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Modelling public-transport users’ behaviour at connection point
Transport Policy 27 (2013) 112–122
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Modelling public-transport users’ behaviour at connection point Avishai Ceder n, Subeh Chowdhury, Nima Taghipouran, Jared Olsen Faculty of Engineering, Department of Civil and Environmental Engineering, University of Auckland, New Zealand
a r t i c l e i n f o
a b s t r a c t
Available online 6 March 2013
Out-of-vehicle times were shown to be perceived as being more onerous than in-vehicle time by transit users when making transfers. The present study has two main objectives. The first objective is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. The second objective is to determine the influence of out-of-vehicle facilities, offered by publictransport (PT) operators, on transit users’ perception of trip attributes related to transfers. A user preference survey was conducted at two major PT terminals in Auckland, New Zealand. The survey data was modelled using cumulative prospect theory and fuzzy logic. The results showed that for all trip attributes, except for comfort, transit users’ exhibited risk averse behaviour; users’ revealed greater preference for the transfer route with less uncertainty in the out-of-vehicle times. For comfort, transit users’ displayed risk-taking characteristics when the waiting time for a seat was less than 5 min. Such findings suggest that increasing the consistency in out-of-vehicle times will increase attractiveness of transfer routes thus enabling a more efficient and integrated network of PT routes to result in enlargement of ridership. Policy makers and PT planners must focus on methods of reducing uncertainty in out-of-vehicle times during transfers. Analysis of transit users’ perception of trip attributes, given their current station, revealed statistical evidence of differences for two trip attributes, transfer waiting time and vehicle delay. Such findings indicate that transit users who are accustomed to better out-of-vehicle facilities have a lower tolerance for uncertainty in transfer waiting times and delay times. To the authors’ knowledge, this study provides for the first time in literature a comparison between the two cognitive models. The comparison revealed that CPT and fuzzy logic models are both capable of representing transit users’ decision making process. However, while CPT provides an indication of transit users’ preference for a transfer route, fuzzy logic is capable of providing a closer approximation of the proportion of transit users preferring a transfer route. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Travel behaviour Public transport Transfer Cumulative prospect theory (CPT) Fuzzy logic
1. Introduction and research objective Trip-making behaviour has grown increasingly complex in the past decade (Currie and Delbosc, 2011). Modern day busy lifestyles have compelled travellers to become time-poor. Increase in trip chaining complexity has been identified as a barrier to the use of public transport (PT) (Ampt, 2004; Ye et al., 2007). Due to the dispersed nature of origins and destinations, PT operators are unable to provide direct connections for all origin-destination pairs (Muller and Furth, 2009). The extra effort required in making transfers has deemed them to be a significant contributor to transit users’ journey inconvenience (Hadas and Ranjitkar, 2012). Guo and Wilson (2011) discussed that the quality of transfer connectivity plays an important role in attracting potential transit users and sustaining the satisfaction of existing users. Iseki and Taylor (2009) explains that although out-of-vehicle times have been recognised to be a crucial element in transit users’ satisfaction, there has only been a limited number of studies on out-of-vehicle travel behaviour and the effect of
n
Corresponding author. Tel.: þ64 9 3652807; fax: þ 64 9 3652808. E-mail address: [email protected] (A. Ceder).
0967-070X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tranpol.2013.01.002
out-of-vehicle trip attributes on PT ridership. As a result, there exists a lack in complete understanding of how improvements in outof-vehicle trip attributes affect transit users’ travel behaviour and thus the effect of these improvements on PT ridership (Iseki and Taylor, 2009). The present study has two main objectives. The first objective is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. The second objective is to determine the influence of out-of-vehicle provisions, offered by PT operators, on transit users’ perception of trip attributes related to transfer routes. The study contributes to existing knowledge by providing policy makers with an understanding of the effects perceived quality of out-of-vehicle times have on transit users’ decision to use transfer routes. Such findings will assist policy makers and operators to increase the ridership of transfer routes. A user preference survey was conducted in two transport centres in Auckland, New Zealand. The results of the survey were modelled using the cumulative prospect theory (CPT) and fuzzy logic. Perceived uncertainty associated with transfer connections can cause travellers to avoid transfer routes (Guo and Wilson, 2011). Depiction of travel behaviour under uncertainty calls for adopting cognitive
A. Ceder et al. / Transport Policy 27 (2013) 112–122
2.1. Out-of-vehicle trip attributes Access to, between and among stations and stops has been recognised to be a key element in PT travel. Reducing perceived walking and waiting times for transfers have been shown to substantially increase the attractiveness of PT (Iseki and Taylor, 2009). There is much support for transfer waiting times being valued higher than transfer walking times (Vande Walle and Steenberghen, 2006; Iseki and Taylor, 2009). Transit users’ perceived waiting time has been shown to be more onerous than the actual waiting time (Iseki and Taylor, 2009). Perceived waiting time is dependent on waiting conditions such as personal safety, reliability of connection and comfort (Iseki and Taylor, 2009). Personal safety at terminals has been revealed to be the most important factor in travellers’ decision to use PT (Atkins, 1990; Kumar et al., 2011; Eboli and Mazzulla, 2012). Missed transfers are a major contributor to the reliability issues of PT services (Hadas and Ceder, 2010). Missed connections and delays are shown to cause anxiety to the user (Cheng, 2010). Reducing the uncertainty of waiting times has been shown to improve passenger satisfaction and thus increase ridership (McCord et al., 2006). A high quality information system is an essential factor in increasing ridership by retaining existing riders and attracting potential users (Eboli and Mazzulla, 2012). Studies (Bachok, 2007; Grotenhuis et al., 2007; Molin and Chorus, 2009) have shown that integrated information systems are required to facilitate transfers among urban and interurban multimodal PT networks. Comfort at the transfer terminal has been identified to be a determining factor in transit users’ perceived ease of making a transfer (Guo and Wilson, 2011). A study by Currie and Willis (1998) has shown that commuters place a high value for basic amenities at stations and stops such as seating and shelter. Perceived walking distance and time have also been shown to be substantially longer than actual walking time. Physical conditions such as layout of terminal and sheltered walkways connecting terminals can reduce the perceived walking times (Iseki and Taylor, 2009). Presence of escalators, longer ramps and same-level interchange have been shown to mitigate the penalty imposed for transfer walking times (Guo and Wilson, 2004). Literature (Guo and Wilson, 2010) has indicated that passengers will choose stations which are well connected over stations which provide better physical amenities. 2.2. Cognitive Models When modelling mode and route choice in travel behaviour studies, it has been a common practice to assume that travellers have perfect knowledge about their choices and make rational decisions based on utility maximisation (Xu et al., 2011). Discrete choice models derived using expected utility theory (EUT) and
2.2.1. Fuzzy logic Traditional crisp choice models are not capable of incorporating vagueness in decision making (Ridwan, 2004). Fuzzy logic, first introduced by Zadeh (1965), enables formation of logical statements to compute vagueness. Using the concept of ‘‘approximate reasoning’’, fuzzy logic makes it possible to model imprecision in human reasoning and thus, decision making. Each fuzzy logic system can be divided into three stages: fuzzification, fuzzy inference and defuzzification. Fig. 1 shows the link among the stages and the input and output of each stage. A disadvantage of fuzzy logic is the task of fine-tuning the membership functions and adjusting the fuzzy rules. Construction of the membership functions and the fuzzy rules is a trial-and-error process until an appropriate fit of the input–output set is achieved. This process can be simplified by use of learning algorithms in programs such as MatLab for tuning (Postorino and Versaci, 2008). It is evident from a number of route and mode choice studies that fuzzy logic is capable of modelling ambiguity in perception and appraisal of trip attributes (Murugesan and Rama Moorthy, 1998; Teodorovic, 1999). In more recent studies, Kikuchi and Miljkovic (2001) used fuzzy logic to predict bus ridership at individual stops based on the factors such as transit service quality and condition of bus stop. Andrade et al. (2006) proposed a hybrid model (multinomial logit model with neuro-fuzzy utility functions) to determine mode choice between PT modes and cars. Manju et al. (2008) conducted a study on commuters’ PT route choice using fuzzy logic, which allowed transit users’ preference for trip attributes to be taken into account. Postorino and Versaci (2008) used an adaptive neuro-fuzzy inference system to investigate the decision criteria followed by users when they select a transport mode. Fuzzy Inference
Input linguistic variables
Linguistic terms Numerical Values
Outputlinguistic variables
Defuzzification
2. Literature review and research methodology
random utility theory (RUT) have been frequently adopted to analyse choice in travel behaviour studies (Liu et al., 1997; O’Fallon et al., 2004; Ridwan, 2004; Postorino and Versaci, 2008). An increasing number of route choice studies have been challenging the assumption of absolute rationality of travellers by showing evidence of violations of EUT (Avineri and Prashker, 2004; Xu et al., 2011). Statistical models using the assumption of utility maximisation overlook the fact that humans’ decision-making process is approximate rather than precise (Andrade et al., 2006; Manju et al., 2008). From literature on route and mode choice behaviour both CPT and fuzzy logic were found to be well established cognitive models which provide a more realistic representation of travellers’ decision in travel conditions with uncertainty. CPT is the most popular non-EU model (Gao et al., 2010). Van de Kaa (2010) provides a comprehensive review on the successful adoption of CPT in travel choice studies. Teodorovic (1999) gives a summary of transport studies which have implemented fuzzy logic with success. Following Sections 2.21 and 2.2.2 discuss fuzzy logic and CPT, respectively, in more detail.
Fuzzification
models such as CPT to capture the mental representation of uncertainty in decision making (Schwanen and Ettema, 2009; Van de Kaa, 2010). A number of route and mode choice studies have shown that fuzzy approach is also capable of modelling the imprecision in transit users’ perception of trip attributes and thus their choice of route (Teodorovic, 1999; Ridwan, 2004). To the authors’ knowledge, for the first time in literature, the present study provides a comparison of the two commonly used cognitive models for travel behaviour. Hereafter, Section 2 provides literature review, Section 3 is data collection, Section 4 gives the two modelling procedures and results, Section 5 provides a discussion of the comparison between the results from CPT and fuzzy logic, and lastly, Section 6 is conclusion.
113
InputNumerical Values
OutputNumerical Values
Fig. 1. Fuzzy Logic Systems.
