally we get te matcing degree of supply and demand of taxi resources among different time and space. In tis paper, we mainly researc on te matematical model of subsidy programs of tose taxi companies. Following we will measure weter subsidy programs of tose taxi companies are elpful to ease te problem of Haing difficulty to take a taxi by setting up te taxi operations balance model based on regions and analyze specifically weter it can sae te drier s driing time and te waiting time of te passengers using a taxi software combined wit concrete reality. 3. Te matcing model of supply and demand based on te mileage utilization ratio and te eicle load ratio In te face of an increasingly competitie urban road traffic system, especially te countries igorously promote energy conseration and emissions reduction, encouraged public transit, taxi operation by a great impact, terefore te companys taxi subsidy sceme came into being, especially wen a taxi introduced a ariety of software solutions preferential promoted te dependence on te taxi passengers, not only makes te taxi drier reduced te rate of empty, but also make te passengers got on te bus fare ISSN is faorable and sae te passengers aluable time. By establising te model based on te regional balance of taxi operation under te specific analysis and combined wit te actual use a taxi driing software weter to sae te driers time and te passengers waiting time to determine te taxi companies weter subsidy sceme are elpful to "difficult to alleiate a taxi". 3.1 Te balance of supply and demand model (1) Te relation between supply and demand of conserati on Assumes tat te road network, including as traffic area se t, directed road set, and respectiely starting area for passen gers and reaces sets,. In te condition of te balance of su pply and demand, passenger eicles from illage to illag e, in addition to te illage to meet te needs of te destinati on for te community, and in te community into te empt y state, namely Dij = Dj i I (1) Formulation: from illage to illage of passengers deman d, to produce te empty of traffic. Passenger eicles in te illage to complete transportatio n into empty, and ten troug te software searc te passengers from te community, in empty state, to te next illage in probability and receied te passengers, tax i from illage to illage is empty of traffic q = DP j = DP ij i I (13) Taxi from te illage to empty state to illage in te sorte st way and in te community into a passenger. From illag e to illage empty eicles to trael te sum total, namely O= q = DP i ij j J j J i I (14) ()Operating time of conseration Taxi total operating time is total passenger time and total e mpty time. Te total passenger time can be expressed as 0 q Dt = i I j J ij ij Total empty time can be expressed as q = ( q t + ω ) i I j J i So te total operation time can be expressed as q= Dt + ( q t + ω ) ij ij i i I j J i I j J (15) (16) (17) In a fixed time, according to te operating time of conser ation, it is q=n (18) 601

6 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. In expression: Nis taxi scale, namely te scope of a taxi to te total numb er of operating eicles in te researc. ISSN Te establisment of te model United expression (14) and expression (18), a taxi ae eq uilibrium using software to searc operation balance mode l for passengers taxi, and te model is q = DP ij = Oi j J j J i I Dt ij ij + ( q t + ωi ) = N i I j J i I j J (19) From (19), under te establised network conditions and taxi demand, te model ariable is te aerage searc time for a taxi in eery district, and te number is equal to te starting area. Figure3 from 01 to 015 taxi application registered users in Cina 3.3 Passengers waiting time Passengers waiting time sould be started from te agreem ent wit driers to te arrial of taxi. For taxi, on te aera ge trael time from j illage to i illage and te sum of t e aerage searc time in i illage constitute te passengers waiting time[6]. So te aerage passenger waiting time is ω i t j Wi = ωi + ni 1 (0) In expression: ni is te number of traffic illage. 