THE ANALYSIS OF ROUTE CHOICE BETWEEN TOLL AND ALTERNATIVE ROAD USING DIVERSION CURVE MODEL: A CASE STUDY IN JAKARTA (INDONESIA) 1

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1 THE ANALYSIS OF ROUTE CHOICE BETWEEN TOLL AND ALTERNATIVE ROAD USING DIVERSION CURVE MODEL: A CASE STUDY IN JAKARTA (INDONESIA) 1 Ofyar Z Tamin 2 Department of Civil Engineering Institute of Technology Bandung Bandung - Indonesia ofyar@trans.si.itb.ac.id ABSTRACT 'Trip assignment' is a step of transportation planning model which objective is to identify the routes chosen by a vehicle moving from its origin to its destination. In choosing its route from certain origin to certain destination, someone will use its best route e.g. the quickest route, the shortest route or the cheapest route. Some factors affecting the route choice are: the traffic flow, speed-flow relationship, distance, safety and comfort. One type of trip assignment model is Diversion Curve Model. By using diversion curve model, the distribution and probability of route choice can be examined as a result of any change in cost of choosing that route. In this research, some behaviour of road users in choosing their best routes will be examined by using the Diversion Curve Model. This study showed the result of using two types of diversion curve models namely: Binomial Logit and Multiplicative Regression model to examine the route chosen by road users amongst toll road and alternative road. Some sensitivity analysis were also carried out to study the effect of varying the toll charge to the percentage of flows using each road. 1. INTRODUCTION 1.1 Background Road transport is an important mode due to its ability to collect and distribute both goods and people to various destinations within one region or from one region to another. The transport sector contributes significantly to the development of many other sectors. Higher demand for transport as a result of increased economic activity will lead to the need for a better quality and quantity of transport supply. Unfortunately, not every transport demand can be supplied with adequate facilities due to limited budget and other factors. This causes delay and congestion, pollution and energy waste problems. Reasons for choosing a particular route rather than another are based on individual preference and such factors as time, distance, cost, navigation, convenience, safety, etc. Different individuals may have different or the same reasons that result in different level of route utilisation; one route is overloaded, while the other is operating below its capacity. To solve this problem, it is needed to know the factors influencing route choice and how sensitive route choice is to any changes in those factors. It is also needed to assess the split of traffic between available routes that will reduce traffic volume on individual route and make efficient utilisation of the system. 1 2 presented in the 1996 IRF Asia-Pacific Regional Meeting, November 1996, Taipeh, Taiwan. Vice Chairman of Magister Programme In Transportation, ITB.

2 1.2 The Objectives The objectives of the study are as follow: a. to analyse route choice between toll and alternative road using Diversion Curve model; b. to analyse the behaviour of road user in choosing the route to factors influencing the route choice such as: fuel, journey time, toll tariff, etc.; c. to analyse the sensitivity of model to any changes in factors influencing the route choice such as: changes in toll tariff or fuel price. 2. LITERATURE REVIEW 2.1 General Conventional travel demand models typically involve a four step sequence which is called a 'Four-Stage Sequential model. They are often called aggregate models because they explain the travel of groups of households. It consists of: a. Trip Generation (trip frequency) b. Trip Distribution (where trips go) c. Modal Split d. Route Assignment Trip generation is the estimation of the total number of trips generated and attracted by each zone in the study area. Trip distribution is the allocation of these trips to particular destinations, in other words, their distribution over space, thus producing a trip matrix. The third step is modal split which allocates the trips in the matrix to different modes, and the last step is to assign the trips by each mode to their corresponding network. Trip assignment can be defined as a part of the process to allocate a given set of trip interchanges to a specific transport network system (Bruton, 1975). This process involves two main parts: - traveller s reason for choosing one route rather than another, and - the development of a model which incorporates a representation of the transport system and the traveller s reasons for choosing a particular route. 2.2 Reasons for Choice of a Particular Route There are three main hypotheses which are used to represent the reasons for choosing a particular route. Each result in a different type of model (Black, 1981): - All-or-Nothing Assignment: Travellers act rationally to choose the shortest route which minimises transport impedance (distance, time or cost). It is assumed that the traveller knows the shortest route and all the travellers use the single shortest route. - Multipath Assignment: It is assumed that travellers do not have perfect information about the uniquely shortest route. Travellers choose what they think is the shortest route. Different perceptions as to what this is lead to different routes being chosen. - Probabilistic Assignment: Travellers include in their choice factors other than mimimising transport impedance. The recognition of the individual choice of travellers can be analysed by giving a probability of any traveller choosing a particular route. Kanafani (1983) states that the selection of route occurs on the basis of route attributes and depends also on the socio-economic characteristics of the trip maker. Hence, the route choice model is basically the same in its logical structure as other transportation choice model. Further, it is said that in dense by trafficked routes, besides attributes such as travel time and travel cost, the effects of traffic flows can not be ignored. 2

