Research on Game Theory of Congestion Pricing and Parking Charging

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1 Internatonal Journal of Enneern and Advanced Research Technoloy (IJEART) ISSN: , Volume-3, Issue-8, Auust 2017 Research on Game Theory of Coneston Prcn and Parkn Charn Tn Pan, Rende Yu, Bn Lu Abstract In order to solve the coneston problem of urban road network, manaers tend to use means of transportaton demand manaement of road coneston charn n dynamc transport. However, f manaers use only one stratey of road coneston charn, ths approach needs nto a dscusson of ts unversal farness, and make t easer for road users have a certan contradcton whch mpedes the mplementaton of the polcy. By analysn the advantaes and dsadvantaes of road coneston charn polcy and conested areas of parkn polcy, and the defnton of urban road coneston as quas-publc oods rather than tradtonal publc oods, use conventonal economcs ame theory and economc levers to reulate the traffc demand, combned wth the cty s parkn polces and urban coneston charn polcy two effectve means to explore and establsh a double-prcn model and make the Stackelber model soluton. Ths paper attempts to snfcantly reduce road coneston tax, whle the ratonal allocaton of coneston wthn the parkn area, chann part of prvate cars to travel, to ensure the effcent allocaton of urban road resources, n order to acheve ease road coneston problems. Index Terms Urban coneston, Road coneston prcn, Parkn chare, Game theory, B-level model. I. INTRODUCTION In recent years, road coneston problem n lare and medum ctes n Chna became more serous, affectn economc development to the cty and resdents' convenent lfe, only From the supply pont of vew to mprove road nfrastructure wll not only can't releve the road network coneston level, but wll attract traffc, enerate an more repar more coneston phenomenon called Braes [1]. So n the protecton of the basc needs of the supply sde, but also from the demand sde, throuh the means of traffc demand manaement, reulaton or suppresson of derved demand. On the bass of predecessors' research, ths paper takes the conested road network of the central cty as an exclusve and compettve quas-publc product, combnn the manaement polces of the road coneston charn and the central cty parkn fee. Ths paper analyzes the travel cost of users n the conested road network by usn the ame method n economcs, establshes the double prcn model of the combned charn stratey, and puts forward the reference and sueston for the manaement of urban road network coneston. Dynamc traffc manaement manly n the control of traffc flow for road network. Snapore bean to mplement a reonal road coneston chare n the 1970s, n drvers nvestaton after the polcy mplementaton, 8% of drvers sad not to drve nto the toll zone [2];London bean to mplement a reonal road coneston chare n 2003, prvate cars entern the cty center each day plummeted to the ornal 70%, and bus speed up by 25% [3,4].The successful mplement of road coneston prcn polcy n many lare ctes n foren countres prove that ths measure can prove effectve manaement of urban road coneston and envronmental problems caused by urban roads. However, n the practce of domestc practce, the man problem of coneston chares s no loner a techncal problem, but the publc questonn and confrontaton for road chares [5]. Cervero ponted out that the publc's resstance came from the hh fee, and they beleve that the mplementaton of the coneston chare polcy s only beneft to the overnment manaers and a small number of hh-ncome [6].Therefore, we need to reduce the publc's senstvty to road prcn n ensurn that the road prcn polcy effect s unchaned or slhtly reduced. Urban parkn s an mportant part of statc traffc. The parkn fee s also one of the elements that make up the marnal cost of the road. The parkn fee n the urban area s an effectve means to control the traffc flow of the center road network. It s also one of the mportant stratees of traffc demand manaement. Throuh the O-D survey of Sydney Cty, Davd used the Lot model to analyze the mpact of parkn chares on the central cty, The results showed that n the case of road network condtons reman unchaned, f central cty parkn chare rate ncrease 1% then the proporton of parkn n the central zone reduce 2.04% [7,8].But merely to reulate traffc by the coneston area parkn chare stratey wll reduce the central cty's attractve and reduce the utlzaton of the parkn faclty n the road network. F.1 Relaton chart of parkn demand-parkn charn As shown n fure 1, n the absence of parkn fee manaement means, the prce and supply of AD and MPC keep balance at N0, then traveler's travel desre larer than travel costs at ths tme; After adjustn the parkn fee rate to ease the coneston stuaton, the parkn fee rased from C0 to C1, parkn facltes demand reduced to N1, that s, we can et best rule coneston effect at N1 pont. MSC s the marnal cost of the socety, the MPC s the marnal cost of the ndvdual, the NS s the number of parkn 1

