QUICK LINK SELECTION METHOD BY USING PRICING STRATEGY BASED ON USER EQUILIBRIUM FOR IMPLEMENTING AN EFFECTIVE URBAN TRAVEL DEMAND MANAGEMENT

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1 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... SHAHRIAR AFANDIZADEH ZARGARI, Ph.D. 1 E-mil: zrgri@iust.c.ir HAMID MIRZAHOSSEIN, Ph.D. Cndidte 1 E-mil: mirzhossein@iust.c.ir (Corresponding Author) YI-CHANG CHIU, Ph.D. 2 E-mil: chiu@emil.rizon.edu 1 Deprtment of Trnsporttion Plnning nd Engineering, School of Civil Engineering, Irn University of Science nd Technology Nrmk, Tehrn, , Irn 2 Deprtment of Civil Engineering nd Engineering Mechnics, College of Engineering, University of Arizon 1209 E. Second St., Tucson, Arizon 85721, USA Trffic Plnning Preliminry Communiction Submitted: Dec. 7, 2015 Accepted: July 14, 2016 QUICK LINK SELECTION METHOD BY USING PRICING STRATEGY BASED ON USER EQUILIBRIUM FOR IMPLEMENTING AN EFFECTIVE URBAN TRAVEL DEMAND MANAGEMENT ABSTRACT This pper presents two-stge model of optimiztion s quick method to choose the best potentil links for implementing urbn trvel demnd mngement (UTDM) strtegy like rod pricing. The model is optimized by minimizing the hidden cost of congestion bsed on user equilibrium (MH- CCUE). It forecsts the exct mount of flows nd tolls for links in user equilibrium condition to determine the hidden cost for ech link to optimize the link selection bsed on the network congestion priority. The results show tht not only the mount of totl cost is decresed, but lso the number of selected links for pricing is reduced s compred with the previous toll minimiztion methods. Moreover, s this model just uses the trffic ssignment dt for clcultion, it could be considered s quick nd optimum solution for choosing the potentil links. KEY WORDS congestion; minimiztion; hidden cost; user equilibrium; link selection method; urbn trvel demnd mngement (UTDM); 1. INTRODUCTION Due to popultion growth in cities nd the helth cre rguments, demnd nd willingness to use privte vehicles (PV) hs incresed. Since the network expnsion could not support ll the PV demnds nd moreover, bsed on the Bress's prdox [1] it is not the best solution most of the time, the demnd hs been greter thn the supply nd this issue mkes disequilibrium in urbn trnsporttion network. The result of this sitution is the congestion nd obstruction of network tht cuses vrious mentl nd environmentl issues. Preventing the congestion in urbn trnsporttion networks is one of the min concerns of trnsporttion plnners nd trffic mngers round the world. In response to this mtter, they try to detil stble condition nd sttus for urbn trffic network in microscopic nd mcroscopic scles. However, some studies improve the microscopic spect of this issue by chnging nd refining trffic light schedules during congestion periods using internl/externl trffic metering strtegy [2], these kinds of strtegies prove to be useful in the short term or for specific loction of sub-network under specific conditions. The min cuse of congestion is lck of blnce nd n unstedy reltionship between the supply nd demnd in the trnsporttion sector. Thus, s previously discussed, incresing the supply lone will not provide long-term solution, nd most experts suggest using urbn trvel demnd mngement (UTDM) strtegies s sustinble solution to control the demnd for utilizing the trnsporttion infrstructure more efficiently. In other words, UTDM strtegies do not encourge decision mkers to expnd nd widen the rods nd highwys s solution for mnging the trffic congestion tht cuses urbn sprwl. Rther, they encourge people to use more efficiently the existing infrstructure. Also, tody sustinbility is controversil issue tht ffects socil, environmentl nd economic spects of humn life. In this regrd, since trvel demnd mngement (TDM) hs been introduced s one of the solutions to rech sustinbility [3], finding the resonble loction to implement its strtegies nd policies in urbn trnsporttion network would be the min or t lest the first question for which the plnners should hve n nswer. Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