3 2.3 Travel Choice Model A variety of models have been developed to estimate and predict travel choice and then represent it in the form of diversion curves. Diversion from one route to another has specific characteristic where the dependent or response variable itself can be dichotomous in nature, taking a 1 or 0 value. It needs a probability model that has two features: a. As Xi (the independent variable) increases, Pi = E(Y=1/Xi) increases but never steps outside 0-1 interval. b. The relationship between Pi and Xi is non-linear, that is one which approaches zero at slower rates as Xi gets small and approaches one at slower rates as Xi gets very large. Geometrically, the model has the sigmoid or S-shaped curve in the Cumulative Distribution Function (CDF) of a random variable. The CDFs chosen to represent the 0-1 response model can be the logistic or the normal. 2.4 Diversion Curves Diversion curves are derived from empirical studies of quantitative measurement of the travel resistance and after examination of the relationship between this measure and the usage of two alternative routes. The diversion curve shows what proportion of drivers is likely to transfer to an alternative route. Numerous diversion curves have been constructed using different measures of travel resistance such as travel time saved, distanced saved, travel time ratio, distance ratio, cost ratio, travel time/distance saved and distance/speed ratio (Bruton, 1985). He stated that three diversion curves are in current use: the time ratio curve, the travel time and distance saved curve and distance and speed ratio curve. The travel time ratio curves as they relate to a motorway or other new facility is the ratio of the travel time via the motorway to the travel time via the quickest alternative route. Figure 1 shows an example of the travel time ratio diversion curve. Figure 1: The Travel Time Ratio Diversion Curve (Source: Bruton, 1985) 3

4 The travel time and distance saved diversion curve developed by The California Division of Highway is given in figure 2. It consists of a family of hyperbolas. The basic assumptions to the derivation of this curve are: - factors other than time and distance cannot be measured explicitly, nor forecasted, and therefore can be ignored; - the greater the travel time and distance saved, the greater the usage; - when only small savings in time and distance occur small number of drivers will transfer to the motorway, other will not; - some drivers will drive any distance to save travel time; few drivers will select the shortest route in terms of distance at the expence of travel time. 2.5 Logit Model Figure 2: The Travel Time and Distance Saved Diversion Curve Source: Bruton (1985) Route choice decision may be considered to be probabilistic in nature. The probability of an individual choosing one alternative depends on the maximum utility he can get. It is assumed that any alternative has utility U, comprising attributes of the alternative (X) modified by attributes of the individual (S). The utility function for an individual comprises a systematic portion of utility, U(X,S), and a random portion of utility, ε(x,s) which can be expressed as: U ij = U(X j,s i )) + ε(x j,s i ) (1) According to Kanafani (1983), the logit model is obtained by assuming that the random components (ε) of the choice utility function are all independent and identically distributed with a Gumbel (double exponential) distribution function. The cumulative distribution function is: F(ε ij )= exp [-Σ j exp(-ε*)] (2) 4