2 Research on Game Theory of Coneston Prcn and Parkn Charn facltes n the conested area, the value of the C0-C1 s the prce of the parkn rate, EF s the dfference between travel cost of the traveler and the marnal cost of the socety, OR s the travel expenses of the traveler. When the parkn fee rate s C0, because there s no parkn chare manaement measures, too many vehcles drve nto the conested area wll make the road saturaton becomes larer, the parade tme to search parkn spaces ncreases, make the road network operaton effcency s low, and total socal effcency loss. When the number of parkn facltes n the area s NS, the correspondn chare rate s CS, the coneston condton of the road network cannot be effectvely allevated at ths chare rate. When the parkn prce s C1, the coneston of the road network can be effectvely allevated. Parkn demand and the prce to acheve balance at N1, but the traveler s parkn demand s less than the number of parkn facltes n the reon, resultn a waste of resources. It can be seen that only use reonal parkn charn polcy cannot solute the problem of reonal coneston very well. In contrast to publc resstance and unsupported of road coneston chares, parkn fees n the central cty are easer for road users to accept. Throuh the publc ntenton nvestaton, Gla analyze and summarze publc senstvty for the road coneston tax and parkn fees, obtaned the resstance of the traveler for the central cty parkn fee polcy s much less than the road coneston chares, and wth the ncrease of travel cost, turn nto a dverent trend [9]. In order to reduce the cost of personal travel, reduce urban road network coneston and mprove road network effcency, Fen Sh establsh a b-level plannn model, set up a parkn transfer pont at the border area of the central cty charn area, thouh parkn To attract low tme value drver to transfer to publc transport [10]. In ths paper, use statc and dynamc combnaton charn stratey, combne the road coneston chares and parkn fee stratey, combned wth the advantaes of the two methods to make up the shortfall for the mplementaton of a snle polcy, the relatonshp shown n fure 2. Consder a prvate car users, from the resdence to work n the urban areas or for busness, there are three ways to travel to choose from: Frstly, drvn a prvate car from the resdental area drectly to the destnaton parkn lot, known as the typcal drvn mode. Secondly, a number of prvate car users drvn one prvate car, followed by ther respectve destnatons, and select the fnal destnaton parkn or drvn out of the crowded area then park, called the no stop travel mode. Thrdly, prvate car users choose to travel by publc transport or choose to cancel travel. Based on the conested road network wth these three travel modes, set up a chare entrance at the border of the conested area of the cty center, and set up a chare parkn n the conested area. By charn the traveler coneston taxes and parkn fee n the conested area, make some prvate car users to chane the travel mode to reduce travel cost, encourae travel by bus and carpool, ncrease the utlzaton of vehcles, allevate the road coneston stuaton, enhance the servce qualty and effcency. Traveler characterstcs Publc transport Road traffc manaement department Travel purpose and expectaton Road network traffc condton The prce of the charn polcy Drvn Parkn demand F.2 Combnaton of toll road coneston manaement daram A. Double layer model II. THEORETICAL BASIS The frst and second prncples about traveler choce path were proposed by Wardrop. The frst prncple s the optmal balance of the user, referred to as UE (user equlbrum); the balance of the second prncple s the optmal balance of the network system, referred to as SO (system optmzaton) [11].Amon them, the optmal balance of the user refers to under the traveler reard personal nterests as the leadn, choose the cheapest travel method or route, make the road network acheve a Pareto optmal problem state, that s to say, any traveler to choose another travel mode wll lead to ther own and other traveler travel costs ncrease. The optmal system of the road network system s that the travel expenses of all the travelers n the whole road network are mnmzed, that s, choose a knd of dstrbuton mode make the network system effcent s maxmzed, unless all the travelers n the road cooperate wth each other, otherwse the road network can t realzed the best balance of ths system. However, f the economc way used to optmze the road network, the optmal balance of the system provdes a decson-makn method for the traffc manaement. Traffc manaement departments to develop oals and stratees to make the whole reonal road network's socal economc effcency hhest or the deree of coneston least. Travelers adjust ther travel mode under the traffc manaement department s stratey and characterstcs chanes n the road network, n order to acheve smallest 2