2 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... This reserch introduces n optimiztion problem to choose the potentil rods network links tht could be considered for TDM implementtion bsed on congestion toll pricing theories by minimizing the hidden cost of congestion bsed on the user equilibrium (MHCUE) model. The concept of the hidden cost comes from congestion pricing principle. It is defined s the difference between the mrginl socil cost (the totl cost tht ll the n+1 drivers experience bsed on the one further decision to trvel including ll privte costs nd lso the cost experienced by people other thn the driver who re exposed to the congestion nd ir pollution resulting from the cr use) nd the privte cost (the cost experienced by the driver of the cr, including the fuel nd oil, mintennce nd so on). Thus, the model by congestion toll pricing tht is considered s one of the TDM methods, not only finds the potentil links tht could be considered cndidte for implementing the TDM, but it lso investigtes the mount of tolls tht yield uncongested conditions for the network. 2. BRIEF LITERATURE OVERVIEW Tody s pplictions of TDM strtegies re not only limited to fcilitting shifts in trvel time or trvel mode they lso ddress shifts in trvel routes [4]. Mny studies show how trnsporttion plnners nd trffic engineers try to implement TDM strtegies in urbn trnsporttion networks [3, 5-9]. But, finding the loction for implementing these strtegies is one of the min concerns of plnners when designing the selected policies. However, some policies, like congestion toll pricing s the first best congestion pricing where totl costs in the city re minimized [10], could be instrumentl in solving this issue if implemented properly. Congestion toll pricing is one of the most effective methods mong TDM policies in urbn trnsporttion networks, which is to overcome two bsic problems: congestion nd environmentl pollution. Theory nd prctice hve shown tht receiving tolls, when designed nd determined properly, cn ply gret role in reducing trffic congestion on links of urbn trnsporttion networks [11]. In other words, imposing tolls cn help opertors to mnge the demnd of trvel nd decrese urbn trffic congestion nd its negtive effects such s totl lost time of humn resources, environmentl pollutnts, nd so on. The bsic principle used in congestion toll pricing methods re bsed on notifying the users of the dditionl cost (mrginl or hidden cost) they impose on other users [12]. In other words, congestion pricing recommends chrges tht force users to dopt these externlities to some extent, thus reducing or eliminting the dedweight loss [13]. In this cse, the tolls re determined in wy tht results in the possibility or impossibility of trip genertion, shifting the trip from the pek to off-pek hours, or choosing lternte routes by users. Without considering the congestion toll pricing, users re not wre of the costs tht they imposed on others by using the route, so by collecting tolls, in fct, users py for the negtive effects of their presence in the congested res. Determining congestion toll pricing on trffic networks is n old problem, which economists nd trnsporttion plnners hve studied extensively in the pst yers, nd these studies hve lwys hd two min objectives. First, network pricing for determining the pproprite tolls to reduce or void the existing congestion, nd second, funding for implementing trnsporttion projects nd their mintennce. Toll collection experts, using certin ssumptions, hve implemented different methods to provide models for trffic demnd mngement in networks in order to pply the pricing policies s well s possible. Pigou [14] ws one of the pioneers who offered the tx model, nd proposed the issue of mrginl socil cost pricing, nd fter him, Knight [15] expnded it for trffic models. Although Knight provided the drivers route choice behviour, it ws Wrdrop [16] who formulted the problems relted to equilibrium using two principles, which re known s Wrdrop principles. Lter, Beckmnn et l. [17] nlysed equilibrium mthemticl models in terms of formuls. In sttic trffic ssignment models, the demnd between ech pir of origin-destintion re the constnts nd the constrints re system-blncing limittions, even though the trvel rte between pirs of origin-destintion is determined bsed on the function of minimum cost between ech origin-destintion. This is known s the trffic ssignment problem with elstic demnd [18], which mens