5 From the distribution function one can define the density function of ε ji and hence define the probability that alternative k has a greater utility than any other alternative. Equation (3) shows the density function: F(ε ji )/ ε ki = exp(-ε ki ) exp[-σ j (-ε ji )] (3) The probability of choosing alternative 1 is found by integrating the probability density function over all possible values of ε*, as shown in equation (4) and replacing exp(-ε*) by t, to yield equation (5). P ik = [exp(-ε*)exp[σ j exp(-ε*)+u ki -U jk ] ε*] (4) P ik = 0 [exp[tσ j exp(-ε*)+u ki -U jk ] t] (5) This integral can be evaluated by noting that, for this integration, the summation term is a contant. The integration is therefore given by equation (6) which is a well-known form of the logit model referred to as the Multi-Nomial Logit (MNL) model. exp[u (X k,s i )] P ik = (6) Σ j [exp[u (X j,s i )]] The logit model has features as follow: - as Pi goes from 0 to 1, the logit L goes from - to + ; - although L is linear in X, the probabilities themselves are not. This is in contrast with the linear model; - the probability can be determined directly from the equation once of the parameters are available. 2.6 Muliplicative Model This approach predicts a relation between probability to choose one route and the transport supply attributes using the basic model as follow: Pr(i) = 1/[1+aX b ] where: (7) Pr(i) = the percentage of travellers using one route; X = ratio of transport supply attributes of the alternative routes; a and b= parameters to be estimated. 2.7 Previous Studies Review Giriana (1990) This thesis deals with an assessment of airport ground traffic behaviour in choosing a route for access to the Soekarno-Hatta airport at Jakarta. Two separate route choice models were developed and applied for air passenger trips and airport employee trips. The models used were the Multi-Nomial Logit model and the Multiplicative Regression model. Independent variables used in the first model were travel cost difference and travel time difference, while the second model used ratio of toll charged to time saved as the independent variable. It was found that time difference was more significant than cost difference. Substantial difference in behaviour between trips serving air passengers and work trips where air passenger trips are seem to be less sensitive to the ratio of toll charged to time saved than work trip. 5

6 Characteristics of choice were also different for different vehicle types. Taxis serving air passenger were the highest users of the toll and are the less toll-time ratio sensitive than other trip categories. A van/box work trip was found to be considerably sensitive to the ratio JICA (1990) Two diversion models were developed on the Cikampek-Cirebon tollway project in order to derive a traffic diversion model for the tollway. a. Model I: This model was estimated with the independent variables of difference between travel time through an arterial route and a tollway route, toll rate and vehicle time values. The model used was Multiplicative Regression model as shown below: P = tollway diversion rate (%) T = A - (T + TR/TV) A = travel time through arterial route (minutes) T = travel time through tollway route (minutes) TR = toll rate (rupiah/vehicle) TV = time value of the vehicle (rupiah/min) a,b = parameters to be estimated P = a T b (8) log P = log a + b log T where: (9) The model was calibrated from Jagorawi and Jakarta-Tangerang data samples. The resulting parameters for different type of vehicles and the values of T are shown in table 1. Table 1: Parameter Values of Model I Type 0 < T < < T < 60.0 T > 60.0 P a b P PC Pick-up b. Model II. This model takes into account the factor derived from a toll rate divided by the corresponding travel time difference i.e. the derived diversion curve implies a distribution for the time values of vehicles. In this model, a shift factor is introduced in order to reflect an increasing willingness to pay for a toll in accordance with a rise in income level. The model formula was calibrated from the same data samples used for the model I and the parameters are given in table 2. a P = where: (10) [1 + b (T/S) c ] P = tollway diversion rate (%) T = toll rate/travel time difference (rupiah/min) S = shift factor (ratio of per capita GDP/annual income in the year 1988) R 2 = coefficient of determination 6

7 Table 2: Parameter Values of Model II Type PC Pick-up b 2.78 x x x 10-5 c R DATA COLLECTION 3.1 Data Requirement Data required for this study is classified into inventory data and field data. Inventory data covers all data which are available in relevant institutions, such as map of study area from Directorate General of Highway. This research was based mainly on the field data. Data required here are: traffic volumes and travel times. 3.2 Method of Data Collection a. Method of Survey: to collect all the above information i.e. travel times and traffic volumes. A manual traffic counting survey was conducted by PT Jasa Marga for both directions. Three types of vehicles used in the survey were: Passenger Car (PC), Bus and b. Location of Survey: the survey was conducted at Cawang-Semanggi, Cawang-Kuningan and Tebet-Semanggi links at points with enough distance from the toll gate to avoid the possibility of congestion or of a long queue occurring along that route. The survey locations given are chosen based on the pilot survey. c. Time of Survey: time and duration of survey were decided on the basis of a compromise between desired data quality and the cost of the survey. The better quality the data, the more the cost will be. The survey was conducted on two working days in September 1988 and in August Table 3 shows the data obtained from the surveys for 1988 and It is shown in table 3 that the higher traffic flows occur, the higher the diversion rate of toll users. It shows that the toll road is more usable during peak hour since the alternative road is more congested compared to toll road during that period. Furthermore, during morning peak hour, the diversion rate from Cawang-Semanggi (heading to city centre) is higher compared to other peak hours e.g. afternoon peak hour and, during afternoon peak hour, the diversion rate from Semanggi to Cawang (heading to residential/sub-urban area) is higher compared to morning peak hour. 7