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2.2.2. Cumulative prospect theory In 1992, Tversky and Kahneman introduced CPT, an extension of the prospect theory (Tversky and Kahneman, 1992). The theory conceives human choice behaviour to be predominantly an intuitive process rather than a conscious deliberate one (Van de Kaa, 2010). The central feature of CPT is that it is able to model diminishing sensitivity in humans’ decision-making process (Brandstatter et al., 2002). Prospect theory assumes that choices are evaluated in two steps: an initial phase of editing and a subsequent phase of evaluation (Avineri, 2004). Individuals are risk averse when outcomes are framed as gains and risk seeking when outcomes are framed as losses, relative to the reference point (Tversky and Kahneman, 1992). The evaluation phase is composed of a value function and a probability weighting function (Avineri, 2004). It has been found in numerous experimental data that the weighting function is relatively sensitive to changes in probability near the end points 0 and 1, but relatively insensitive to changes in probability in the middle region. This implies that individuals are risk seeking in small probability prospects and risk averse in large probability prospects (Wakker and Fennema, 1997). Refer to the study by Xu et al. (2011) for a comprehensive summary of CPT parameters’ definitions. Pesendorfer (2006) discussed that one of the main shortcomings of CPT is the dependency of the outcome framing on the reference point. The reference point is often obtained by the researcher from experimental settings and thus essentially unobservable outside the experiment. Researchers have often dealt with this issue by treating the reference point as a free variable chosen to match the observed behaviour. Others have proposed the use of multiple reference points (Senbil and Kitamura, 2004). In regard to travel behaviour studies, Li and Hensher (2011) discussed that using the values estimated by Tversky and Kahneman (1992) for the parameters could lead to biased results. Van de Kaa (2010) suggested that, for the moment, the estimates of the CPT parameters obtained by Tversky and Kahneman (1992) offer the best functional description of choice under uncertainty in a wide variety of travel behaviour context. From recent literature, Avineri and Prashker (2004) study on route choice behaviour found two violation of EUT and suggested CPT to be a better alternative for modelling travellers’ preferences. Avineri (2004) adopted CPT for modelling the route choice behaviour of travellers waiting for a bus given different headway distributions. A study by Gao et al. (2010) investigating travellers’ within-day route choice in a risky network showed that CPT provides a better framework than EUT for a routing policy choice model which captures travellers’ adaption to real-time information. Similarly, Xu et al. (2011) used CPT to develop a general rule for commuters’ risky route choice behaviour which takes into account individual differences. 2.3. Research methodology Subjective judgment has been shown to be present when dealing with route choice (Teodorovic, 1999). The amount of uncertainty in out-of-vehicle times, such as the possibility of delays in connecting vehicles, has been shown to play a key role in transit users’ decision to use transfer routes (Iseki and Taylor, 2009). For the present study, the two models (CPT and fuzzy logic) have been selected to understand travellers’ choice between transfer routes and direct routes given the level of uncertainty in out-of-vehicle times when making transfers. An example of such a choice case for transit users is the PT services offered between North Shore and Auckland CBD in Auckland, New Zealand. A total of 55 bidirectional routes are available with approximately 40% of these routes involving at least one transfer. A study by Ceder et al. (2009) has shown that some transit users prefer the direct routes over the alternative transfer routes with better
connectivity values. The percentage of transit users from the North Shore making a transfer is around 36% (Chowdhury and Ceder, in press). This example illustrates the need for better understanding of the effects uncertainty in out-of-vehicle times during transfers have on transit users’ willingness to use transfer routes. Provided enough demand shifts from the direct routes to the transfer routes will allow the direct routes to be terminated, thereby increasing the efficiency of the PT network and reducing operational cost. 3. Data collection 3.1. Trip attributes As discussed in Section 2.1, several studies have identified personal safety, reliability of connections, and transfer walking and waiting times as the most sensitive indicators for transit users’ perception of out-of-vehicle times when making transfers (Vande Walle and Steenberghen, 2006; Zhou et al., 2007; Muller and Furth, 2009; Kumar et al., 2011; Hadas and Ranjitkar, 2012). For the present study, trip attributes selected to measure transit users’ perception of out-of-vehicle times are reliability of service (delay time), transfer walking time, and transfer waiting time. Transit users’ perception of personal security and comfort were measured for a given transfer waiting time. 3.2. Questionnaire design Travel time has been found to be more significant than transfer waiting and walking time for commuters (Vande Walle and Steenberghen, 2006; Beirao and Sarsfield-Cabral, 2007; Xumei et al., 2011). High quality transfer connections have the potential to save journey time for transit users (Ceder, 2007). Respondents of the survey were presented with a total of 15 hypothetical cases, three cases (A, B, C) for each of the trip attributes. Each case consisted of a direct route (Scenario 3) and two transfer routes (Scenario 1 and 2) with an equal travel time saving of 15–20 min in comparison to the direct route. For the transfer routes, one of the scenarios was designed to be perceived as being ‘‘less conservative’’ (risky route) and the other to be ‘‘more conservative’’ (less risky route). Three cases with varying probabilities of uncertainty in trip attributes were presented to better understand the variations in users’ risk-taking behaviour with variations in risk probabilities. Respondents were instructed to select one of the three scenarios for each case. The cases were designed in accordance with past route choice studies (Avineri, 2004; Avineri and Prashker, 2004; Xu et al., 2011) which considered uncertainty in decision making. Personal safety was defined as the transit users’ probable waiting time to reach a security guard when feeling unsafe. Comfort was defined as the probable waiting time to get an available seat in the station during peak hour periods. Cases for personal safety and comfort were measured under the assumption that the transfer waiting time is 10 min. Respondents were given multi-choice questions to estimate the reference point (Verplanken et al., 1998) of each trip attribute for the CPT model (Van de Kaa, 2010). Fig. 2 illustrates one of the cases presented. 3.3. Survey locations and implementation Britomart Transport Centre and Newmarket Train Station, in Auckland, New Zealand, were chosen as the two survey locations. The objective of the survey was to collect data from stations with varying level of out-of-vehicle facilities, to determine differences in transit users’ perception of out-of-vehicle trip attributes given their current station facilities. Britomart is Auckland CBD’s public transport hub. All buses entering and leaving the Auckland CBD begin and end their trip at Britomart. The hub provides a link between the main bus, train, and ferry services of the Auckland Region
A. Ceder et al. / Transport Policy 27 (2013) 112–122
115
Transfer Waiting Time Case A Scenario 1 15 mins of waiting
Scenario 2
Tick One
20 mins of waiting
- Scenario 1 (more conservative)
20%
30% 80%
9 mins of waiting
- Scenario 2
70%
(less conservative)
- Scenario 3
5 mins of waiting
Fig. 2. Case A for transfer waiting time.
(Auckland Transport, 2012). This allows transit users with an opportunity to make transfers at Britomart. Newmarket Train Station is Auckland city’s second busiest terminal after Britomart and is a key junction in the rail network. The station caters to the Southern and Western lines of the Auckland railway network (Auckland Transport, 2011). Site observations during the morning peak periods revealed the possibility of intermodal (train/bus) transfers due to bus stops with high frequency services (on average every 10 min) located near the train station. Being a transport hub, Britomart provides travellers with more facilities, such as an information centre, ticketing booths, dedicated waiting area, and short intermodal transfer walking times (less than 5 min), compared to Newmarket Train Station. The survey was conducted for 12 working days from 7 am to 10 am to capture commuters. Respondents were invited to participate in the survey while waiting for the arrival of their vehicle.
Table 1 Chi-squared test with df¼ 1.
4. Analysis of results and discussion
p þ ðpi Þ ¼ w þ ðpi þ::: þ pn Þw þ ðpi þ 1 þ . . . þpn Þ;
4.1. Testing for site specific characteristics in data
p ðpj Þ ¼ w ðpm þ::: þ pj Þw ðpm þ. . . þ pj1 Þ;
Prior to modelling the survey data, obtained from the hypothetical scenarios, using CPT and fuzzy logic, the data were assessed for influence of site specific characteristics. Chi-squared test using a 2 2 contingency table was used to verify that the responses were independent of the two stations (Ruxton and Neuhauser, 2010). The results of the analysis illustrated that data from the two stations are independent of the site and can be combined to form one data set. Table 1 gives the chi-squared value and the p-value for each trip attribute. 4.2. Modelling using CPT The responses for the direct route were excluded from modelling as the present study focuses on transit users’ route choice based on the degree of uncertainty in out-of-vehicle times when making transfers. Estimates for the parameters in Eqs. (1)–(6) (a ¼ Z ¼0.88, l ¼2.25, g ¼0.61, d ¼0.69), used to calculate the cumulative prospect values for the transfer route scenarios, were adopted from the study by Tversky and Kahneman (1992). Although the experimental context in which the estimates were derived is different from travel behaviour, these estimates have been successfully used by past studies to explain route choice (Avineri and Prashker, 2003, 2004; Avineri, 2004). ( xa if x Z 0 vðDxi Þ ¼ ð1Þ lðxÞb if x o 0
Trip attribute
Chi-squared
p-Value
Transfer waiting time Transfer walking time Transfer delay time Comfort while waiting Safety while waiting
0.9172 0.1369 0.0176 0.5681 0.8779
0.338 0.711 0.894 0.451 0.348
Table 2 Calculation of weighted probabilities and gain/loss value. Delay Times
Probability
Gain/Loss value
3 min 12 min
0.8 0.2
4.5 4.5
0ri rn
ð2Þ
m r j o 0 ð3Þ
g
g
w þ ðpi Þ ¼ pi =½pi þð1pi Þg 1=g
ð4Þ
w ðpi Þ ¼ pdi =½pdi þ ð1pi Þd 1=d
ð5Þ
uðxi, pi Þ ¼
n X i¼0
vðDxi Þp þ ðpi Þ þ
1 X
vðDxi Þp ðpj Þ
ð6Þ
j ¼ m
The weighted sum approach was undertaken to derive the RP values for each trip attribute from the survey data. Table 3 gives the RP values, the cumulative prospect values and the proportion of respondents willing to use the transfer routes for each trip attribute. The scenarios which were presented as being ‘‘more conservative’’ are highlighted. Cumulative prospect values were calculated using two other RP values ( 75 min for operational attributes and 72 min for comfort and safety) to determine the degree of fluctuation in the values with respect to the respondents’ preference (Xu et al., 2011). An example of the calculation for one of the scenarios is as follows. Case A, Scenario 1: 80% probability of waiting for 3 min when the vehicle is delayed and 20% probability of waiting for 12 min when the vehicle is delayed.