3.3 Te analysis of taxi software subsidy sceme Taxi software company offering subsidy sceme is mainly for te purpose of quickly occupying te market, improing product awareness, letting more people experience te Internet age and bring conenience to life, cultiating customers using abit. Te figure 3 sows tat after 013 years in our country accumulatie total number of registered users increased sarply. Taxi software sows a booming trend. By figure 4, Click a taxi and fast taxi sare. Te national market as ig as 90.81%. Te two taxi companies wic use subsidy sceme ae monopolized te domestic software market. Businesses possess te market quickly troug subsidies; expand te market for te purpose of basic implementation. Figure4 te market sare of a taxi software Now using te establised model to explore te way of using a taxi software weter can effectiely sorten te passenger waiting time.(19)is systems of nonlinear equations, if directly use in a complex actual traffic network, te amount of calculation will be ery large. Ten reduce (19), te system of equations contains equations and ariables. Tis model does not exist exact solution. (19) can be conerted to q Oi = 0 j J Dt ij ij + ( q tij + ωi) N= 0 i I j J i I j J (1) Because of te exact solutions of equations dont exist only; it sould as far as possible narrow (0) equals te left items, making it approximate te rigt and side alue. Setting te absolute error alue, ten q j J i I j J i I j J e rr = α t ij O i + β Dt ij ij + ( t ij + ωi) N () Among tem: respectiely are (18) and (1) te undetermined weigt of absolute error to total error.model in tis paper from te conseration equations into unconstrained optimization problem, namely q 60

7 q IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. j J i I j J i I j J min e rr = α t ij O i + β Dt ij ij + ( t ij + ωi) N By using MATLAB genetic algoritm can sole. Com muni ty q (3) According to simple network te feasibility of te model and algoritm are tested. In order to be more generally reflect te urban traffic [7]. Now create a traffic plot of fie traffic models, sown in figure 5. Among tem, circles wit number represent point of eac traffic area, connecting lines wit arrow represent adjacency relations, and weigt alues are different between two points on te direction of te sortest trael time. Trael demand of taxi OD matrix are sown in table Com muni ty O i O i Figure5 simple traffic network Table OD matrix way Assume tat taxi driers pat in eac traffic zone is te sortest pat, ISSN we can determine te sortest trael time between te traff ic areas, and te results are sown in table 3. Table3 te sortest trael time between c and D Because te software to te drier side took te subsidy sceme, so te driers income improed correspond, Penetration of te software, te deelopment of te economic, social deelopment and transportation links, [8], according to te report in Marc 014, te taxi drier income year-on-year increase of yuan per mont. Wit te taxi driers income as increased, and te present situation of te firsttier cities in sort supply, we can foresee tat te number of city operation cab will continue to improe in te future wit te popularity of a taxi software promotion. At te same time, software to take a taxi car way to constantly promote te city of te actual operation of passenger eicles will continue to grow suc as Uber. Following, we discuss taxi scale expansions influence on te passenger waiting time. Set different N to calculate different area of te aerage searc time. According to te example data and introduced aboe algoritm, using of genetic algoritm toolbox of Matlab programming, te global optimal solution can be obtained,(see appendix).we can determine te aerage searc time in eac traffic area and fie district oerall aerage searc time,among tem α = β = 0.5. Finally results are sown in table 4 Table 4 te aerage searc time N ω 1 ω ω 3 ω 4 ω 5 ω 6 e rr Table 5 sows tat wit te taxi scale increasing, te aera ge searc time is on te decline of eac district. Using gen etic algoritm as better searc ability, te absolute error o f optimization problem under different N alues are witin te acceptable range. Using (0) to calculate te passenge rs aerage waiting time, are sown in table 5, wit te inc rease of number of te taxi, t te aerage waiting time sorten. Table5 eac district aerage passenger waiting time N ω 1 ω ω 3 ω 4 ω