8 8 Table 3: Travel Times, Traffic Volumes and Diversion Rate (1988 and 1989) Travel Times (Minutes) Traffic Volumes Link Time Tol ALT Tol ALT Diversion Rate Cawang- Semanggi (1988) Cawang- Kuningan (1988) Tebet- Semanggi (1988) Semanggi- Cawang (1988) Semanggi- Tebet (1988) Kuningan- Cawang (1988) Cawang- Tebet (1989) Tebet- Kuningan (1989) Kuningan- Semanggi (1989) Semanggi- Kuningan (1989) Kuningan- Tebet (1989) Tebet- Cawang (1989) Table 4 shows the traffic flows of each type of vehicle and their corresponding diversion rates for Cawang-Semanggi link. It is shown in table 4 that the flows in Cawang-Semanggi link

9 consists of mainly passenger cars (80%). The highest diversion rate obtained is for trucks either for 1988 and 1989 data, followed by buses and passenger cars. Year Table 4: Diversion Rate and Traffic Volumes for each Type of Vehicle Traffic Volumes Vehicle Toll ALT Type Vol % Vol % Vol % PC Bus PC Bus Diversion Rate DATA ANALYSIS Data analysis was conducted to determine the most representative correlation of the observed data. The Binomial Logit and Multiplicative Regression models were selected to study the relationships between route choice, represented by diversion rate (P), and impedance factors represented in the form of Travel Cost Saved in rupiahs (TCS), Travel Cost Ratio (TCR), Travel Time Saved in minutes (TTS), Travel Time Ratio (TTR) and the ratio of toll tariff to travel time saved (Rupiah/minutes). The former (P) will acts as dependent variable, while the latter (TCS,TCR,TTS,TTR,X) is the independent variable or regressor. The models consist of the Binomial Logit model for difference in travel impedance factors (TCS,TTS) and the Multiplicative Regression model for ratio in impedance factors (TCR,TTR,X) as shown in Table 5. Table 5: Variables Used in Each Model Model Dependent Variables Independent Variables Binomial Logit Case 1 TCS Model (Model 1) Case 2 TTS P (Diversion Rate) Multiplicative Regression Model (Model 2) Case 1 Case 2 Case Binomial Logit Model (Case 1) 9 TCR TTR X P (Diversion Rate) The basic form of the Binomial Logit model is shown as equation (6). By subtituting the utility function with Travel Cost Saved (TCS) in rupiahs, the Binomial Logit model can then be represented by the following equation: P = Diversion Rate TCS = Travel Cost Saved in rupiahs a and b = Regression Coefficients to be estimated exp [a + b (TCS)] P = where: (11) 1 + exp [a + b (TCS)] To change the division term in equation (11) into additive term, logarithmic transformation is required as follow: P [1 + exp [a + b(tcs)]] = exp [a + b(tcs)] (12)