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A. Ceder et al. / Transport Policy 27 (2013) 112–122
Table 3 Prospect values and proportion of responses for each RP. Case A S1 Transfer waiting time Reference Point (min) 4 9 14
Transfer walking time Reference Point (min) 1.5 6.5 11.5
Delay Time Reference Point (min) 2.5 7.5 12.5
Comfort (seating while waiting) Reference Point (min) 2.5 4.5 6.5
Personal Security (at terminal) Reference Point (min) 1 3 5
Case B S2
Cumulative prospect value 11.66 9.97 4.16 2.80 4.27 0.14 1.93 0.12 4.43 Proportion of respondents from survey data 67.7% 23.7% 38.3% Cumulative prospect value 7.01 7.22 5.67 0.09 0.14 0.21 3.72 4.28 4.36 Proportion of respondents from survey data 37.0% 55.0% 32.0% Cumulative prospect value 5.10 6.69 6.25 0.11 0.80 1.12 4.62 4.90 3.11 Proportion of respondents from survey data 22.0% 70.0% 31.7% Cumulative prospect value 14.02 12.54 6.25 10.86 9.04 3.71 7.55 14.48 1.97 Proportion of respondents from survey data 53.3% 38.3% 51.0% Cumulative prospect value 7.57 9.07 7.40 4.54 5.60 4.54 2.79 2.50 2.79 Proportion of respondents from survey data 37.7% 54.3% 24.7%
Table 2 gives the gain and loss values for RP of 7.5 min which was directly derived from the survey data. Step 1: Calculate value functions for gains and losses using Eq. (1).
nðxÞ ¼ xa ¼ ð4:50:88 Þ ¼ 3:757 nðxÞ ¼ lðxÞb ¼ 2:25ðð4:5ÞÞ0:88 ¼ 8:453 Step 2: Calculate the decision weights for gains and losses using Eq. (2)–(5), respectively.
piþ ¼ w þ ð0:80Þw þ ð0Þ ¼ 0:6070 ¼ 0:607 pi ¼ w ð0:20Þw ð0Þ ¼ 0:2570 ¼ 0:257 Step 3: Calculate the prospect gain value, prospect loss value and cumulative prospect value using Eq. (6). n 1 X X vðDxi Þp þ ðpi Þ þ vðDxi Þp ðpj Þ Vðf Þ ¼ i¼0
S1
Case C S2
S1
S2
6.11 0.71 4.55
5.55 0.98 3.67
6.11 0.71 4.55
53.7%
34.3%
56.3%
7.02 0.58 4.55
7.22 1.18 4.55
5.27 1.71 5.47
60.0%
22.7%
69.3%
10.33 1.30 3.64
6.17 0.76 4.12
7.15 0.55 4.49
59.7%
30.7%
61.0%
10.88 5.93 3.27
17.02 14.83 8.23
9.46 5.93 3.27
40.3%
21.0%
71.0%
8.08 3.63 1.45
9.03 6.03 4.19
8.48 5.00 1.84
67.3%
21.0%
71.0%
the cases, the scenario which has the higher cumulative prospect value between the two routes also has the greater observed proportion of respondents willing to use the route. The cumulative prospect values were seen to be highly dependent on the RP. Despite the changes in the prospect values with changing RP values, comparison between the prospect values and the proportions from survey data showed that in majority of the cases, CPT was capable of modelling PT users’ route choice. The two additional reference points supported the prospect values derived using the main RP from the survey data, in most cases. The verification process of the model was undertaken by randomly dividing the data set into two sets: 200 data-points (Set A) and 100 data-points (Set B). This division created a data set, Set A, which was used to develop the CPT model and a separate data set, Set B, which was used to validate the output of the model. Table 4 gives the results of the verification process. The steps of the process are as follows:
j ¼ m
¼ 2:282 þ ð2:172Þ ¼ 0:109
Hence, the cumulative prospect value for Scenario 1 (S1) is equal to 0.11. It is evident from the results that CPT is capable of modelling transit users’ choice between the two transfer routes. For majority of
(1) RP for Set A was determined by using the weighted sum approach and was used to calculate the cumulative prospect values. (2) RP of Set A was used to calculate the cumulative prospect values for Set B. (3) A chi-squared test was used to determine any evidence of significant difference between the proportion of responses for the 200 data points and the 100 data points.
A. Ceder et al. / Transport Policy 27 (2013) 112–122
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Table 4 Cumulative prospect values and proportion of responses from Set A and Set B. S1 Transfer waiting time RP¼ 9 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Transfer walking time RP¼6.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Transfer delay time RP¼ 7.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Comfort RP¼4.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Personal Security RP¼ 3.0 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value
S2
S1
4.27 25.6%
0.14 40.7%
4.27 26.8%
0.14 42.3%
0.14 59.9%
0.21 34.6%
0.14 60.8%
0.21 35.1%
0.80 74.7%
1.12 33.0%
0.80 79.4%
1.12 36.8%
10.86 59.2%
9.04 40.8%
3.71 55.3%
Case A 10.86 55.8% 0.355/0.838
9.04 44.2%
3.71 56.8%
5.60 60.9%
4.54 27.4%
5.60 55.7%
4.54 25.8%
Case A 2.80 74.4% Case A 2.80 73.2% 0.018/0.991
Case A 0.09 39.2% 0.086/0.958
Case A 0.11 20.6% 0.430/0.807
Case A 4.54 44.3% 0.092/0.955
0.71 57.7%
0.98 37.2%
0.58 65.4%
1.18 23.6%
0.58 64.9%
1.18 26.8%
1.30 67.0%
0.76 33.1%
1.30 63.2%
0.76 34.0%
5.93 44.7%
14.83 22.9%
5.93 43.2%
14.83 22.7%
3.63 72.6%
6.03 20.7%
3.63 74.2%
6.03 26.8%
1.71 73.2%
Case C 0.55 66.9% Case C
Case B
0.55 66.0%
Case C
Case B
5.93 77.1% Case C
Case B
5.93 77.3%
Case C
Case B
4.3.1. Fuzzification Fuzzification is the process of defining ‘‘crisp’’ inputs as fuzzy linguistic variables by associating the input with membership values (Hawas, 2011). The membership function expresses the degree that an element of the universal set belongs to the fuzzy set. A fuzzy set can take any value within the closed interval [0,1] (Teodorovic, 1999). The grade of the membership represents the confidence that the member belongs to the fuzzy set; larger values (closer to 1) denote higher degrees of membership (Zhang and Prevedouros, 2011). The shape of the membership function can be triangular, trapezoidal, Gaussian and sigmoidal but other shapes can be considered (Postorino and Versaci, 2008). For the present study, a triangular
1.71 76.4% Case C
Case B
4.3. Analysis using fuzzy logic
0.71 62.8%
Case C
Case B
Results show that, in majority of the cases, the prospect values calculated for Set B using the RP from Set A are able to represent the observed proportions. The chi-squared values attained illustrate that there is no statistical evidence of significant difference between the two data sets for transit users’ preference for the transfer route scenarios. Such finding suggest that once the RP is determined using a survey data set, this value can be used as an estimate to calculate the prospect values for another data set given that the routes’ services are very similar.
0.71 61.9% Case C
Case B
Case A 4.54 39.1%
0.98 38.1%
Case B
Case A
S2
Case C 0.71 59.3%
Case B
Case A 0.11 25.3%
S1
Case B
Case A 0.09 40.1%
S2
5.00 79.3% Case C 5.00 73.2%
shape has been adopted. Each trip attribute (input) and the difference in weighted times of the two transfer route scenarios (WT) (input) were classified into three groups: low, moderate and high. Transit users’ preference for a transfer route scenario (output) was grouped into seven ridership categories: A, B, C, D, E, F, G and H. The ridership categories represent the proportion of transit users willing to use the transfer route. The membership functions had to be fine-tuned through manual calibration. A trial-and-error approach was used to adjust the location of the base and peak (Kikuchi and Miljkovic, 2001). 4.3.2. Fuzzy inference Fuzzy inference is based on a Sugeno inference system, which contains a set of ‘‘If-Then’’ logic statements (Andrade et al., 2006). A typical Sugeno’s fuzzy rule has the form: If x is A and y is B then z where A and B are antecedents and z is the consequent (Postorino and Versaci, 2008). Fuzzy inference handles the degree of approximate match between the input and the antecedent of the rule (Kikuchi and Miljkovic, 2001). The number of fuzzy rules is dependent on the combination of input variables (Zhang and Prevedouros, 2011). The data set was divided into two equal data sets (Set A and B), each with 150 data-points. Each data set was created by randomly selecting 75 data-points from Britomart and 75 data-points from Newmarket. A chi-squared test was undertaken to determine
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Table 5 Chi-squared and p-value for Set A and Set B, df ¼1.
Low
µ 1
Trip Attribute
Chi-squared
p-Value
Transfer waiting time Transfer walking time Transfer delay time Comfort while waiting Safety while waiting
0.866 0.001 0.219 0.003 0.882
0.352 0.969 0.641 0.871 0.347
Moderate
High
5
1
0
10 15 20 25 transfer waiting time (mins)
Low
Moderate
High
µ
The entire fuzzy inference process can be demonstrated with an example. The following scenario is from transfer delay time (DT), Case A.
4.3.3. Defuzzification Defuzzification is the final stage of the fuzzy system. The process involves converting the fuzzy inference outputs into a crisp value. A common approach is the centre of gravity method (Zhang and Prevedouros, 2011). It should be noted that the crisp value, denoted y*, will change continuously with continuous change in the input values (Broekhoven and De Baets, 2006). The expression used to derive the crisp output value y* is shown below (Kikuchi and Miljkovic, 2001; Zhang and Prevedouros, 2011). R yn ¼ mðyÞy dy R mðyÞdy For the example above, the resulting ridership categories from the fuzzy inference were F (0.38) and G (0.62). The centre of gravity method (McGuckin et al., 2005) is illustrated in Fig. 4. The shaded area represents the ridership categories (F and G) for which the CG calculation was undertaken (Zhang and Prevedouros, 2011). The calculation is as follows:
CG ¼
f
Low
1 0.8 0.6 0.4 0.2 0
Moderate
6
1 0.8 0.6 0.4 0.2 0
Moderate
5
Low
5
µ
1 0.8 0.6 0.4 0.2 0
2
Moderate
10
High
15
Low
0
2.4
High
0
Moderate
10
15
G
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
10
Moderate
0.2 0.4 0.6 0.8
2.4 High
1
1.2 1.4
WT of personal safety (mins) High
20
F
High
0.8 1.2 1.62 WT of delay (mins)
Low
µ 1 0.8 0.6 0.4 0.2 0
20
Moderate
0.4
µ
1 0.8 0.6 0.4 0.2 0
Low
1
25
Moderate
1.4 1.8 2.2 2.6
Seating availability (mins) µ
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 WT of walking time (mins)
8 10 12 14 16 18 20 transfer delay (mins)
Low
1 0.8 0.6 0.4 0.2 0
High
High
3
3.4 3.8
WT of seating (mins) E
D
C
B
A
20 30 40 50 60 70 80 90 Proportion of transit users willing to use transfer route (%)
100
Fig. 3. Fuzzy sets for input and output variables.