8 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. In conclusion, a taxi software searc metod compared wit te traditional searc metod, it as te adantage of a sort time and a better line. At te same time, along wit te popularity of a taxi software, operating eicle size increases. Under te influence of te two kinds of function, te aerage waiting time of te passenger s sortens. Te passengers aerage waiting time is te important measure of "difficult to take a taxi". Wen te passengers waiting time is more tan 10 minutes, te passenger will ae te idea of "difficult to take a taxi". So a taxi software company subsidy sceme makes use of software on te rise of te taxi, a taxi operation on te number of eicles increases, under te action of te two, passenger bus waiting time reduced. Subsidy sceme indeed makes Cina eased te problem of "difficult to take a taxi". In te process of soling te aboe, oweer, is te premise of a taxi passenger taxi ride USES software, oweer, currently using a taxi software is only 15.61% of te proportion of te taxi ride. Taking a taxi software utilization rate is low. Te current subsidy sceme for bot passengers and driers is not attractie enoug, taking a taxi softwares entusiasm is not ig. It elps ease Cinas present situation of "difficult to take a taxi" but it is limited. Aimed at tis penomenon, in tis paper designed a taxi company directly, and subsidies will be part of te profits to te rental car company subsidy sceme, te following will be detailed in tis paper. 4 Subsidy sceme design based on eolutionary game teory 4. Te establisment of te eolutionary game model 4.1 Te establisment of te eolutionary game model Assuming tat te taxi drier groups take strategy Sd1 ratio is X, te corresponding (1 - X) strategy for Sd probability. Passenger groups take strategy Sp1 ratio is Y, te corresponding (1 - Y) as te strategy of Sp probability [9]. Wen te taxi drier selection strategy of Sd1 expected return as follows: Ud1 = Y 0 + π (1 Y) = π (1 Y) (4) Coosing a strategy Sd expected return for: Ud = Y π1 + π1 (1 Y) = π1 (5) Te taxi drier group aerage expected return as follows: Rd = X π (1 Y) + π1 (1 X) (6) According to te aboe conclusions, te taxi drier group replicated dynamic equation: ISSN dy Y = = Y[ U p1 Rp] = Y (1 Y )[ XV0 + V1(1 X ) XV (1 X ) V0] dt (7) Placed for replication dynamic relationsip in twodimensional axis, as sown in te figure below: Figure 6 taxi driers and passengers under te new strategy of taking a taxi is te software eolution game According to te picture aboe, it can get a taxi drier and passengers in te game, X = 0 Y = 1 and X = 1 Y = 0 for te eolutionary stable strategy of te game. In tis game te replication dynamic eolution game, wen te initial X, Y fall in A region, it will eentually be stable in te eolutionary stable strategy X =0 Y =1 point, wic is te drier groups dont insist on using te proposed tariffs as te new sceme, at te same time, te passenger groups insist to use existing car rental pricing rules. Wen te initial X, Y fall in te D area, it will eentually be stable in te eolutionary stable strategy point, wic is te drier groups insist on using te proposed tariffs as te new sceme, at te same time, te passenger groups dont insist on using existing car rental pricing rules. 4. Te analysis by eolution game teory Troug te final result of eolution game teory for area is more likely to fall to D, taxi driers and passengers will coose a new sceme proposed in tis paper. From te perspectie of a taxi serice platform, cooperating wit te taxi company means tat more taxi driers and passengers use te serice of taxi. A taxi company accepted te legitimacy of te software. Cooperation means more software popularization, and taking a taxi serice platform can be deposit payment for inestment troug online. In te software into some sponsorsip means adertising reenue. Obiously, in cooperation wit te taxi company, a taxi tird-party software company will be muc more profitable. Aboe all, taken after te operation and subsidy sceme, a taxi will furter enance utilization rate of te software. 604