users hve mny choices, nd they ctully decide on the bsis of their economic sitution. In this cse, the mrginl cost toll is imposed on the users to chnge the flow pttern from user equilibrium to system optimum (SO) with fix demnd. Thus, by ssessing proper toll on ech user using specific network link, the trffic flow sitution will be close to system optimum in terms of minimizing the totl trvel cost. This solution could be pproprite for forecsting the potentil links for implementing TDM strtegies. Since, this pproch tries to close the gp between UE to SO, its purpose is to erdicte congestion. Moreover, pricing hs big dvntge over other TDM policies in tht it encourges users nd systems to djust ll spects of their behviour: number of trips, destintion, mode of trnsport, time of dy, route, nd so on [19]. As the theoreticl bckground of congestion toll pricing is bsed on the fundmentl economic principles, this subject hs hd lot of interest in recent yers for both economists nd trnsporttion plnners. Yng nd Hung found theoreticl method to 606 Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

3 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... show how this clssicl economic principle could work in congested urbn network [20]. In this regrd, different mthemticl models for pricing re presented in reserch literture [21-25]; they propose frmework for congestion toll pricing with different objectives to clculte the mrginl cost of congestion in n effective wy, in which objectives re eventuted by some constrints tht re imposed on the objective function. Some of the most fmous ones re MinSys, MinMx, nd MinTB models [21-23, 25]. The models re compred with the mrginl socil cost pricing (MSCP) tht is the min trditionl pproch for congestion pricing. The models hve been presented s two stge optimiztion problem tht ll use the rc-node formultion of fesible flows. For instnce, the MinSys lgorithm [21] ims to minimize the totl tolls collected while constrining the toll vector to be non-negtive nd it contins two sections s bi-level minimiztion problem. In step 1, the model solves the system optimum problem to obtin n optiml solution represented s v* by following equtions: min s(v) T v (1) Subject to: v=zx (2) Ax=b (3) x 0 (4) In step 2, the lgorithm goes to minimize β T v* over the polyhedron w(v*) tht is defined by the following inequlities: T * T Z ( s( v ) + b $ A t (5) * T ^v h ^ * T s^v h+ bh (6) = b t b $ 0 (7) In these formultion prmeters defined on the bsis of the following nottion, g=(n,a) is network with N being the node nd A being the rc set; AW is the incidence mtrix of g; b(k) is demnd vector ssocited to ech k (commodity); β is the toll vector; x(k) is the commodity (k) flow (vrible) vector nd the sum of ll the commodity flow vectors becomes the ggregte flow vector denoted s v nd the cost of tht ggregte flow is s(v). Also, the system fesible flows re introduced s follows: v = x() k (8) k Ax() k = b() k 6 k! K (9) xk () $ 0 6k (10) In ddition, in regrd to the presented formultion for MinSys, other formultions of MinMx, nd MinTB re presented in Hern nd Rmn reserch s the bse study for compring these formultions [22]. MinMx minimizes the mximum toll on the trnsporttion network: min z (11) Subject to: ^bt, h! W^v * h (12) z $ b 6! A (13) b $ 0 (14) Also, the MinTB minimizes the number of toll booths [25]. The formultion requires positive constnt M tht exceeds the lrgest toll nd vector y of binry vrible y. Its formultion is s follow: min (15) y! A Subject to: ^b,ph! W^v * h (16) b # Mz! A (17) 6 y! " 01,, (18) b $ 0 (19) Although the trffic ssignment problem tht the previous models used refers to different optimiztion nd equilibrium problems, in this pper we just mention the system optimum (SO) nd the user equilibrium (UE). The reders re referred to [26] for more bckground bout these kinds of trffic ssignment problems. In summry, most of the reserch on congested networks tries to evlute the mrginl cost or the hidden cost of using the urbn trnsporttion network by users. Finding the hidden cost is very importnt issue for trnsport plnners to mnge the network by some TDM methods to encourge or discourge the people to use the rods more efficiently by considering the equilibrium condition tht could be reched by congestion toll pricing. However, people wnt to py for something tht they wnt to ern nd not for something tht they do not wnt, like congestion [27], so finding the best price nd solution for users bsed on the pproprite loctions is bsolutely essentil. Moreover, people do not wnt to py for something tht they once used s free service [28]. However, despite ll the efforts in the lst yers, there is no generl nd optimized result for considering the congestion pricing Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