10 P + P exp [a + b(tcs)] = exp [a + b(tcs)] (13) P = exp [a + b(tcs)] - P exp [a + b(tcs)] (14) P = (1-P).[exp [a + b(tcs)]] (15) P/(1-P) = exp [a + b(tcs)] (16) Finally, Ln [P/(1-P)] = a + b(tcs) (17) The resulting model was then tested using the 1988 and 1989 data as shown in table 3. The estimated parameters (a and b) for each type of vehicle together with their corresponding R 2 were given in table 6 and the estimated models for each type of vehicle were also drawn as shown in figure 3. It is shown that the diversion rate for each type of vehicle is higher in 1989 compared to in It is also shown that for trucks, the use of toll road is becoming one of their only best choice since nearly 80% of them in 1989, were using toll road in the condition of zero travel cost saved. Year Table 6: Binomial Logit Model Using Travel Cost Saved (Case 1) Vehicle Type Coeficients a b PC Bus PC 1989 Bus R However, for buses, lower diversion rate is found which may be due to boarding and alighting passengers were not allowed on the toll road. The more travel cost saved, the higher the diversion rate of passenger car. It is found that the diversion rate is around 50% in 1989 in the condition of zero travel cost saved. It can be seen that, using the 1989 data, the best fit in terms of values of R 2 is found for passenger cars followed by trucks but not for buses. However, using the 1988 data, none of them has good fits in terms of R Binomial Logit Model, Case 2 The following model is the Binomial Logit model using the Travel Time Saved (TTS) in minutes as the utility function. The linear form of the logit model is represented as follow: Ln [P/(1-P)] = a + b(tts) where: (18) TTS is the difference between travel time in minutes via toll road and via the alternative road and P is the diversion rate. The estimated regression coefficients (a and b) were given in table 7. 10

11 Figure 3: Diversion Curve Using Binomial Logit Model (Case1) Year Tabel 7: Binomial Logit Model Using Travel Time Saved (Case 2) Vehicle Type Coefficients a b R 2 PC Bus PC Bus

12 It can be seen that similar result is obtained. Using the 1989 data, the best fit is found for passenger cars followed by trucks but not for buses. However, using 1988 data, none of them has good fits in terms of R 2. Using the 1989 data, the value of R 2 is slightly lower compared to Case 1, however, using 1988 data, the value of R 2 showed considerably better result compared to Case Multiplicative Regression Model (Case 1) The other model used for analysing the behaviour of road users in choosing their own routes is the Multiplicative Regression model. This model shows the relation between the diversion rate that the ratio of Travel cost of choosing the toll road and the alternative road. This formula is as follow: 1 P = (19) 1 + a (TCR) b Equation (19) can be arranged to make simpler calculation as follow: P. [1 + a (TCR) b ] = 1 (20) P + P a (TCR) b = 1 (21) P a (TCR b ) = 1-P (22) (1-P)/P = a (TCR) b (23) Log [(1-P)/P] = Log a + b Log (TCR) (24) The resulting model was then tested using the 1988 and 1989 data and the estimated parameters (a and b) for each type of vehicle with their corresponding R 2 were given in table 8. The estimated models for each type of vehicle were drawn in figure 4. It is shown that the diversion rate for each type of vehicle is higher in 1989 compared to in It is also shown that for trucks, the use of toll road is becoming one of their only best choice since nearly 80% of them, in 1989, were using toll road in the condition of travel cost ratio is equal to one. Year Tabel 8: Multiplicative Regression Model Using Travel Cost Ratio (Case 1) Vehicle Type Coefficients a b R PC Bus PC 1989 Bus

13 Figure 4: Diversion Curve Using Multiplicative Regression Model (Case1) However, for buses, lower diversion rate is found which may be due to boarding and alighting passengers were not allowed on the toll road. The higher travel cost ratio, the higher the diversion rate of passenger car. It is found that the diversion rate in 1989 is around 50% in the condition of travel cost ratio is equal to one. It can be seen that, using the 1989 data, the best fit in terms of values of R 2 is found for passenger cars followed by trucks but not for buses. However, using the 1988 data, none of them has good fits in terms of R 2. 13

14 4.4 Multiplicative Regression Model (Case 2) The following model is the Multiplicative Regression model using the Travel Time Ratio (TTR) as the utility function. The linear form of the model is as follow: Log [P/(1-P)] = Log a + b Log (TTR) where: (25) TTR is the ratio between travel time using toll road and the alternative road and P is the diversion rate. The estimated regression coefficients (a and b) for each type of vehicle and their corresponding R 2 values were given in table 9. Year Tabel 9: Multiplicative Regression Model Using Travel Time Ratio (Case 2) Vehicle Type Coefficients a B R PC Bus PC 1989 Bus Multiplicative Regression Model (Case 3) The following model is the Multiplicative Regression model showing the relation between the Diversion Rate with X in rupiah/minute (the ratio of toll tariff with travel time saved). The linear form of the model is as follow: Log [(1-P)/P] = Log a + b Log X where: (26) P = Diversion Rate, X = Ratio of Toll Tariff and Travel Time Saved (in rupiah/minute) a and b = Regression Coefficients The resulting model was then tested using the 1988 and 1989 data and the estimated parameters (a and b) for each type of vehicle with their corresponding R 2 were given in table 10. The estimated models for each type of vehicle were drawn in figure 5. Tabel 10: Multiplicative Regression Model Using Toll Tariff-Travel Time Saved Ratio (Case 3) Coefficients Year Vehicle Type R 2 a b 1988 PC Bus 1989 PC Bus It can be seen that the more the travel time saved, the more vehicles were attracted to use the toll road especially for the trucks.