9 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. Go out by taxi software will become a kind of life abits. In iew of te conclusion, iger proportion of taxi software using can sorten te waiting time of passengers. It as an important role for a taxi to alleiate te current "ard" situation. It can be seen tis solution as te effect to improe urban traffic in Cina. At te same time, a taxi driers and software company earnings are improing, and it as an important role for te ealty deelopment of te taxi market in Cina. 4.3 Tird party a taxi serice platform for subsidy sceme to determine te taxi company s, s represents If electricity serice expected profit is A, 1 money feasible allocation. Two companies feasible assignment collection is S = {(s 1,s ) 0 si A,s 1+ s A}, i = 1,. And it assumes d = (d 1,d ) tat te burst point by said. d 1,d Respectiely taxi companies and software companies burst profits. Te problem of configuration utility,in conclusion B = (S,d;u 1, u ). At te same time it satisfy te pare to efficiency, symmetry, linear transformation inariance, independent of te independent coice four axioms of unique solution for Nas solution, Nas solution for te following constrained optimization problem of te solution: max[(u 1(s) u 1(d))(u (s) u (d))] S1, S (8) ST..(s 1,s ) S &(s 1,s ) (d 1,d ) Tis solution is Nas solution. For tis problem, it needs to satisfy te following Nas by te constraints of te optimization problem max[(s1-d 1)(s-d )] S1, S S.T. s 1+s =A (9) According to te constraint conditions to get into (9), cange to a single ariable optimization problem max[(s1-d 1)(A-s1-d )] S 1 Can be obtained finally * * Ad - + d1 s1= u1= * * A+ d-d1 s= u= Troug * Ad - -d1 s1 -d 1= Aailable s * >d 1 1, by te same token s * >d, te inequality s * 1 >d1 and s * >d, and tus ae proed to be a taxi serice platform for te optimal alues of te taxi ISSN company subsidies. Visible, in te face of reality, a taxi software company desires to te taxi company is te most optimal alue subsidies, can aciee mutual benefit and win-win results, to alleiate te present situation of "difficult to take a taxi". 5 Conclusions In tis researc, te matematical models of subsidy programs of taxi are built. We make te urban taxi s reasonable scale model based on te balance between supply and demand, and we can get te matcing degree of supply and demand of taxi resources among different time and space. Additionally, we take te difference of Haing difficulty to taking a taxi between different cities in consideration, and reflects te situation of taxis supply and demand in te wole country. Analyzing te balance of supply and demand, setting up te taxi operations balance model based on regions and explaining te problem using data seems to be pitier and clearer. t j Wi = ωi + Passengers waiting time ni 1 offers reference for te optimization of passengers taxi experience. te taxi s reasonable scale during morning and eening ig peak period and during leisure time period in Sangai is respectiely 77555e and 34076e.Wile.te taxi s reasonable scale in Harbin is 9491e.Troug te * Ad - -d1 s1 -d 1= formula we can acquire tat te optimization of wic taxi serice platforms gie taxi * * companies subsidies is ( s1, s),wic as a certain reference for te urban taxi resources reasonable planning. Acknowledgments Supported by Hebei Natural Science Foundation of Cina (NO. A015099) References [1] Scballer,B.Gilbert.G,Fixing New York City Taxi Serice,Transportation Quarterly[J],1996,50():8596. [] Herman R,Prigogine I. A two-fluid approac to town traffic [J].Science,1979,04(4389): [3] Akcelik R. Traffic signals:capacity and timing analysis. Researc Report N o.13,melbourne:australian Road Researc Board,198. [4]Hai Yang,S.C.Wong.A Network Model of Urban Taxi Serices.Transportation Researc PartB,Vol.3,No.4,(1998) [5]Daniel Flores-gurl. An economic analysis of regulated taxicab market[j].reiew of industrial organization,003,3(3):

10 IJISET - International Journal of Innoatie Science, Engineering & Tecnology, Vol. Issue 11, Noember 015. [6] Young and glowei jameslu. Urban taxi operation network equilibrium model [J]. Journal of transportation engineering, 007, 7 (1) : [7] Stuart J.Russell,Peter Norig. Te information in te taxi cab industry under te conditions of te power and responsibility to inestigate [J]. Higway traffic science and tecnology (tecnology), 013, () : [8] Greenberg H.An analysis of traffic flow[j],opera-ffons Researc,1959,7(1): [9] ]Muller G.Index of Urban transportation mode selection of eolutionary game analysis [J]. Journal of management engineering, 009, 3 () : ISSN