4 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... models s the one solution to determine the potentil TDM loction in urbn trnsporttion network. 3. PROBLEM SOLUTION The concept of minimizing the hidden cost of congestion bsed on the user equilibrium (MHCCUE) model is presented in this chpter. In this regrd, the tolls in the whole network should be optimized bsed on the user equilibrium to find the most considerble links for implementing TDM policies on them. As we know from the equilibrium concepts, nd especilly the expression of equilibrium in trnsporttion, the user equilibrium is not the sme s the optimized system sitution nd the totl cost of the network in user equilibrium condition is more thn the totl cost of the network in optimized system sitution. Therefore, the objective function in this model tries to optimize the flow bsed on the user equilibrium condition by solving two stges of optimiztion progrmming tht in the first stge solve the trffic ssignment to clculte the trffic flow on ech link nd then clculte the mount of dedicted toll for ech link. In this model, s in the mentioned models in literture review, the hidden cost is imposed on the users ccording to vlue of time (VOT) the vlue of one unit of time for users who pss the determined link hs n equl weight s trvel time, for instnce, nd it cn be one dollr per unit of time. As the previous models use the sme vlue for time nd imposed cost, this ssumption is considered conservtive nd better comprison between the results of proposed model nd the ones introduced in the previous section. 3.1 Objective function This section presents the model tht hs been developed in this reserch for quick estimtion of the potentil links tht cn be considered for TDM implementtion. The model is two-stge optimiztion problem tht first solves the UE s sub problem to find the link flows bsed on the user perspective nd then solve the upper level to find the optimized hidden cost of congestion. Therefore, by finding the VOT tht could be considered s cost for the entire network, the model introduces the rtionl priority for links to be selected s potentil cndidte for implementing the TDM policies in urbn trnsporttion network. The objective function nd constrints re presented in Equtions 20 to 27. First: # 0 (20)! A Minimize Z = xt ^x hdx Subject to: 1 k! Krs f = q 6rs k rs (21) d kfk = x 6! A (22) rs k! Krs f $ 0 6k! K, rs (23) k Second: Minimize Z2 = bx 6! A (24) UE Subject to: qrsurs $ ^t^x UE h+ bhx UE (25) rs urs # dk ^t^x UE h+ bh 6rsk,! Krs, rs (26) b $ 0 6 (27) The nottion in mentioned equtions comes s follows: Z 1 - function tht controls the user equilibrium; Z 2 - function tht controls the minimum hidden cost; - represents link in the trnsporttion network; x - flow in link ; x UE - flow in link bsed on user equilibrium (UE) condition, obtined from stge one; t (x ) - Trvel Time in link ; β - toll on link ; k - fesible pths in the network; f k - flow in pth k; rs - Origin-Destintion set in the network; q rs - Demnd Mtrix between rs; 1 forech! fk d k = ' 0 u rs - Trvel Time in shortest pth between rs; K rs - set of fesible pths between rs. This model is solved in two stges, first, Objective 20 is solved, which is the user equilibrium trffic ssignment tht shows the summtion of the flows bsed on the trvel times of ech link. By optimizing this function, the model tries to rech optimized user equilibrium condition of trffic flow. Constrint 21 ensures tht the demnd of ech pir of origin-destintion is stisfied; in other words, the summtion of ll flows in ll origin-destintion pirs is equl to the totl demnd. Constrint 22 mkes the ggregted flow become equl to the optimized system flow in ll of the network links. Constrint 23 limits the pths flow to non-negtive flows. In the second stge, objective 24 tries to minimize the totl hidden cost by considering the number of tolled links. Constrints 25 nd 26 re supplementry ones nd cuse tht ech origin-destintion pir rs, only the routes k! Krs which cost equl to the shortest route bsed on the lowest cost u rs hve non-zero flow. Constrint 27 shows tht the congestion toll rs 608 Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