4.3.4. Verification of model The outputs of the model were verified using Set B. A chi-squared test was used to determine any evidence of significant difference between the proportions of users selecting each scenario given by the fuzzy logic model and the survey data of Set B using Eq. (7).
w2 ¼
X ðOi Ei Þ2 i
Ei
R 16:2
R 23:8 R 26 R 36 R 40 ð0:1y1Þy dy þ 16:2 0:62y dy þ 23:8 ð0:1yþ 3Þy dy þ 26 0:38 y dy þ 36 ð0:1yþ 4Þy dyÞ g R 23:8 R 26 R 36 R 40 R 16:2 f 10 ð0:1y1Þ dy þ 16:2 0:62 dy þ 23:8 ð0:1y þ3Þ dy þ 26 0:38 dy þ 36 ð 0:1y þ 4Þdy g
10
¼ 24.03% for Scenario 1. Of the proportion of transits users who were willing to use transfer routes, 24% preferred Scenario 1 and 76% preferred Scenario 2.
Low
Personal Safety (mins) µ
1.2
0
0
Scenario 1. 80% probability of waiting for 3 min when the vehicle is delayed and 20% probability of waiting for 12 min when the vehicle is delayed. Based on Fig. 3, the input data DT and WT are fuzzified. Based on the fuzzified input data, the corresponding fuzzy rules were used. The max–min composition method is applied for making the fuzzy inference. This procedure is shown in Table 6 (Kikuchi and Miljkovic, 2001; Zhang and Prevedouros, 2011).
1
2 4 6 8 10 12 14 transfer walking time (mins)
4
IF ½trip attribute is ½X TA and ½D weighted time is ½X WT , THEN ridership is ½Y R
0.8
0.5
0
µ
0.4
WT of waiting time (mins)
0
µ
High
0
0
µ
Moderate
1 0.5
0.5
0.5
independence of the two data sets. Table 5 gives the results of the analysis. As can be seen, the two data sets are independent. The rules were derived using Scenario 1 for all cases from Set A. The proportion of respondents who selected the direct route was excluded in development of the fuzzy rules. The model therefore reflects respondents’ preference for the transfer route scenarios, with the output of the fuzzy system being proportion of users choosing Scenario 1 and the remainder is the proportion of users choosing Scenario 2. Each fuzzy rule has two inputs, quality of the trip attribute and the difference in weighted time between two transfer route scenarios. The general format for the fuzzy rules is as follows:
Low
µ
Oi ¼ith observed frequency Ei ¼ ith expected frequency
ð7Þ
A. Ceder et al. / Transport Policy 27 (2013) 112–122
119
Table 6 Fuzzification and fuzzy inference example. Fuzzification of input data for Scenario 1 Input variable DT
Input data 3 min 12 min 1.1
Fuzzy inference for Scenario 1 Input data Rule no. DT 9 Low (1.0) 3 Low (1.0) 1 Moderate (0.88) 2 High (0.12) 8 High (0.12) 7 Moderate (0.88)
WT Low (0.38) Moderate (0.62) Moderate (0.62) Moderate (0.62) Low (0.38) Low (0.38)
Membership value (μ)
WT
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Fuzzified category Low Moderate High Low Moderate
Membership grade 1.0 0.88 0.12 0.38 0.62
Ridership F G G G F F
Max–min composition Min (1.0, 0.38)¼ 0.38 Min (1.0, 0.62) ¼ 0.62 Min (0.88, 0.62) ¼ 0.62 Min (0.12, 0.62) ¼ 0.12 Min (0.12, 0.38) ¼ 0.12 Min (0.88, 0.38) ¼ 0.38 Ridership F: Max (0.38, 0.12, 0.38) ¼0.38 Ridership G: Max (0.62, 0.12,0.62) ¼ 0.62
Table 7 Comparison between model output and survey data. Trip attribute
Case Scenario Fuzzy output Survey data (Set B) (Set B)
Chi-squared/ p-value
Transfer waiting time
A B C
0
10 20 30 24% Proportion of transit users willing to use transfer route (Scenario 1)
40
Transfer walking time
B C
Fig. 4. Defuzzification using centre of gravity method.
The analysis revealed that there is no statistical evidence of significant difference. Table 7 gives the results of the analysis.
A
Transfer delay time
A B C
4.3.5. Final model The final model was developed using the complete survey data set of 300 data-points. Only the fuzzy rules of the system needed to be updated. Table 8 provides a sample of the new 45 fuzzy rules for Scenario 1. The outputs of the fuzzy system for the complete set are compared with the actual responses given by respondents to assess the final model. Table 9 gives the results of the comparison. The analysis revealed no statistical evidence of significant difference between the model outputs and the actual responses attained from the survey data.
Comfort
A B C
Safety
A B C
S1 S2 S1 S2 S1 S2
97 42 56 84 56 83
107 32 54 86 49 90
1.773/0.183
S1 S2 S1 S2 S1 S2
56 84 56 84 28 112
59 81 54 86 33 107
0.191/0.662
S1 S2 S1 S2 S1 S2
28 112 42 97 42 98
37 103 47 92 41 99
1.041/0.307
S1 S2 S1 S2 S1 S2
82 55 68 68 27 110
83 54 73 63 29 108
0.175/0.675
S1 S2 S1 S2 S1 S2
55 82 27 110 27 110
50 87 34 103 29 108
0.071/0.789
4.4. Statistical analysis of transit users’ perception One of the objectives of the present study is to determine transit users’ perception of the trip attributes related to transfers, given the facilities available at their current station during out-ofvehicle times. A two sample t test was conducted for each trip attribute and the results are shown in Table 10. The results show strong statistical evidence (p-value: 0.0091) for the expected waiting time at Britomart to be lower than the expected time at Newmarket. This means that transit users at Newmarket, on average, are willing to wait 1.8 min longer for transfers than users from Britomart. There is statistical
evidence (p-value: 0.024) that Newmarket users expect delay in connection to be 1.0 min more than Britomart users. There is no statistical evidence of significant difference in transit users’ preference for any of the other trip attributes from the two stations. Such findings suggest that a stronger contrast must exist between the operational and physical facilities offered at the terminals to witness a statistically significant influence of the facilities on transit users’ preference.
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Table 8 Fuzzy rules (sample set) for 300 data-points.
Table 10 Two sample t test results.
Scenario 1 Rule no. 1 2 3 4 . . . 37 38 39 40 41 42 43 44 45
IF IF IF IF . . .
[TWT1] [TWT1] [TWT1] [TWT1]
is is is is
[high] and [WT] is [low] THEN [ridership] is [B]. [moderate] and [WT] is [low] THEN ridership is [B]. [low] and [WT] is [low] THEN ridership is [B]. [moderate] and [WT] is [high] THEN ridership is [E].
Personal security IF [safety] is [high] and [WT] is [high] THEN ridership is [E]. IF [safety] is [moderate] and [WT] is [high] THEN ridership is [E]. IF [safety] is [low] and [WT] is [high] THEN ridership is [E]. IF [safety] is [high] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [moderate] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [low] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [high] and [WT] is [low] THEN ridership is [G]. IF [safety] is [moderate] and [WT] is [low] THEN ridership is [G]. IF [safety] is [low] and [WT] is [low] THEN ridership is [G].
Newmarket (mean)
Difference of mean values
pvalue
Transfer waiting time Transfer walking time Transfer delay time Comfort Safety and security
8.3 6.6
10.1 6.9
1.8 0.3
0.0091 0.5146
6.9 4.5 3.1
7.9 4.1 2.8
1.0 0.4 0.3
0.0239 0.2134 0.2258
Scenario
Fuzzy Output
Survey Data
Chi-squared/ p-value
Transfer waiting time
A
S1 S2 S1 S2 S1 S2
192 82 110 166 109 162
203 71 115 161 103 169
0.403/0.525
S1 S2 S1 S2 S1 S2
110 166 110 166 55 221
111 165 96 180 68 208
1.873/0.171
S1 S2 S1 S2 S1 S2
69 207 82 192 83 193
66 210 95 179 92 183
1.084/0.297
S1 S2 S1 S2 S1 S2
165 110 137 137 55 221
160 115 153 121 63 213
2.156/0.142
S1 S2 S1 S2 S1 S2
110 166 83 221 55 221
113 163 74 202 63 213
0.301/0.583
C Transfer walking time
A B C
Transfer delay time
A B C A B C A B C
Trip attribute
Case Scenario Prospect value
Fuzzy output
Survey data
Transfer waiting time
A B C A B
Case
B
Table 11 Comparison between fuzzy system output and CPT.
Transfer walking time
Trip Attribute
Safety
Britomart (mean)
Transfer waiting time (TWT1)
Table 9 Comparison between fuzzy system outputs and survey data.