3 Internatonal Journal of Enneern and Advanced Research Technoloy (IJEART) ISSN: , Volume-3, Issue-8, Auust 2017 travel costs or the reatest expectatons cost.ths s a typcal complex system called decson maker-follower, whch can be represented by mathematcal models (1) and (2). mn G ( u u, p ( u )) (1) s. t. ( u, p( u)) 0 (2) Amon them, G( u, p( u )) s the objectve functon of the traffc manaement department, u s the set of decsons set for the taret, s the constrant functon of the decson set, and pu ( ) s the decson functon of the traveler under the u decson. Travelers hold ther own nterests as the reatest oal that can be represented by mathematcal models (3) and (4): mn F ( u p, p ) (3) s. t. f ( u, p) 0 (4) Amon them, F s the expectaton functon of the traveler, p s the travel stratey for the traveler, f represents the constrant functon of the travel. B. Stackelber ame In the classcal ame model, the competton status s equal, such as the Cournot model and the cockroach ame model, ther behavor and characterstcs are smlar, they wll make decsons at the same tme n the ame. When makes a decson, he does not know what knd of decson the other partcpant chooses. But n fact, the poston of the partcpants s not entrely symmetrcal n some ames, and the lower status partcpant wll choose ther own stratec decsons based on the hh-level partcpants. As n the economc feld, small busnesses wll choose ther own stratec decsons based on the b busness. The model establshed by German economst Stackelber reflects ths asymmetrc competton [12]. Stackelber mode s a typcal decson maker-follower. Partcpants n the ame have an obvous prortes n the decson. Leader selecton one decson, followers choose ther own stratec decson after the leader, n order to ensure ther own nterests. However, the decson of the follower can also be observed by the leader, when the leader choce the decson, he can also understand what knd of stratec decson the followers wll make, that s, followers reflect functon. So the leader wll expect the nfluence that ther own decsons make on the followers. In ths case, the decson of the leader s actually a utlty functon wth the partcpant s decson-makn as a varable, that s, the leader no loner needs to make ts parameters as a varable to reflect the functon. III. ESTABLISHMENT OF PRICING MODEL The study of ame prcn n economcs s very thorouh, and the double-layer model s wdely used n the feld of transportaton plannn. Based on the exstn ancestors research, combned wth the theory of Stackelber and Double-layer model. Ths secton wll dscuss and desn the method about jont prcn the road coneston chares and parkn chares. A. Problem descrpton: Due to the rratonal structure of resdents' travel and urban plannn problems, resultn n a cty center road network overcrowdn, resultn n resdents nconvenence and socal economc losses. The road manaement department plans to adjust the travel cost of the travelers throuh the mplementaton of the reonal road coneston charn and parkn chares, and lead the road users choose an approprate travel mode to allevate the coneston of road. But also need to consder the nfluence that rate of chares makes on the road traffc and the needs for travelers and the road saturaton of road network and other factors, to solve the problem of urban coneston, but also to ensure the effectve use of urban resources. B. Double layer ame model Road manaement departments understand the needs and expectatons of travelers throuh the collecton of data n the road network, and travelers understand the traffc manaement s polces and requrements throuh the meda, electronc dsplay on road network and other means, The conton between them s accurate, and the road manaement and traveler s actons have order, ths competton s consstent wth the characterstcs of nformaton dynamc ame. Ths paper sets the ame between the road manaement department and the traveler as the frst layer ame. In contrast, the traveler's nternal competton ame has no obvous order, and s set to the second layer of the complete nformaton statc ame. The frst layer s the charn ame between the road manaement and road users. Road manaement departments develop rate of chares and coneston area parkn rates accordn to the road traffc and the needs for travelers and the road saturaton of road network, the utlty functon s the formula (5): U U I( p1, p2, q) (5) Where, U s the expected functon of the traffc manaement department, the sum of the total cost ncome of the traveler s total expected beneft and the road coneston chare and the parkn chare; U s the expected beneft