5 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... obtined for ech link in the set of the network links, should be positive. By solving the model nd finding the nswer bsed on the objective functions nd the defined constrints, the requirements of first-order condition of optimlity re prcticlly stisfied. Also, s in ll symmetric mtrices, like Hessin mtrix, if nd only if ll eigenvlues of the mtrix be positive, then the mtrix is positive-definite [18]. Thus, the Hessin mtrix for controlling the requirements for second-order condition of optimlity is checked, nd s the function is convex for ll vribles, so, the hessin mtrix of the model is positive-definite nd the uniqueness of the nswer is controlled. 3.2 Numericl simultion network This pper employed the nine-node network tht ws used in mny reserch literture [21-23, 25, 29-31] s testbed for providing better comprison of the MHCCUE model versus the previous ones tht hd solution bsed on UE nd SO for this network. The network topology is presented in Figure 1. Origin 1 (5,12) (6,18) 5 (9,20) (4,11) (2,11) (3,25) 7 (8,26) (6,24) (4,26) 9 (2,19) (4,36) Destintion (3,35) (8,30) (7,32) (8,39) 2 (9,35) 6 (6,33) 8 (6,43) 4 Origin Destintion O-D Pir: [1,3] [1,4] [2,3] [2,4] Demnd: Figure 1 Nine-Node network: the tuple ner link is (T,C) As shown in Figure 1, the network hs nine nodes, eighteen links with the sme structure of cost function, nd four pirs of origin-destintion (OD): (1,3), (1,4), (2,3) nd (2,4). As shown in the bottom of Figure 1, the demnd of node one to node three equls 10 trvels; node one to node four equls 20 trvels; node two to node three equls 30 trvels, nd node two to node four equls 40 trvels. The link performnce function or its time-trvel (TT) is bsed on the Bureu of Public Rods (BPR) function s follows: t T c x = 4 : + k D (28) The prmeters T nd C re constnt vlues, which respectively represent free flow trvel time nd prcticl cpcity of the links in the network, nd their vlues re shown next to ech link. For exmple, for the link (rc) from node 1 to 5, the prmeters re ( T, C ) / ^512, h; it mens tht the free flow trvel 3 time is 5 nd the prcticl cpcity is 12 for the mentioned link. 3.3 Solution results Tble 1 shows the results of running the codified model in Mple, tht is obtined by solving the minimiztion hidden cost of congestion bsed on the user equilibrium (MHCCUE) model. The user equilibrium ssignment s the first stge of formultion showed the flow pttern x UE of the network. This progrm includes convex objective function nd liner constrint, so it is solved bsed on the convex combintions lgorithm. This lgorithm is mostly pproprite for solving the UE progrm since the direction finding step cn be executed reltively efficiently [18]. The lgorithm cn be summrized s follows: Step 0: Initiliztion. Perform ll-or-nothing ssignment bsed on free flow trvel times. This yields initil flows. Set counter n: =1. Step 1: Updte trvel time for ech link bsed on BPR function. Step 2: Direction finding. Perform ll-or-nothing ssignment bsed on the updted trvel times nd find the uxiliry flows y n. Step 3: Line serch. Finding coefficient ^0 # n # 1h n n n x + ^y -xh tht solves min # t ^~ hdx 0 Step 4: Move. Set n x + 1 n n n = x + n ^ y -x h Step 5: Convergence test. If convergence criterion is met, stop (the x n + 1 is the set of equilibrium link flows); otherwise, set n= n+1 nd go to step 1. The Tble hs seven columns, which respectively from left to right include link numbers in which 18 links re numbered bsed on the network topology. The next column is Arc; it shows the strt nd end node of the links. Flow x UE column prcticlly shows the flows obtined from the user equilibrium objective function, which mens the flow is ssigned bsed on the user equilibrium to find the minimum trvel time by considering this ssumption tht they know trffic sitution in the long term. The trvel time ^t^x