1、The number of tollbooths is always more than the number of lanes on the highway. Afterpassing tollbooths, vehicles enter lanes through a merging area. The shape, size andmerging pattern of the merging area can affect its capacity of accident prevention,throughput and cost. After a performance analys
2、is of a merging area following the tollbarrier, a solution is put forward. The solution considers capacity of accident prevention,throughput and cost. Then the optimal designing of merging area is obtained.Furthermore, the performances of solutions in the situation of different traffic flow areevalu
3、ated. As more autonomous (self-driving) vehicles are added to the traffic mix, thesolution will be influenced.Firstly, the performances of merging areas is analyzed by the capacity of accidentprevention, throughout and cost. The result indicates that the capacity of accidentprevention is inversely a
4、ssociated with gradient of merging area; the cost of constructionis directly proportional to the area of toll plazas; throughput determines the mergingpattern of toll plaza following the toll barrier.Secondly, in order to determine the shape, size and merging pattern of the mergingarea, a multi-obje
5、ctive optimal model is proposed based on dual objective function,where the decision variable is the length of toll plaza following the toll barrier, theobjective functions are construction cost and the capacity of accident prevention. Then,the model is simplified to a Single-objective optimal model.
6、 In this way, the length oftoll plaza following the toll barrier, the length of other sides and all angles can beobtained with varying number of lanes. And the throughput can be calculated underdifferent merging pattern.Thirdly, the performance of our solution in light and heavy traffic is analyzed
7、andverified. As more autonomous (self-driving) vehicles are added to the traffic mix, somehuman-staffed tollbooths will be replaced by electronic toll collection booths. Under thecircumstances, the throughput will increase with the traffic flow increasing, though thetraffic efficiency will decrease.
8、 Taking 4-tollbooth into 2-lane as an example, the trafficefficiency of toll mode with 2 electronic toll collection booths and 2 human-staffedtollbooths decrease 2.44 %.Fourthly, the throughput will also increase as the proportions of human-staffedtollbooths, automated tollbooths and electronic toll
9、 collection booths change. Thespecific varying circumstance is listed in Page 13.Finally, we offer the non-technical suggestion to New Jersey Turnpike Authority forreference.2017MCM/ICMSummary SheetENJOYAHAPPYJOURNEYSummaryFor office use onlyT1 _T2 _T3 _T4 _ Team Control Number63650Problem ChosenB F
10、or office use onlyF1 _F2 _F3 _F4 _Contents1 Introduction 21.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Restatement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Assumptions and Notations 32.1 General Assumptions . . . . . . . . . .
11、 . . . . . . . . . . . . . . . . . . . . 32.2 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Model One 43.1 Establishing the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1.1 Evaluation Model . . . . . . . . . . . . . . . . . . . . . . . .
12、 . . . . 43.1.2 Optimization Model . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Calculating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2.1 Optimization Model . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Our Optimization Scheme . . . . . . . . . . .
13、 . . . . . . . . . . . . . . . . 94 Model Two 104.1 Establishing the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.1.1 Performance Analysis Model of Light and Heavy Flow . . . . . . 104.1.2 The Impact of Tollbooths Proportions on the Solution . . . . . . . 104.2 Calculating the
14、 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.1 The Impact of Tollbooths Proportions on the Solution . . . . . . . 115 Sensitivity Analysis 146 Evaluation of the Model 147 Strengths and Weaknesses 147.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15、. . . . . . 157.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Conclusions 15Team # 63650 Page 2 of 161 Introduction1.1 BackgroundWith the rapid development of the national economy, the highway transportation in-dustry of America has made considerable progress
16、. As the most basic transportationfacilities, highway has become an important pillar of national economic development.Highway toll station is a significant service facilities on the highway, whose servicelevel directly affects the highway capacity.The design of highway toll station, as a vital part
17、of the highway traffic manage-ment service facilities, obtains more and more attention from the construction sector.Obviously, with the continuous progress of the social economy, the highway trafficflow is growing.It is observed that some sections of the actual traffic flow growth rate is far greate