Comfort
Trip Attribute
C Transfer delay time A B C Comfort
A B C
Safety
A B C
5. Discussion and comparison of CPT and fuzzy logic The main objective of the study is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. Analysis of the survey data revealed that for all trip attributes, except for comfort, transit users’ exhibited greater preference for the scenario that was perceived to be ‘‘more conservative’’ despite a higher probability of shorter out-of-vehicle time in the ‘‘less
S1 S2 S1 S2 S1 S2
2.80 4.27 0.14 0.71 0.98 0.71
192 82 110 166 109 162
203 71 115 161 103 169
S1 S2 S1 S2 S1 S2
0.09 0.14 0.21 0.58 1.18 1.71
110 166 110 166 55 221
111 165 96 180 68 208
S1 S2 S1 S2 S1 S2
0.11 0.80 1.12 1.30 0.76 0.55
69 207 82 192 83 193
66 210 95 179 92 183
S1 S2 S1 S2 S1 S2
10.86 9.04 3.71 5.93 14.83 5.93
165 110 137 137 55 221
160 115 153 121 63 213
S1 S2 S1 S2 S1 S2
4.54 5.60 4.54 3.63 6.03 5.00
110 166 83 221 55 221
113 163 74 202 63 213
conservative’’ scenario. For comfort, transit users’ displayed risktaking characteristics when the waiting time for an available seat was less than 5 min. Such findings support the study by Eboli and Mazzulla (2012) which discussed that although comfort has been identified to be an important factor in service satisfaction, it is less important in the transit user’s decision process than other service factors. Results in Table 3 and Table 9 from the CPT and fuzzy logic model, respectively, illustrate that the two models are capable of representing transit users’ out-of-vehicle behaviour when making transfers. The cumulative prospect values were able to accurately reflect transit users’ preferences for the various transfer route scenarios. It was seen in most of the cases that as the difference between the cumulative prospect values for the two scenarios increased, the difference in the proportion of respondents’ preference also increased, with respondents favouring the higher cumulative prospect value scenario. Analysis also revealed no statistical evidence of significant difference between outputs from the fuzzy system developed and the survey data. Outputs of the fuzzy system were within 5% of the actual
A. Ceder et al. / Transport Policy 27 (2013) 112–122
response. Therefore, while the cumulative prospect value is able to provide an indication of transit users’ preference, fuzzy logic is capable of providing the proportion of transit users preferring a transfer route. Table 11 provides a comparison between the outputs of the fuzzy system, the cumulative prospect values and the actual survey responses for each transfer route scenarios for the complete data set (300 data-points). The cumulative prospect values included in the comparison had RP of 9.0 min for transfer waiting time, RP of 6.5 min for transfer walking time, RP of 7.5 min for transfer delay time, RP of 4.5 min for comfort and RP of 3.0 min for personal safety. As can be seen, both models are capable of representing the survey data. The fuzzy logic model represented the survey data more closely than the CPT model. Therefore, transit users’ out-of-vehicle travel behaviour can be modelled using either CPT or fuzzy logic. It should be noted that the cumulative prospect values are strongly dependent on the reference point and the outputs of the fuzzy system are strongly dependent on the membership functions and fuzzy rules. Development of the fuzzy system was a more iterative process than the one undertaken for CPT.
6. Conclusion It has been well established in literature that issues with the quality of PT services such as reliability issues, lack of information on connections and personal safety at transfer location contributed towards transit users’ feeling anxious (McCord et al., 2006; Cheng, 2010). Such factors were shown to cause out-of-vehicle times to be perceived as being more onerous than in-vehicle time by transit users (Iseki and Taylor, 2009). The present study provides researchers and practitioners with a better understanding of transit users’ decision to use transfer routes based on the degree of uncertainty which exist in out-of-vehicle times. A user preference survey was conducted in Auckland, New Zealand. The survey data was modelled by two commonly used cognitive models: cumulative prospect theory (CPT) and fuzzy logic. Results showed that for all trip attributes, except for comfort, transit users’ exhibited greater preference for the scenario that was perceived to be ‘‘more conservative’’ (less difference in range of out-of-vehicle times) despite a higher probability of shorter out-of-vehicle time in the ‘‘less conservative’’ scenario. Transit users’ perceived the attractive transfer route to be one that has a lower variability in out-of-vehicle times. Such findings suggest that policy makers and PT operators are required to focus on methods of reducing the uncertainty in outof-vehicle times. In other words, increasing the consistency in out-of-vehicle times will increase attractiveness of transfer routes thus enabling a more efficient and integrated PT network to result in enlargement of ridership. Analysis of transit users’ perception of trip attributes, given their current station, revealed statistical evidence for difference in two trip attributes, transfer waiting time and vehicle delay. Transit users who were accustomed to better out-of-vehicle facilities had a lower tolerance for uncertainty in transfer waiting times and delays. A comparison of the two models revealed that transit users’ willingness to use transfer routes based on their perception of outof-vehicle times can be modelled using either CPT or fuzzy logic; both models are capable of representing transit users’ route choice. However, while CPT provides an indication of transit users’ preference for a transfer route, fuzzy logic is capable of providing a closer approximation of the proportion of transit users preferring a transfer route. It should be noted that development of fuzzy system is a more iterative process than the one required for CPT.
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Transport Policy journal homepage: www.elsevier.com/locate/tranpol
Modelling public-transport users’ behaviour at connection point Avishai Ceder n, Subeh Chowdhury, Nima Taghipouran, Jared Olsen Faculty of Engineering, Department of Civil and Environmental Engineering, University of Auckland, New Zealand
a r t i c l e i n f o
a b s t r a c t
Available online 6 March 2013
Out-of-vehicle times were shown to be perceived as being more onerous than in-vehicle time by transit users when making transfers. The present study has two main objectives. The first objective is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. The second objective is to determine the influence of out-of-vehicle facilities, offered by publictransport (PT) operators, on transit users’ perception of trip attributes related to transfers. A user preference survey was conducted at two major PT terminals in Auckland, New Zealand. The survey data was modelled using cumulative prospect theory and fuzzy logic. The results showed that for all trip attributes, except for comfort, transit users’ exhibited risk averse behaviour; users’ revealed greater preference for the transfer route with less uncertainty in the out-of-vehicle times. For comfort, transit users’ displayed risk-taking characteristics when the waiting time for a seat was less than 5 min. Such findings suggest that increasing the consistency in out-of-vehicle times will increase attractiveness of transfer routes thus enabling a more efficient and integrated network of PT routes to result in enlargement of ridership. Policy makers and PT planners must focus on methods of reducing uncertainty in out-of-vehicle times during transfers. Analysis of transit users’ perception of trip attributes, given their current station, revealed statistical evidence of differences for two trip attributes, transfer waiting time and vehicle delay. Such findings indicate that transit users who are accustomed to better out-of-vehicle facilities have a lower tolerance for uncertainty in transfer waiting times and delay times. To the authors’ knowledge, this study provides for the first time in literature a comparison between the two cognitive models. The comparison revealed that CPT and fuzzy logic models are both capable of representing transit users’ decision making process. However, while CPT provides an indication of transit users’ preference for a transfer route, fuzzy logic is capable of providing a closer approximation of the proportion of transit users preferring a transfer route. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Travel behaviour Public transport Transfer Cumulative prospect theory (CPT) Fuzzy logic
1. Introduction and research objective Trip-making behaviour has grown increasingly complex in the past decade (Currie and Delbosc, 2011). Modern day busy lifestyles have compelled travellers to become time-poor. Increase in trip chaining complexity has been identified as a barrier to the use of public transport (PT) (Ampt, 2004; Ye et al., 2007). Due to the dispersed nature of origins and destinations, PT operators are unable to provide direct connections for all origin-destination pairs (Muller and Furth, 2009). The extra effort required in making transfers has deemed them to be a significant contributor to transit users’ journey inconvenience (Hadas and Ranjitkar, 2012). Guo and Wilson (2011) discussed that the quality of transfer connectivity plays an important role in attracting potential transit users and sustaining the satisfaction of existing users. Iseki and Taylor (2009) explains that although out-of-vehicle times have been recognised to be a crucial element in transit users’ satisfaction, there has only been a limited number of studies on out-of-vehicle travel behaviour and the effect of
n
Corresponding author. Tel.: þ64 9 3652807; fax: þ 64 9 3652808. E-mail address: [email protected] (A. Ceder).
0967-070X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tranpol.2013.01.002
out-of-vehicle trip attributes on PT ridership. As a result, there exists a lack in complete understanding of how improvements in outof-vehicle trip attributes affect transit users’ travel behaviour and thus the effect of these improvements on PT ridership (Iseki and Taylor, 2009). The present study has two main objectives. The first objective is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. The second objective is to determine the influence of out-of-vehicle provisions, offered by PT operators, on transit users’ perception of trip attributes related to transfer routes. The study contributes to existing knowledge by providing policy makers with an understanding of the effects perceived quality of out-of-vehicle times have on transit users’ decision to use transfer routes. Such findings will assist policy makers and operators to increase the ridership of transfer routes. A user preference survey was conducted in two transport centres in Auckland, New Zealand. The results of the survey were modelled using the cumulative prospect theory (CPT) and fuzzy logic. Perceived uncertainty associated with transfer connections can cause travellers to avoid transfer routes (Guo and Wilson, 2011). Depiction of travel behaviour under uncertainty calls for adopting cognitive
A. Ceder et al. / Transport Policy 27 (2013) 112–122
2.1. Out-of-vehicle trip attributes Access to, between and among stations and stops has been recognised to be a key element in PT travel. Reducing perceived walking and waiting times for transfers have been shown to substantially increase the attractiveness of PT (Iseki and Taylor, 2009). There is much support for transfer waiting times being valued higher than transfer walking times (Vande Walle and Steenberghen, 2006; Iseki and Taylor, 2009). Transit users’ perceived waiting time has been shown to be more onerous than the actual waiting time (Iseki and Taylor, 2009). Perceived waiting time is dependent on waiting conditions such as personal safety, reliability of connection and comfort (Iseki and Taylor, 2009). Personal safety at terminals has been revealed to be the most important factor in travellers’ decision to use PT (Atkins, 1990; Kumar et al., 2011; Eboli and Mazzulla, 2012). Missed transfers are a major contributor to the reliability issues of PT services (Hadas and Ceder, 2010). Missed connections and delays are shown to cause anxiety to the user (Cheng, 2010). Reducing the uncertainty of waiting times has been shown to improve passenger satisfaction and thus increase ridership (McCord et al., 2006). A high quality information system is an essential factor in increasing ridership by retaining existing riders and attracting potential users (Eboli and Mazzulla, 2012). Studies (Bachok, 2007; Grotenhuis et al., 2007; Molin and Chorus, 2009) have shown that integrated information systems are required to facilitate transfers among urban and interurban multimodal PT networks. Comfort at the transfer terminal has been identified to be a determining factor in transit users’ perceived ease of making a transfer (Guo and Wilson, 2011). A study by Currie and Willis (1998) has shown that commuters place a high value for basic amenities at stations and stops such as seating and shelter. Perceived walking distance and time have also been shown to be substantially longer than actual walking time. Physical conditions such as layout of terminal and sheltered walkways connecting terminals can reduce the perceived walking times (Iseki and Taylor, 2009). Presence of escalators, longer ramps and same-level interchange have been shown to mitigate the penalty imposed for transfer walking times (Guo and Wilson, 2004). Literature (Guo and Wilson, 2010) has indicated that passengers will choose stations which are well connected over stations which provide better physical amenities. 2.2. Cognitive Models When modelling mode and route choice in travel behaviour studies, it has been a common practice to assume that travellers have perfect knowledge about their choices and make rational decisions based on utility maximisation (Xu et al., 2011). Discrete choice models derived using expected utility theory (EUT) and
2.2.1. Fuzzy logic Traditional crisp choice models are not capable of incorporating vagueness in decision making (Ridwan, 2004). Fuzzy logic, first introduced by Zadeh (1965), enables formation of logical statements to compute vagueness. Using the concept of ‘‘approximate reasoning’’, fuzzy logic makes it possible to model imprecision in human reasoning and thus, decision making. Each fuzzy logic system can be divided into three stages: fuzzification, fuzzy inference and defuzzification. Fig. 1 shows the link among the stages and the input and output of each stage. A disadvantage of fuzzy logic is the task of fine-tuning the membership functions and adjusting the fuzzy rules. Construction of the membership functions and the fuzzy rules is a trial-and-error process until an appropriate fit of the input–output set is achieved. This process can be simplified by use of learning algorithms in programs such as MatLab for tuning (Postorino and Versaci, 2008). It is evident from a number of route and mode choice studies that fuzzy logic is capable of modelling ambiguity in perception and appraisal of trip attributes (Murugesan and Rama Moorthy, 1998; Teodorovic, 1999). In more recent studies, Kikuchi and Miljkovic (2001) used fuzzy logic to predict bus ridership at individual stops based on the factors such as transit service quality and condition of bus stop. Andrade et al. (2006) proposed a hybrid model (multinomial logit model with neuro-fuzzy utility functions) to determine mode choice between PT modes and cars. Manju et al. (2008) conducted a study on commuters’ PT route choice using fuzzy logic, which allowed transit users’ preference for trip attributes to be taken into account. Postorino and Versaci (2008) used an adaptive neuro-fuzzy inference system to investigate the decision criteria followed by users when they select a transport mode. Fuzzy Inference
Input linguistic variables
Linguistic terms Numerical Values
Outputlinguistic variables
Defuzzification
2. Literature review and research methodology
random utility theory (RUT) have been frequently adopted to analyse choice in travel behaviour studies (Liu et al., 1997; O’Fallon et al., 2004; Ridwan, 2004; Postorino and Versaci, 2008). An increasing number of route choice studies have been challenging the assumption of absolute rationality of travellers by showing evidence of violations of EUT (Avineri and Prashker, 2004; Xu et al., 2011). Statistical models using the assumption of utility maximisation overlook the fact that humans’ decision-making process is approximate rather than precise (Andrade et al., 2006; Manju et al., 2008). From literature on route and mode choice behaviour both CPT and fuzzy logic were found to be well established cognitive models which provide a more realistic representation of travellers’ decision in travel conditions with uncertainty. CPT is the most popular non-EU model (Gao et al., 2010). Van de Kaa (2010) provides a comprehensive review on the successful adoption of CPT in travel choice studies. Teodorovic (1999) gives a summary of transport studies which have implemented fuzzy logic with success. Following Sections 2.21 and 2.2.2 discuss fuzzy logic and CPT, respectively, in more detail.