UE hh column shows the trvel time in UE condition bsed on its flow ^x UE h. The totl trvel time ^ UE x $ t^x UE hh column is clculted by multiplying the flow by trvel time for ech link. Toll (β ) column shows the clcultion of tolls bsed on the second-stge objective function (Z 2 ), nd finlly the totl hidden cost ^b$ x UE h column is considered s the multipliction of the toll (β ) by UE flow ^x UE h. As shown in Tble 1, the model finds the two potentil links tht could be considered for implementing the TDM policies. In fct, these two links re the criticl links in the network which the system should consider for plcing control on their demnd. In other words, the network could be in n equilibrium condition if the system imposed the tolls on the introduced links Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

6 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... Tble 1 Results of the MHCCUE model for the Nine-node network Flow x UE Link Trvel Time Totl Trvel Time Toll Totl Hidden Cost Arc 6! A t^x h UE x $ t^x h β b$ x (No. 1 nd 9). Also, the trffic mngers could distinguish their preferences bsed on the mount of the hidden cost defined by the model clcultion. In this regrd, the link with the bigger hidden costs, which in this cse is link number 9, should be considered s the first potentil link for TDM policies implementtion. 4. COMPARISON OF RESULTS To confirm tht using the MHCCUE performs better in finding the best potentil link for implementing TDM strtegies thn the previous models, first, the SO nd UE conditions for the nine-node network re presented in Tble 2. Second, the finl results of the MCSP, Min- Sys, MinTB, nd MinMx re summrized in Tble 3. These outputs re compred with MHCCUE; nd the results obtined from this comprison re presented in Tble 4. x UE - trffic flow bsed on the user equilibrium (UE); x SO - trffic flow bsed on the system optimum (SO). Tble 2 shows the sum of totl trvel time, which is flow multiplied by trvel time, for UE is nd it is for SO condition. It mens by closing the flow from UE to SO, the sum of totl trvel time will be decresed. But s we re trying to consider the user behviour before implementing ny TDM policies, we use UE condition. Tble 3 shows the results of the mentioned models in literture review for the ninenode network. By compring the result of the previous models with the suggested model, the preference of the proposed model could be cler. Although the previous models hd been concentrted on the congestion toll pricing, in this pper, the suggested model tries to investigte the method to find the possible links for implementing the TDM policies in terms of trffic congestion bsed on benefit priorities nd their estimted costs. To evlute the model nd ensure tht more desirble results re obtined in the proposed model, it hs been compred with the Tble 3 models. Therefore, the mentioned network in this pper ws once solved by UE condition nd the solution results were compred with ech other in cse of finding the minimum number of links. In other words, the second prt of objective function (Z 2 ) hs been designed bsed on minimizing the cost of trvel in MHCCUE model nd other models. One cn conclude tht if the MHCCUE model is solved without considering SO condition, but just by using the UE condition, it prcticlly mens solving the congestion toll pricing problem. But, s the min gol of these problems is finding the best price bsed on minimum trvel time for the whole network, they need to consider the SO condition. In other words, they minimize the number of tolled links but fter implementing SO conditions in their first level of optimiztion, the MHCCUE model predicts the suitble links before implementing ny TDM strtegy like congestion pricing. Also, it will minimize the totl number of selected links bsed on its formultion. Tble 4 summrizes the model s finl results nd compres them with MSCP, MinSys, MinMx, nd 610 Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

7 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... Tble 2 UE nd SO results for Nine-node problem Link 6! A Arc Flow x UE UE Condition Trvel Time t ^x h UE Totl Trvel Time UE x $ t ^x h UE Flow x SO SO Condition Trvel Time t ^x h SO Totl Trvel Time SO x $ t ^x h SO Tble 3 Results of MSCP, MinSys, MinMx, nd MinTB models for Nine-node network [21-23, 25]. MSCP MinSys MinMx MinTB Link 6! A Arc Toll β Totl Hidden Cost b $ x SO Toll β Totl Hidden Cost Toll β Totl Hidden Cost b $ x SO Toll β Totl Hidden Cost b $ x SO Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