18、rthan predicted. The capacity of freeway toll stations are often not so satisfying and thetraffic capacity of the expressway, resulting in traffic congestion, often occurs in thetoll station. Highway toll station has become a key impact aspects of the Expresswaylogistics circulation, the travel time
19、 of vehicles and the traffic cost.Figure 1: A Toll HighwayIn recent years, with the rapid development of the economy, highway traffic flowincreases rapidly, which brings highway toll station service great pressure.Some modern toll facilities require all payment to be made by electronic transpon-der,
20、 so that vehicles do not have to slow down in order to pay the toll. But on manyolder toll ways moving to all-electronic payment is not an option, while mounting con-gestion means that planners are faced with the problem of configuring their existinginfrastructure to provide the best possible servic
21、e. Therefore, it is an effective wayto improve the level of traffic capacity and service by optimizing the shape, size andmerging pattern of the area following the toll barrier.Team # 63650 Page 3 of 161.2 Restatement of the ProblemConsider a toll highway having L lanes of travel in each direction a
22、nd a barrier tollcontaining B tollbooths (B L) in each direction.The problems that need to solve in this paper are:Determine the shape, size, and merging pattern of the area following the tollbarrier in which vehicles fan in from B tollbooth egress lanes down to L lanesof traffic. Particularly, acci
23、dent prevention, throughput and cost should be takeninto consideration.Analyze any particular toll plaza design that may already be implemented,determineif there are better solutions.Determine the performance of the solution in light and heavy traffic.Illustrate how the solution change as more auton
24、omous vehicles are added to thetraffic mix.Illustrate how the solution affected by the proportions of conventional tollbooths,exact-change tollbooths, and electronic toll collection booths.2 Assumptions and Notations2.1 General AssumptionsA car comes to a complete stop at a tollbooth.Once a driver p
25、ays the toll, they maneuver to a highway lane and accelerate tohighway speeds.Outflux is the rate (in cars/h) of cars exiting all booths of the plaza.All drivers accelerate from a toll booth to the lanes of travel at the same accelera-tion.No driver delays in the plaza on purpose.The service time of
26、 all toll booths is the same, and vehicles do not distinguishamong them.Under the above and basic assumptions, we can set out to construct our model(show our approach in detail).Team # 63650 Page 4 of 162.2 NotationsTable1: VariablesSymbol DescriptionB The amount of tollboothsL The amount of lanesl
27、The length of the plaza foraaccelerationtan The gradient of the merging areaC The cost of toll plaza constructionS The area of toll plaza constructionP The price of per square meter toll plaza constructionT The throughputt The time for reaching the station of congestionF The amount of vehicles passi
28、ng by the tollbooths per hourm The time of passing per vehicle in a tollboothac The acceleration of vehicles3 Model One3.1 Establishing the Model3.1.1 Evaluation ModelAccident prevention, throughput and cost should be taken into consideration whenestablishing the evaluation model, the process is as
29、follows.Accident PreventionThe toll plaza outlet transition section, should guide the vehicle go out of toll plazasmoothly. It is required that the merging area varies mildly. Otherwise, it is easy tomake drivers feel traffic deviation, resulting in improper operation which endangersthe safety of dr
30、iving.The relationship between the gradient of the merging pattern and the traffic acci-dent is shown in the graph. It is reflected from the figure that with the gradual increaseof the gradient, the number of traffic accidents increase while the safety of toll plazadecrease.Based on the regression a
31、nalysis of the data, the correlation model between the rateand the number of traffic accidents is obtained as follows:y = 1:4231e8:0664x (1)Team # 63650 Page 5 of 16Figure 2:The Relationship Between the Gradient and Traffic Accidentswhere:y describes the predicted number of traffic accident,x descri
32、bes the gradient.The correlation coefficient R2 = 0:8621 in this model, which implies that the modelhas a high correlation.The model exhibits that the frequency of traffic accidents is proportional to the gra-dient. If the gradient of the merging pattern is excessively large , sight distance of thed
33、river will be decreased, leading to the occurrence of traffic accidents. Therefore, thedesign of gradient is a momentous factor in accident prevention.The gradient of the merging area is the ratio of the extra width of the highwayscompared with the barrier toll and the length of the gradient area,th