after the mplementaton of the polcy of the traveler, (1,, n), I s the total revenue of road chares and parkn chares, s the road traffc parameter q and two chares functon p 1 and p 2, p 2 rane s about the road network traffc Q, parkn parade tme t 2, the number of parkn facltes n, the functon of the formula for the formula (6): p2 P2 ( Q, t2, n) ( C1, C0 ) (6) The traveler travels throuh travel costs (ncludn crowdn costs and parkn fees) and the expected benefts to make travel choces. The expected utlty functon s equaton (7): Where, U E C (7) E s the utlty proft for the traveler to reach the destnaton, and C s the travel cost of the traveler, and the dfference between the two s the desred utlty of the traveler. The second layer s the competton ame between the road users, they want to make ther own nterests maxmze. Each traveler chooses the travel mode accordn to hs own travel cost, and the travel cost s a functon of the rate and travel tme. The ultmate oal of the ame model s to fnd the best road coneston rates p 1 and conested area parkn rates p 2. It s expected that thouh adjust the rates of the two chares and the traveler's travel structure to make the road 3

4 Research on Game Theory of Coneston Prcn and Parkn Charn network n the conested area can acheve the Pareto optmal state, p1 and p 2 can acheve the best chare rate of Pareto optmal. C. Establshment of the model 1) The competton ame between the travelers: Each traveler has a choce of travel method set s S, then the traveler's travel method set s S, ts travel polcy after the mplementaton of the travel stratey s s. The behavor of the other traveler after the mplementaton of the charn polcy s s, and s s S, each traveler s ndependent of each other and competes wth each other to seek maxmum beneft. The expected utlty functon of the stratey based on the road coneston rate p 1 and the parkn rate p 2 s equaton (8): U ( s ( p1, p2), s ( p1, p2), p1, p2) E C (8) In order to obtan the maxmum expected return, the traveler s stratey should be the formula (9): s ( p, p ) armax U ( s ( p, p ), s ( p, p ), p, p ) (9) Snce the traveler has the same basc characterstcs, ths formula s also true for other travelers. 2) The dynamc ame between traffc manaement and traveler: Let the set of road coneston chares p 1 be P 1, the set of coneston rate p 2 n crowded area s P 2, and the traveler's stratey s s ( p1, p2) at the chare rate p1 and p 2, then the expected utlty functon of the traffc manaement department s equaton (10): U ( s ( p1, p2 ), p1, p2) U I( p1, p2, q) (10) In order to maxmze the total utlty of the socety, the traffc manaement department s charn stratey should be the formula (11): p, p armax U( s ( p, p ), p, p ) (11) At ths tme to et the p 1, p 2 value, that s the traffc manaement department of the chares. IV. MODEL SOLUTION A. Soluton Process As the competton between the traveler s smple relatvely and does not have too much mpact on the road coneston charn rate and the parkn charn rate, ths paper manly analyzes and solves the model between the traffc manaement department and the traveler. The ame between the traffc manaement department and the traveler s a typcal complete nformaton dynamc ame, so we can use the Stackelber ame to analyze and the process as follows. 1) After analyzn the traffc condtons (traveler OD survey, road traffc, number of parkn facltes and parkn tme, etc.) n the conested area, select the road coneston charn rate and the coneston parkn charn rate. 2) The traveler chooses the travel mode accordn to the road coneston charn rate and the coneston parkn charn rate of the conested area set by the road manaement department, as shown n fure.3. Parkn S =1 Drvn Travel Don't stop S =2 Traveler Publc transport S =3 Don't travel S =4 F.3. Game tree of travelers optons stratees 3) Calculate the travel cost of the traveler and the total socal cost n the road network: When drvn a car nto a conested area, the travel cost of the traveler s a utlty functon wth respect to the travel tme and the charn rate, and the functon s equaton (12): C ( p1, p2, t ) t 1 p1 2 p2 (12) Amon them, the varable s not ncludn road coneston chares and parkn fees travel tme cost factor, manly ncludn the traveler s unt tme value, unt tme fuel costs and vehcle losses, etc., 1 and 2, respectvely, road coneston chares and parkn fees value s 0 or 1. When the drver chooses a publc transportaton trp, the travel cost s the sum of the tme value and the publc transportaton rate, whch can be expressed as the formula (13): C ( p1, p2, t ) t p (13) Amon them, s on the travel tme value, comfort and other aspects of the unt cost coeffcent, p for publc transport rates, such as bus tckets, tax fare and so on. When the traveler chooses to cancel the trp, the travel cost s 0. The traveler s expectaton utlty functon can be expressed as formula (14): E ( t p1 p2) Drvn Parkn travel U E ( t p1 ) Drvn No parkn travel (14) E ( t p ) Publc transport travel 0 Don ' t travel The utlty functon after the mplementaton of the charn polcy of the traffc manaement department can be expressed as formula (15): U U I( p, p, q) 1 2 (15) 4) Traffc manaement department and traveler choose the optmal stratey, customze an approprate road coneston chares and parkn fees, such as formula (16), (17): s ar max U (16) p1, p 2 ar maxu (17) B. Examples A cty center area mply the road coneston chares and parkn chares stratey, there are four travel stratees for 4