8 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... Tble 4 Results of the suggested model (MHCCUE) in comprison with other studies Solutions No. of Selected Links Totl Hidden Cost Totl Trvel Time Totl Cost MSCP 14 1, , , MinSys , , MinMx 7 1, , , MinTB , , MHCCUE , , MinTB, since they hve been used in mny pricing studies with the sme testbed [21-23, 25]. It shows tht the totl cost in MHCCUE model is 2, which covers the totl trvel time which is 2, plus totl hidden cost which is As shown, not only the number of links tht need to be modified by TDM policies is decresed in this model in comprison with the others, but lso the totl cost of the MHCCUE model hs been reduced when compred with the mentioned models. As shown in Tble 4, the number of tolled links decresed from 14 to 2 in MSCP model to MHCCUE model. Since, both trditionl or the more modern toll sensing sttions, re costly, decresing the number of tolled links becme the min concerns of trffic mngers. Moreover, by using the new technology like Globl Positioning System (GPS) tht llows ccurte determintion of loction, rte, direction, nd time of trips, opertors could trck the user routes. In this regrd, it would be interesting for trffic mngers to reduce the number of tolled links s much s possible nd return bck to optimum condition. Also, Figure 2 shows in the cse of pplying MHC- CUE with the considertion of user equilibrium conditions for the nine-node network, the totl hidden cost nd the totl cost decrese by bout 77% nd 25%, respectively. However, the totl trvel time increses bout 9% for the nine-node network. Cost , , , , , , , , , , ,5 1 1,5 2 2,5 3 3,5 Totl Hidden Cost Totl Trvel Time Totl Cost MSCP MinSys MinTB MinMx MHCCUE Figure 2 Totl cost of suggested model compred with Previous Studies On the other hnd, Tble 4 nd Figure 2 lso show tht by pplying the MHCCUE model, not only is the number of tolled links reduced but lso t the sme level of totl trvel time due to equilibrium condition, congestion nd obstruction stte will not occur in the network. 5. CONCLUSIONS This pper presents new model for choosing the potentil loction for implementing the TDM policies in urbn trnsporttion networks bsed on the link priority condition. The concept of minimizing the hidden cost of congestion bsed on user equilibrium (MHCCUE) model is presented in this regrd. As the model is well-defined optimiztion problem in its first step, which is trffic ssignment bsed on users equilibrium, urbn plnners nd trnsporttion engineers cn potentilly use this model s quick estimtion tool for deciding on which loction to implement the TDM strtegies in the urbn trnsporttion network, since it just tkes trffic ssignment dt s input to predict the best loctions. Although the min gol of this reserch is not to clculte the congestion toll pricing, the result shows improvements in this re by considering tht the clcultion is bsed on the user equilibrium (UE) rther thn system optimum (SO). This ssumption helps us to select the possible links bsed on user behviour. Thus, the hidden cost of congestion becomes more vluble nd helps the plnner to consider it s prmeter for choosing the potentil links to implement the TDM mong ll of the network links for mnging the demnd to void urbn congestion. Also, s shown in Figure 2, the model reduces the number of links in comprison with the previous studies. It shows tht only by implementing the potentil TDM policies in two selected links, the network cn be close to equilibrium conditions. Moreover, for better comprison between MHCCUE nd previous models, the results of the forementioned model re shown in Tble 3 for the nine-node network. Of course, for better presenttion of the results, the mount of totl hidden cost, totl trvel time, nd finlly totl cost re shown in Figure 2. In this figure, the totl cost is the summtion of the totl hidden cost nd the totl trvel time in the network. As shown in Figure. 2, the proposed model hs minimum totl cost s compred with the others. 612 Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