Fuzzification
models such as CPT to capture the mental representation of uncertainty in decision making (Schwanen and Ettema, 2009; Van de Kaa, 2010). A number of route and mode choice studies have shown that fuzzy approach is also capable of modelling the imprecision in transit users’ perception of trip attributes and thus their choice of route (Teodorovic, 1999; Ridwan, 2004). To the authors’ knowledge, for the first time in literature, the present study provides a comparison of the two commonly used cognitive models for travel behaviour. Hereafter, Section 2 provides literature review, Section 3 is data collection, Section 4 gives the two modelling procedures and results, Section 5 provides a discussion of the comparison between the results from CPT and fuzzy logic, and lastly, Section 6 is conclusion.
113
InputNumerical Values
OutputNumerical Values
Fig. 1. Fuzzy Logic Systems.
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2.2.2. Cumulative prospect theory In 1992, Tversky and Kahneman introduced CPT, an extension of the prospect theory (Tversky and Kahneman, 1992). The theory conceives human choice behaviour to be predominantly an intuitive process rather than a conscious deliberate one (Van de Kaa, 2010). The central feature of CPT is that it is able to model diminishing sensitivity in humans’ decision-making process (Brandstatter et al., 2002). Prospect theory assumes that choices are evaluated in two steps: an initial phase of editing and a subsequent phase of evaluation (Avineri, 2004). Individuals are risk averse when outcomes are framed as gains and risk seeking when outcomes are framed as losses, relative to the reference point (Tversky and Kahneman, 1992). The evaluation phase is composed of a value function and a probability weighting function (Avineri, 2004). It has been found in numerous experimental data that the weighting function is relatively sensitive to changes in probability near the end points 0 and 1, but relatively insensitive to changes in probability in the middle region. This implies that individuals are risk seeking in small probability prospects and risk averse in large probability prospects (Wakker and Fennema, 1997). Refer to the study by Xu et al. (2011) for a comprehensive summary of CPT parameters’ definitions. Pesendorfer (2006) discussed that one of the main shortcomings of CPT is the dependency of the outcome framing on the reference point. The reference point is often obtained by the researcher from experimental settings and thus essentially unobservable outside the experiment. Researchers have often dealt with this issue by treating the reference point as a free variable chosen to match the observed behaviour. Others have proposed the use of multiple reference points (Senbil and Kitamura, 2004). In regard to travel behaviour studies, Li and Hensher (2011) discussed that using the values estimated by Tversky and Kahneman (1992) for the parameters could lead to biased results. Van de Kaa (2010) suggested that, for the moment, the estimates of the CPT parameters obtained by Tversky and Kahneman (1992) offer the best functional description of choice under uncertainty in a wide variety of travel behaviour context. From recent literature, Avineri and Prashker (2004) study on route choice behaviour found two violation of EUT and suggested CPT to be a better alternative for modelling travellers’ preferences. Avineri (2004) adopted CPT for modelling the route choice behaviour of travellers waiting for a bus given different headway distributions. A study by Gao et al. (2010) investigating travellers’ within-day route choice in a risky network showed that CPT provides a better framework than EUT for a routing policy choice model which captures travellers’ adaption to real-time information. Similarly, Xu et al. (2011) used CPT to develop a general rule for commuters’ risky route choice behaviour which takes into account individual differences. 2.3. Research methodology Subjective judgment has been shown to be present when dealing with route choice (Teodorovic, 1999). The amount of uncertainty in out-of-vehicle times, such as the possibility of delays in connecting vehicles, has been shown to play a key role in transit users’ decision to use transfer routes (Iseki and Taylor, 2009). For the present study, the two models (CPT and fuzzy logic) have been selected to understand travellers’ choice between transfer routes and direct routes given the level of uncertainty in out-of-vehicle times when making transfers. An example of such a choice case for transit users is the PT services offered between North Shore and Auckland CBD in Auckland, New Zealand. A total of 55 bidirectional routes are available with approximately 40% of these routes involving at least one transfer. A study by Ceder et al. (2009) has shown that some transit users prefer the direct routes over the alternative transfer routes with better
connectivity values. The percentage of transit users from the North Shore making a transfer is around 36% (Chowdhury and Ceder, in press). This example illustrates the need for better understanding of the effects uncertainty in out-of-vehicle times during transfers have on transit users’ willingness to use transfer routes. Provided enough demand shifts from the direct routes to the transfer routes will allow the direct routes to be terminated, thereby increasing the efficiency of the PT network and reducing operational cost. 3. Data collection 3.1. Trip attributes As discussed in Section 2.1, several studies have identified personal safety, reliability of connections, and transfer walking and waiting times as the most sensitive indicators for transit users’ perception of out-of-vehicle times when making transfers (Vande Walle and Steenberghen, 2006; Zhou et al., 2007; Muller and Furth, 2009; Kumar et al., 2011; Hadas and Ranjitkar, 2012). For the present study, trip attributes selected to measure transit users’ perception of out-of-vehicle times are reliability of service (delay time), transfer walking time, and transfer waiting time. Transit users’ perception of personal security and comfort were measured for a given transfer waiting time. 3.2. Questionnaire design Travel time has been found to be more significant than transfer waiting and walking time for commuters (Vande Walle and Steenberghen, 2006; Beirao and Sarsfield-Cabral, 2007; Xumei et al., 2011). High quality transfer connections have the potential to save journey time for transit users (Ceder, 2007). Respondents of the survey were presented with a total of 15 hypothetical cases, three cases (A, B, C) for each of the trip attributes. Each case consisted of a direct route (Scenario 3) and two transfer routes (Scenario 1 and 2) with an equal travel time saving of 15–20 min in comparison to the direct route. For the transfer routes, one of the scenarios was designed to be perceived as being ‘‘less conservative’’ (risky route) and the other to be ‘‘more conservative’’ (less risky route). Three cases with varying probabilities of uncertainty in trip attributes were presented to better understand the variations in users’ risk-taking behaviour with variations in risk probabilities. Respondents were instructed to select one of the three scenarios for each case. The cases were designed in accordance with past route choice studies (Avineri, 2004; Avineri and Prashker, 2004; Xu et al., 2011) which considered uncertainty in decision making. Personal safety was defined as the transit users’ probable waiting time to reach a security guard when feeling unsafe. Comfort was defined as the probable waiting time to get an available seat in the station during peak hour periods. Cases for personal safety and comfort were measured under the assumption that the transfer waiting time is 10 min. Respondents were given multi-choice questions to estimate the reference point (Verplanken et al., 1998) of each trip attribute for the CPT model (Van de Kaa, 2010). Fig. 2 illustrates one of the cases presented. 3.3. Survey locations and implementation Britomart Transport Centre and Newmarket Train Station, in Auckland, New Zealand, were chosen as the two survey locations. The objective of the survey was to collect data from stations with varying level of out-of-vehicle facilities, to determine differences in transit users’ perception of out-of-vehicle trip attributes given their current station facilities. Britomart is Auckland CBD’s public transport hub. All buses entering and leaving the Auckland CBD begin and end their trip at Britomart. The hub provides a link between the main bus, train, and ferry services of the Auckland Region
A. Ceder et al. / Transport Policy 27 (2013) 112–122
115
Transfer Waiting Time Case A Scenario 1 15 mins of waiting
Scenario 2
Tick One
20 mins of waiting
- Scenario 1 (more conservative)
20%
30% 80%
9 mins of waiting
- Scenario 2
70%
(less conservative)
- Scenario 3
5 mins of waiting
Fig. 2. Case A for transfer waiting time.