34、at is:tan = bL (2)According to the experience of the United States and Japan,when the vehicle driv-ing from a straight line into another lane , if the deflection ratio is 0.9 m/s or so, thedriver generally do not feel traffic deviation or uncomfortable. Therefore, the gradientneeds to be in a suitab
35、le range, that is:tan min tan tan max (3)Therefore,the accident prevention rate of any square can be analyzed by the gradi-ent.CostTaking the high cost of land and road construction into consideration, how to savecost is another noteworthy factor in the design of the merging area.Firstly, estimate t
36、he merging area following the toll barrier. It is approximated as aregular geometric trapezoid shape, that is:S = l (Ld1 +Bd2)2 (4)Team # 63650 Page 6 of 16where:S describes the area of toll plaza construction,d1 describes the width of per lane,d2 describes the width of per tollbooth.Supposed that t
37、he construction of per square meter requires P dollars, that is:C = SP = l (Ld1 +Bd2)2 P (5)Therefore, it can be used to analyze the cost of any square.ThroughputThe sum of the throughput is accumulated by the throughput of each tollbooth,that is:T =BXi=1Ti (6)Due to the different position of tollbo
38、oths, the time to travel to the merge can be differ-ent. Therefore, the throughput of the tollbooths at different locations is related to thepassing time when vehicles driving through the tollbooths,that is :T = L3600m +B LXi=13600m+ t (7)where:m describes the time of passing per vehicle in a tollbo
39、oth,t describes the delay time (time difference of position).The delay time of the lane align with the tollbooth is 0, while the delay time of therest tollbooths ascend with the increase of distance between the tollbooths and the laneSupposed that vehicles do uniform acceleration in this distance,th
40、at is:t =r2l0ac r2lac (8)By the Pythagorean theorem, we can obtain this formula:l0 =pl2 + Bd2 Ld1 d2(i 1)2 ; i = 1;2 (9)After finishing, the throughout model is as follows:T = L3600m +B LXi=13600m+q2pl2+Bd2 Ld1 d2(i 1)2m q2lm; i = 1;2 (10)Team # 63650 Page 7 of 16Expressed by piecewise function:T =F
41、 ; 0 Lmin tan maxl lmin(13)3.2 Calculating the Model3.2.1 Optimization ModelConsulting the relevant literature and taking the three lane highway as an example,the data obtained are as follows:8:min = 1=7max = 1=5lmin = 75L = 3(14)Put them into the single objective optimization model.After calculatio
42、n, the results is as follows:Team # 63650 Page 8 of 16Table2: Calculation resultsL B l(m)1 3 75.752 3 76.503 4 75.754 5 75.75The relationship between the traffic flow or throughout and the tollbooths is shownin the following picture.Figure 3: The Relationship between The Traffic Flow/Throughout and
43、The TollboothsTable 3: The Data of Figure 3When the number of lanes is small, there is little difference between F and T, indi-cating that congestion is not easy to produce.Team # 63650 Page 9 of 16Table 4: The Theoretical Traffic Flow per Tollbooths3.3 Our Optimization SchemeIt is known that the tr
44、aditional single kiosk toll station entrance layout is a toll roadwith one toll booth, and double pavilion style toll lane is set up two toll booths in thesame toll island, in the same lane driving the two car, corresponding to the front andrear of the two toll booths, two toll collectors charge two
45、 cars at the same time.On the basis of the above, combined with the advantages of single Pavilion anddouble Pavilion style kiosks, by the principle of saving land resources, establish a newtype of single-way-in and double-way-out composite toll station model, as shown inthe following figure:Figure 4
46、:The Composite Toll StationAs can be seen from the figure, the new composite toll station model, design a laneafter the original toll booths, form a single-way-in and double-way-out toll station.Thecomposite toll station can optimize the toll booth arrangement, in the case of the samenumber of booth
47、s, effectively reducing the width of the toll station. With the decreaseof the width, the gradient is reduced, and the cost of land construction is further saved.Team # 63650 Page 10 of 164 Model Two4.1 Establishing the Model4.1.1 Performance Analysis Model of Light and Heavy FlowF can be expressed
48、as the total number of vehicles running through one hour in B tollstation with service capacity of a (service a vehicle in unit of time).F = aB (15)In the process of vehicle flow vary from light to heavy, the degree of congestion inthe merger area will be affected.Set the time needed for attaining c
49、ongestion state to represent the performance ofthe scheme under heavy traffic. That is:t =1; 0 F F0ks=(F T) ; F0 F Fmax (16)where:F0 describes the demarcation point of light and heavy flow,k describes the amount of parking vehicles unit area.When the traffic is heavy, assume that the unit time accumulation is traffic flowof the toll station minus the throughput at the moment, t is the maximum acceptablevehicles minus the nit time accumulation.t = kSa1B01 +a2B2 T(17)whe