9 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... REFERENCES [1] Murchlnd JD. Bress's prdox of trffic flow. Trnsporttion Reserch. 1970;4(4): [2] Afndizdeh SH, Dehghni N, Mirzhossein H, Hmedi M. Improving SCATS opertion during congestion periods using internl/externl trffic metering strtegy. Promet Trffic & Trnsporttion. 2016;28(1): [3] Jriw K. Trnsport demnd mngement Impcts on congestion llevition nd rod sfety enhncement in urbn res. Journl of Locl nd Globl Heth Science. 2015(2):83. [4] Luten K, Binning K, Driver D, Hll T, Schreffler E. Mitigting trffic congestion the role of demnd-side strtegies. US Deprtment of Trnsporttion, Federl Highwy Administrtion; [5] Ungemh D, Dusz C. Trnsporttion demnd mngement benchmrk. Trnsporttion Reserch Record: Journl of the Trnsporttion Reserch Bord. 2009;2118(1): [6] Trintis K, Srngi S, Teodorović D, Rzzolini L. Trffic congestion mitigtion: combining engineering nd economic perspectives. Trnsporttion Plnning nd Technology. 2011;34(7): [7] Shw J. The implementtion nd effectiveness of trnsport demnd mngement mesures: n interntionl perspective. Journl of Trnsport Geogrphy. 2010;18(6):762. [8] Broddus A, Litmn T, Menon G. Trnsporttion demnd mngement: Trining document. Eschborn, Germny: Federl Ministry for Economic Coopertion nd Development; [9] Sleh W, Smmer G. Trvel demnd mngement nd rod user pricing: Success, filure nd fesibility. Ashgte Publishing, Ltd.; [10] De Lr M, de Plm A, Kilni M, Piperno S. Congestion pricing nd long term urbn form: Appliction to Pris region. Regionl Science nd Urbn Economics. 2013;43(2): [11] Yildirim MB. Congestion toll pricing models nd methods for vrible demnd networks. University of Florid; [12] Tezcn HO. Evluting rod pricing with n engineering perspective: ggregte nd disggregte nlysis. Cndin Journl of Civil Engineering. 2009;36(6): [13] Smll KA, Verhoef ET. The economics of urbn trnsporttion: Routledge; [14] Pigou AC. The economics of welfre. 4th ed. London: Mcmilln; [15] Knight FH. Some fllcies in the interprettion of socil cost. Qurterly Journl of Economics. 1924;38(4): [16] Wrdrop JG. Some theoreticl spects of rod trffic reserch. Proceedings of the Institution of Civil Engineers. 1952;1(3): [17] Beckmnn M, McGuire C, Winsten CB. Studies in the Economics of Trnsporttion; New Hven: Yle University Press; [18] Sheffi Y. Urbn trnsporttion networks: equilibrium nlysis with mthemticl progrmming methods. Englewood Cliffs, New Jersey: Prentice-Hll, Inc.; [19] De Plm A, Lindsey R. Trffic congestion pricing methods nd technologies. HAL rchive; Avilble from: document [20] Yng H, Hung H-J. Principle of mrginl-cost pricing: how does it work in generl rod network? Trnsporttion Reserch Prt A: Policy nd Prctice. 1998;32(1): [21] Bergendorff P, Hern DW, Rmn MV. Congestion toll pricing of trffic networks. Springer; [22] Hern DW, Rmn MV. Solving congestion toll pricing models. Springer; [23] Hern DW, Yildirim MB. A toll pricing frmework for trffic ssignment problems with elstic demnd. Springer; [24] Ptriksson M, Rockfellr RT. A mthemticl model nd descent lgorithm for bilevel trffic mngement. Trnsporttion Science. 2002;36(3): [25] Yildirim MB, Hern DW. A first best toll pricing frmework for vrible demnd trffic ssignment Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,

10 S. A. Zrgri, et l.: Quick Link Selection Method by Using Pricing Strtegy Bsed on User Equilibrium for Implementing n Effective Urbn... problems. Trnsporttion Reserch Prt B: Methodologicl. 2005;39(8): [26] Florin M, Hern D. Network equilibrium models nd lgorithms. Hndbooks in Opertions Reserch nd Mngement Science. 1995;8: [27] Thorpe N, Hills P, Jensirisk S. Public ttitudes to TDM mesures: comprtive study. Trnsport Policy. 2000;7(4): [28] Goodwin P, Lyons G. Public ttitudes to trnsport: interpreting the evidence. Trnsporttion plnning nd technology. 2010;33(1):3-17. [29] Gendreu M, Lucotte M, editors. Trnsporttion nd network nlysis: Current trends Miscellne in honor of Michel Florin. Springer Science & Business Medi; [30] Prdlos P, Hern D, Hger WW. Network optimiztion. Springer; [31] Hern D, Riber J. Bounded flow equilibrium problems by penlty methods. Proceedings of IEEE Interntionl Conference on Circuits nd Computers; Promet Trffic&Trnsporttion, Vol. 28, 2016, No. 6,