15 Figure 5: Diversion Curve Using Multiplicative Regression Model (Case 3) 4.6 Sensitivity Analysis Some sensitivity analysis were carried out using the Binomial Logit model (Case 1) by changing the values of toll tariff as one of the vehicle operating cost components. The results of changing the toll tariff to the diversion rate for each type of vehicle were given in figure 6. 15

16 Figure 6: Sensitivity Analysis It is shown that buses have very small sensitivity to changing in toll tariff. This is quite logical since most of buses have fixed route. However, trucks and passenger cars have quite large sensitivity and have fairly similar sensitivity. It can be calculated that 20% increasing in toll tariff resulting in decreasing 7% of total traffic volumes and 11.6% increasing in toll road income. Furthermore, 40% increasing in toll tariff resulting in decreasing 14% of total traffic volumes and 20.4% increasing in toll road income. 16

17 5. CONCLUSION AND RECOMMENDATION 5.1 Conclusion a. The models used to relate diversion rate and various regressor variables i.e. travel time saved, travel time ratio, travel cost saved, travel cost ratio and the ratio of toll tariff to travel time saved gave R 2 values between 0.16 to This may be due the small amount of data. b. It is found that the diversion rate for each type of vehicle is higher in 1989 compared to in It is also found that for trucks, the use of toll road is becoming one of their only best choice since nearly 80% of them, in 1989, were using toll road in the condition of zero travel cost difference. However, for buses, lower diversion rate is found which may be due to boarding and alighting passengers were not allowed on the toll road. For passenger cars, the higher travel cost and time difference, the higher the diversion rate (around 50% in the condition of zero travel time difference). c. It can be seen that the more the travel time saved, the more vehicles were attracted to use the toll road especially for the trucks. d. The diversion rate is more sensitive to travel cost and time differences than travel cost and time ratios. This is may due to short journey trips within urban area. e. It is found that buses have very small sensitivity to changing in toll tariff. This is quite logical since most of buses have fixed route. However, trucks and passenger cars have quite large sensitivity and have fairly similar sensitivity. It can be estimated that 20% increasing in toll tariff resulting in decreasing 7% of total traffic volumes and 11.6% increasing in toll road income. Furthermore, 40% increasing in toll tariff resulting in decreasing 14% of total traffic volumes and 20.4% increasing in toll road income. 5.2 Recommendation a. To analyse how sensitive the choice of the trip maker is to any changes in impedance factor (i.e. time and cost), the observations should cover different origin destination which specific vehicles types, and time groupings in order to get a better understanding of diversion rate changes due to the various impedance factors. REFERENCES Ben Akiva, M.E. and Richards, M.G.A. (1975) Disaggregated Travel Demand Model. London, Saxon House. Black, J. (1981) Urban Transport Planning. London, Croom Helm. Bruton, M.J. (1985) Introduction to Transportation Planning (3 rd Edition). London, Hutchinson & Co. (Publisher) Ltd. Cherwony, W. and Lutin, J. (1976) Two Dimensional Logit Modal Split Model. Transportation Engineering Journal, Vol.102, p Chesher, A. and Harrison, R. (1987) Vehicles Operating Cost. Washington, The International Bank for Recontruction and Development, World Bank. Giriana, M. (1990) Diversion Onto Local Street from The Toll Highway Serving Soekarno-Hatta Airport, Jakarta. MSc Thesis, Pasca Sarjana ITB. JICA (1988) Traffic Survey. Technical Report No. 4, Jakarta. Japanese Team Management Services For Tollway System. Kanafani, A. (1983) Transportation Demand Analysis. McGraw-Hill Book Company, New York. 17