(Auckland Transport, 2012). This allows transit users with an opportunity to make transfers at Britomart. Newmarket Train Station is Auckland city’s second busiest terminal after Britomart and is a key junction in the rail network. The station caters to the Southern and Western lines of the Auckland railway network (Auckland Transport, 2011). Site observations during the morning peak periods revealed the possibility of intermodal (train/bus) transfers due to bus stops with high frequency services (on average every 10 min) located near the train station. Being a transport hub, Britomart provides travellers with more facilities, such as an information centre, ticketing booths, dedicated waiting area, and short intermodal transfer walking times (less than 5 min), compared to Newmarket Train Station. The survey was conducted for 12 working days from 7 am to 10 am to capture commuters. Respondents were invited to participate in the survey while waiting for the arrival of their vehicle.
Table 1 Chi-squared test with df¼ 1.
4. Analysis of results and discussion
p þ ðpi Þ ¼ w þ ðpi þ::: þ pn Þw þ ðpi þ 1 þ . . . þpn Þ;
4.1. Testing for site specific characteristics in data
p ðpj Þ ¼ w ðpm þ::: þ pj Þw ðpm þ. . . þ pj1 Þ;
Prior to modelling the survey data, obtained from the hypothetical scenarios, using CPT and fuzzy logic, the data were assessed for influence of site specific characteristics. Chi-squared test using a 2 2 contingency table was used to verify that the responses were independent of the two stations (Ruxton and Neuhauser, 2010). The results of the analysis illustrated that data from the two stations are independent of the site and can be combined to form one data set. Table 1 gives the chi-squared value and the p-value for each trip attribute. 4.2. Modelling using CPT The responses for the direct route were excluded from modelling as the present study focuses on transit users’ route choice based on the degree of uncertainty in out-of-vehicle times when making transfers. Estimates for the parameters in Eqs. (1)–(6) (a ¼ Z ¼0.88, l ¼2.25, g ¼0.61, d ¼0.69), used to calculate the cumulative prospect values for the transfer route scenarios, were adopted from the study by Tversky and Kahneman (1992). Although the experimental context in which the estimates were derived is different from travel behaviour, these estimates have been successfully used by past studies to explain route choice (Avineri and Prashker, 2003, 2004; Avineri, 2004). ( xa if x Z 0 vðDxi Þ ¼ ð1Þ lðxÞb if x o 0
Trip attribute
Chi-squared
p-Value
Transfer waiting time Transfer walking time Transfer delay time Comfort while waiting Safety while waiting
0.9172 0.1369 0.0176 0.5681 0.8779
0.338 0.711 0.894 0.451 0.348
Table 2 Calculation of weighted probabilities and gain/loss value. Delay Times
Probability
Gain/Loss value
3 min 12 min
0.8 0.2
4.5 4.5
0ri rn
ð2Þ
m r j o 0 ð3Þ
g
g
w þ ðpi Þ ¼ pi =½pi þð1pi Þg 1=g
ð4Þ
w ðpi Þ ¼ pdi =½pdi þ ð1pi Þd 1=d
ð5Þ
uðxi, pi Þ ¼
n X i¼0
vðDxi Þp þ ðpi Þ þ
1 X
vðDxi Þp ðpj Þ
ð6Þ
j ¼ m
The weighted sum approach was undertaken to derive the RP values for each trip attribute from the survey data. Table 3 gives the RP values, the cumulative prospect values and the proportion of respondents willing to use the transfer routes for each trip attribute. The scenarios which were presented as being ‘‘more conservative’’ are highlighted. Cumulative prospect values were calculated using two other RP values ( 75 min for operational attributes and 72 min for comfort and safety) to determine the degree of fluctuation in the values with respect to the respondents’ preference (Xu et al., 2011). An example of the calculation for one of the scenarios is as follows. Case A, Scenario 1: 80% probability of waiting for 3 min when the vehicle is delayed and 20% probability of waiting for 12 min when the vehicle is delayed.
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Table 3 Prospect values and proportion of responses for each RP. Case A S1 Transfer waiting time Reference Point (min) 4 9 14
Transfer walking time Reference Point (min) 1.5 6.5 11.5
Delay Time Reference Point (min) 2.5 7.5 12.5
Comfort (seating while waiting) Reference Point (min) 2.5 4.5 6.5
Personal Security (at terminal) Reference Point (min) 1 3 5
Case B S2
Cumulative prospect value 11.66 9.97 4.16 2.80 4.27 0.14 1.93 0.12 4.43 Proportion of respondents from survey data 67.7% 23.7% 38.3% Cumulative prospect value 7.01 7.22 5.67 0.09 0.14 0.21 3.72 4.28 4.36 Proportion of respondents from survey data 37.0% 55.0% 32.0% Cumulative prospect value 5.10 6.69 6.25 0.11 0.80 1.12 4.62 4.90 3.11 Proportion of respondents from survey data 22.0% 70.0% 31.7% Cumulative prospect value 14.02 12.54 6.25 10.86 9.04 3.71 7.55 14.48 1.97 Proportion of respondents from survey data 53.3% 38.3% 51.0% Cumulative prospect value 7.57 9.07 7.40 4.54 5.60 4.54 2.79 2.50 2.79 Proportion of respondents from survey data 37.7% 54.3% 24.7%
Table 2 gives the gain and loss values for RP of 7.5 min which was directly derived from the survey data. Step 1: Calculate value functions for gains and losses using Eq. (1).
nðxÞ ¼ xa ¼ ð4:50:88 Þ ¼ 3:757 nðxÞ ¼ lðxÞb ¼ 2:25ðð4:5ÞÞ0:88 ¼ 8:453 Step 2: Calculate the decision weights for gains and losses using Eq. (2)–(5), respectively.
piþ ¼ w þ ð0:80Þw þ ð0Þ ¼ 0:6070 ¼ 0:607 pi ¼ w ð0:20Þw ð0Þ ¼ 0:2570 ¼ 0:257 Step 3: Calculate the prospect gain value, prospect loss value and cumulative prospect value using Eq. (6). n 1 X X vðDxi Þp þ ðpi Þ þ vðDxi Þp ðpj Þ Vðf Þ ¼ i¼0
S1
Case C S2
S1
S2
6.11 0.71 4.55
5.55 0.98 3.67
6.11 0.71 4.55
53.7%
34.3%
56.3%
7.02 0.58 4.55
7.22 1.18 4.55
5.27 1.71 5.47
60.0%
22.7%
69.3%
10.33 1.30 3.64
6.17 0.76 4.12
7.15 0.55 4.49
59.7%
30.7%
61.0%
10.88 5.93 3.27
17.02 14.83 8.23
9.46 5.93 3.27
40.3%
21.0%
71.0%
8.08 3.63 1.45
9.03 6.03 4.19
8.48 5.00 1.84
67.3%
21.0%
71.0%
the cases, the scenario which has the higher cumulative prospect value between the two routes also has the greater observed proportion of respondents willing to use the route. The cumulative prospect values were seen to be highly dependent on the RP. Despite the changes in the prospect values with changing RP values, comparison between the prospect values and the proportions from survey data showed that in majority of the cases, CPT was capable of modelling PT users’ route choice. The two additional reference points supported the prospect values derived using the main RP from the survey data, in most cases. The verification process of the model was undertaken by randomly dividing the data set into two sets: 200 data-points (Set A) and 100 data-points (Set B). This division created a data set, Set A, which was used to develop the CPT model and a separate data set, Set B, which was used to validate the output of the model. Table 4 gives the results of the verification process. The steps of the process are as follows:
j ¼ m
¼ 2:282 þ ð2:172Þ ¼ 0:109
Hence, the cumulative prospect value for Scenario 1 (S1) is equal to 0.11. It is evident from the results that CPT is capable of modelling transit users’ choice between the two transfer routes. For majority of
(1) RP for Set A was determined by using the weighted sum approach and was used to calculate the cumulative prospect values. (2) RP of Set A was used to calculate the cumulative prospect values for Set B. (3) A chi-squared test was used to determine any evidence of significant difference between the proportion of responses for the 200 data points and the 100 data points.
A. Ceder et al. / Transport Policy 27 (2013) 112–122
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Table 4 Cumulative prospect values and proportion of responses from Set A and Set B. S1 Transfer waiting time RP¼ 9 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Transfer walking time RP¼6.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Transfer delay time RP¼ 7.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Comfort RP¼4.5 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value Personal Security RP¼ 3.0 min Set A Prospect value Proportion Set B Prospect value Proportion Chi-squared/ p-value
S2
S1
4.27 25.6%
0.14 40.7%
4.27 26.8%
0.14 42.3%
0.14 59.9%
0.21 34.6%
0.14 60.8%
0.21 35.1%
0.80 74.7%
1.12 33.0%
0.80 79.4%
1.12 36.8%
10.86 59.2%
9.04 40.8%
3.71 55.3%
Case A 10.86 55.8% 0.355/0.838
9.04 44.2%
3.71 56.8%
5.60 60.9%
4.54 27.4%
5.60 55.7%
4.54 25.8%
Case A 2.80 74.4% Case A 2.80 73.2% 0.018/0.991
Case A 0.09 39.2% 0.086/0.958
Case A 0.11 20.6% 0.430/0.807
Case A 4.54 44.3% 0.092/0.955
0.71 57.7%
0.98 37.2%
0.58 65.4%
1.18 23.6%
0.58 64.9%
1.18 26.8%
1.30 67.0%
0.76 33.1%
1.30 63.2%
0.76 34.0%
5.93 44.7%
14.83 22.9%
5.93 43.2%
14.83 22.7%
3.63 72.6%
6.03 20.7%
3.63 74.2%
6.03 26.8%
1.71 73.2%
Case C 0.55 66.9% Case C
Case B
0.55 66.0%
Case C
Case B
5.93 77.1% Case C
Case B
5.93 77.3%
Case C
Case B
4.3.1. Fuzzification Fuzzification is the process of defining ‘‘crisp’’ inputs as fuzzy linguistic variables by associating the input with membership values (Hawas, 2011). The membership function expresses the degree that an element of the universal set belongs to the fuzzy set. A fuzzy set can take any value within the closed interval [0,1] (Teodorovic, 1999). The grade of the membership represents the confidence that the member belongs to the fuzzy set; larger values (closer to 1) denote higher degrees of membership (Zhang and Prevedouros, 2011). The shape of the membership function can be triangular, trapezoidal, Gaussian and sigmoidal but other shapes can be considered (Postorino and Versaci, 2008). For the present study, a triangular
1.71 76.4% Case C
Case B
4.3. Analysis using fuzzy logic
0.71 62.8%
Case C
Case B
Results show that, in majority of the cases, the prospect values calculated for Set B using the RP from Set A are able to represent the observed proportions. The chi-squared values attained illustrate that there is no statistical evidence of significant difference between the two data sets for transit users’ preference for the transfer route scenarios. Such finding suggest that once the RP is determined using a survey data set, this value can be used as an estimate to calculate the prospect values for another data set given that the routes’ services are very similar.