5 Traveler A Internatonal Journal of Enneern and Advanced Research Technoloy (IJEART) ISSN: , Volume-3, Issue-8, Auust 2017 travelers to choose: S 1 s traveler enter the chare area 30 S 1, S 1 and parkn n the area. S 2 s traveler enter the chare 25 S 1, S 2 20 S 1, S 1, 2 area but not parkn. S 3 s traveler to ve up drvn 35 S 2, 2 (, ) S t S S (18) travel turn to publc transport. S 4 s traveler ve up 30 S 2, S 1, 2 45 S 3, S 3 the travel. All traveler arrves at ther respectve destnatons 40 3, 3 wth equal utlty and E 1, t does not nclude road S S 0 S 4 coneston chares and parkn chares for personal tme Accordn to the formula (14) and the formula (18) can travel costs 2, 2.1. Publc transport travel rates are determne the travel utlty as shown n table 1: much smaller than road coneston chares and parkn chares,.e. p1, p2 p 2. And the travel tme of the traveler s (18): Table 3 Game table of travelers utlty Traveler B S 1 S 2 S 3 S 4 S 1 40 p1 p2,40 p1 p2 50 p1 p2,30 p1 60 p1 p2,16 60 p1 p2,0 S 2 30 p1,50 p1 p2 30 p1,30 p1 40 p1,16 40 p1,0 S 3 16,60 p1 p2 16, 40 p 1 5.5,5.5 16,0 S 4 0,60 p1 p2 0,40 p 1 0,16 0,0 The total socal utlty n ths stratey s shown n table 2: Table2 Total socal utlty from travelers stratey Other travelers S 1 S 2 S 3 S 4 Traveler S S S S In the prcn of the Stan Kohlber model, the rane of the parkn chare rate p 2 s 0,16 after comparn the utlty sze wth S 1 and 1 20,. Amon them, p 2 value of0,16, drvn vehcles nto the conested area of the traveler wll choose to pay parkn fees, fal to ease the purpose of traffc coneston. When the value of p 2 s20,, the traveler wll pay more than the expected parkn beneft. The traveler chooses to stop, the parkn rate s reduced, and the parkn facltes cannot be fully utlzed The When the value of p 2 s 16,20, the traveler chooses a dfferent stratey to acheve hs maxmum beneft, that s, at p 2 16, the parkn faclty resources are S, 16,20 and maxmzed and the traveler has the reatest utlty. By analyzn the data of S 2, 3, 4 and S 2,3,4, selected the rane of urban road charn rates s 0,14, 14, 24 and 24,.When the value of p1 s 0,14, travelers drvn vehcles nto the coneston area wll choose to pay parkn fees, fal to ease the condton of traffc coneston. When the value of p1 s 24,, the cost that the traveler have to pay wll more than the expected parkn beneft, then the traveler wll chooses not to stop, so the parkn rate s reduced, and the parkn facltes cannot be fully utlzed. When the value of p1 s 14,24, the traveler wll choose to travel by publc transportaton to acheve ther maxmum beneft, that s, here makes the parkn facltes and the traveler to et the most utlty. V. CONCLUSION 1) After analyzn the advantaes and dsadvantaes of dynamc traffc manaement and statc traffc manaement, ths paper puts forward the concept of jont prcn of road coneston chare and parkn chares. 2) The ame model s establshed and calculated, and the feedback mechansm of the prcn rate for the traveler to ensure ts utlty s taken as a reference, formn a human, road fee human, road feedback mechansm. Compared to consder the external cost prcn model human road fee human feedback mechansm s more drect. Ths concept and model provde some reference for the prcn of road coneston and parkn chares. 3) The downsde s that there are no specfc parameters of the traveler's utlty, so that the study s stll only between the pen and paper, follow-up research plan usn the questonnare, access to effectve and relable traveler parameters and traveler utlty functon to fnd more practcal, concrete soluton. VI. REFERENCES [1] Sheff Y. Urban Transportaton Networks: Equlbrum Analyss wth Mathematcal Prorammn Models [M] [2] Olszewsk P, Xe L. Modelln the effects of road prcn on traffc n Snapore [J]. Transportaton Research Part a Polcy & Practce, 2005, 39(7-9): [3] Lee S. 11. Transferrn London coneston charn to US ctes: how mht the lkelhood of successful transfer be ncreased [J]. Road Coneston Prcn n Europe: Implcatons for the Unted States, 2008: 212. [4] Beevers S D, Carslaw D C. The mpact of coneston charn on vehcle emssons n London [J]. Atmospherc Envronment, 2005, 39(1):

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