0.71 61.9% Case C
Case B
Case A 4.54 39.1%
0.98 38.1%
Case B
Case A
S2
Case C 0.71 59.3%
Case B
Case A 0.11 25.3%
S1
Case B
Case A 0.09 40.1%
S2
5.00 79.3% Case C 5.00 73.2%
shape has been adopted. Each trip attribute (input) and the difference in weighted times of the two transfer route scenarios (WT) (input) were classified into three groups: low, moderate and high. Transit users’ preference for a transfer route scenario (output) was grouped into seven ridership categories: A, B, C, D, E, F, G and H. The ridership categories represent the proportion of transit users willing to use the transfer route. The membership functions had to be fine-tuned through manual calibration. A trial-and-error approach was used to adjust the location of the base and peak (Kikuchi and Miljkovic, 2001). 4.3.2. Fuzzy inference Fuzzy inference is based on a Sugeno inference system, which contains a set of ‘‘If-Then’’ logic statements (Andrade et al., 2006). A typical Sugeno’s fuzzy rule has the form: If x is A and y is B then z where A and B are antecedents and z is the consequent (Postorino and Versaci, 2008). Fuzzy inference handles the degree of approximate match between the input and the antecedent of the rule (Kikuchi and Miljkovic, 2001). The number of fuzzy rules is dependent on the combination of input variables (Zhang and Prevedouros, 2011). The data set was divided into two equal data sets (Set A and B), each with 150 data-points. Each data set was created by randomly selecting 75 data-points from Britomart and 75 data-points from Newmarket. A chi-squared test was undertaken to determine
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Table 5 Chi-squared and p-value for Set A and Set B, df ¼1.
Low
µ 1
Trip Attribute
Chi-squared
p-Value
Transfer waiting time Transfer walking time Transfer delay time Comfort while waiting Safety while waiting
0.866 0.001 0.219 0.003 0.882
0.352 0.969 0.641 0.871 0.347
Moderate
High
5
1
0
10 15 20 25 transfer waiting time (mins)
Low
Moderate
High
µ
The entire fuzzy inference process can be demonstrated with an example. The following scenario is from transfer delay time (DT), Case A.
4.3.3. Defuzzification Defuzzification is the final stage of the fuzzy system. The process involves converting the fuzzy inference outputs into a crisp value. A common approach is the centre of gravity method (Zhang and Prevedouros, 2011). It should be noted that the crisp value, denoted y*, will change continuously with continuous change in the input values (Broekhoven and De Baets, 2006). The expression used to derive the crisp output value y* is shown below (Kikuchi and Miljkovic, 2001; Zhang and Prevedouros, 2011). R yn ¼ mðyÞy dy R mðyÞdy For the example above, the resulting ridership categories from the fuzzy inference were F (0.38) and G (0.62). The centre of gravity method (McGuckin et al., 2005) is illustrated in Fig. 4. The shaded area represents the ridership categories (F and G) for which the CG calculation was undertaken (Zhang and Prevedouros, 2011). The calculation is as follows:
CG ¼
f
Low
1 0.8 0.6 0.4 0.2 0
Moderate
6
1 0.8 0.6 0.4 0.2 0
Moderate
5
Low
5
µ
1 0.8 0.6 0.4 0.2 0
2
Moderate
10
High
15
Low
0
2.4
High
0
Moderate
10
15
G
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
10
Moderate
0.2 0.4 0.6 0.8
2.4 High
1
1.2 1.4
WT of personal safety (mins) High
20
F
High
0.8 1.2 1.62 WT of delay (mins)
Low
µ 1 0.8 0.6 0.4 0.2 0
20
Moderate
0.4
µ
1 0.8 0.6 0.4 0.2 0
Low
1
25
Moderate
1.4 1.8 2.2 2.6
Seating availability (mins) µ
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 WT of walking time (mins)
8 10 12 14 16 18 20 transfer delay (mins)
Low
1 0.8 0.6 0.4 0.2 0
High
High
3
3.4 3.8
WT of seating (mins) E
D
C
B
A
20 30 40 50 60 70 80 90 Proportion of transit users willing to use transfer route (%)
100
Fig. 3. Fuzzy sets for input and output variables.
4.3.4. Verification of model The outputs of the model were verified using Set B. A chi-squared test was used to determine any evidence of significant difference between the proportions of users selecting each scenario given by the fuzzy logic model and the survey data of Set B using Eq. (7).
w2 ¼
X ðOi Ei Þ2 i
Ei
R 16:2
R 23:8 R 26 R 36 R 40 ð0:1y1Þy dy þ 16:2 0:62y dy þ 23:8 ð0:1yþ 3Þy dy þ 26 0:38 y dy þ 36 ð0:1yþ 4Þy dyÞ g R 23:8 R 26 R 36 R 40 R 16:2 f 10 ð0:1y1Þ dy þ 16:2 0:62 dy þ 23:8 ð0:1y þ3Þ dy þ 26 0:38 dy þ 36 ð 0:1y þ 4Þdy g
10
¼ 24.03% for Scenario 1. Of the proportion of transits users who were willing to use transfer routes, 24% preferred Scenario 1 and 76% preferred Scenario 2.
Low
Personal Safety (mins) µ
1.2
0
0
Scenario 1. 80% probability of waiting for 3 min when the vehicle is delayed and 20% probability of waiting for 12 min when the vehicle is delayed. Based on Fig. 3, the input data DT and WT are fuzzified. Based on the fuzzified input data, the corresponding fuzzy rules were used. The max–min composition method is applied for making the fuzzy inference. This procedure is shown in Table 6 (Kikuchi and Miljkovic, 2001; Zhang and Prevedouros, 2011).
1
2 4 6 8 10 12 14 transfer walking time (mins)
4
IF ½trip attribute is ½X TA and ½D weighted time is ½X WT , THEN ridership is ½Y R
0.8
0.5
0
µ
0.4
WT of waiting time (mins)
0
µ
High
0
0
µ
Moderate
1 0.5
0.5
0.5
independence of the two data sets. Table 5 gives the results of the analysis. As can be seen, the two data sets are independent. The rules were derived using Scenario 1 for all cases from Set A. The proportion of respondents who selected the direct route was excluded in development of the fuzzy rules. The model therefore reflects respondents’ preference for the transfer route scenarios, with the output of the fuzzy system being proportion of users choosing Scenario 1 and the remainder is the proportion of users choosing Scenario 2. Each fuzzy rule has two inputs, quality of the trip attribute and the difference in weighted time between two transfer route scenarios. The general format for the fuzzy rules is as follows:
Low
µ
Oi ¼ith observed frequency Ei ¼ ith expected frequency
ð7Þ
A. Ceder et al. / Transport Policy 27 (2013) 112–122
119
Table 6 Fuzzification and fuzzy inference example. Fuzzification of input data for Scenario 1 Input variable DT
Input data 3 min 12 min 1.1
Fuzzy inference for Scenario 1 Input data Rule no. DT 9 Low (1.0) 3 Low (1.0) 1 Moderate (0.88) 2 High (0.12) 8 High (0.12) 7 Moderate (0.88)
WT Low (0.38) Moderate (0.62) Moderate (0.62) Moderate (0.62) Low (0.38) Low (0.38)
Membership value (μ)
WT
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Fuzzified category Low Moderate High Low Moderate
Membership grade 1.0 0.88 0.12 0.38 0.62
Ridership F G G G F F
Max–min composition Min (1.0, 0.38)¼ 0.38 Min (1.0, 0.62) ¼ 0.62 Min (0.88, 0.62) ¼ 0.62 Min (0.12, 0.62) ¼ 0.12 Min (0.12, 0.38) ¼ 0.12 Min (0.88, 0.38) ¼ 0.38 Ridership F: Max (0.38, 0.12, 0.38) ¼0.38 Ridership G: Max (0.62, 0.12,0.62) ¼ 0.62
Table 7 Comparison between model output and survey data. Trip attribute
Case Scenario Fuzzy output Survey data (Set B) (Set B)
Chi-squared/ p-value
Transfer waiting time
A B C
0
10 20 30 24% Proportion of transit users willing to use transfer route (Scenario 1)
40
Transfer walking time
B C
Fig. 4. Defuzzification using centre of gravity method.
The analysis revealed that there is no statistical evidence of significant difference. Table 7 gives the results of the analysis.
A
Transfer delay time
A B C
4.3.5. Final model The final model was developed using the complete survey data set of 300 data-points. Only the fuzzy rules of the system needed to be updated. Table 8 provides a sample of the new 45 fuzzy rules for Scenario 1. The outputs of the fuzzy system for the complete set are compared with the actual responses given by respondents to assess the final model. Table 9 gives the results of the comparison. The analysis revealed no statistical evidence of significant difference between the model outputs and the actual responses attained from the survey data.
Comfort
A B C
Safety
A B C
S1 S2 S1 S2 S1 S2
97 42 56 84 56 83
107 32 54 86 49 90
1.773/0.183
S1 S2 S1 S2 S1 S2
56 84 56 84 28 112
59 81 54 86 33 107
0.191/0.662
S1 S2 S1 S2 S1 S2
28 112 42 97 42 98
37 103 47 92 41 99
1.041/0.307
S1 S2 S1 S2 S1 S2
82 55 68 68 27 110
83 54 73 63 29 108
0.175/0.675
S1 S2 S1 S2 S1 S2
55 82 27 110 27 110
50 87 34 103 29 108
0.071/0.789
4.4. Statistical analysis of transit users’ perception One of the objectives of the present study is to determine transit users’ perception of the trip attributes related to transfers, given the facilities available at their current station during out-ofvehicle times. A two sample t test was conducted for each trip attribute and the results are shown in Table 10. The results show strong statistical evidence (p-value: 0.0091) for the expected waiting time at Britomart to be lower than the expected time at Newmarket. This means that transit users at Newmarket, on average, are willing to wait 1.8 min longer for transfers than users from Britomart. There is statistical
evidence (p-value: 0.024) that Newmarket users expect delay in connection to be 1.0 min more than Britomart users. There is no statistical evidence of significant difference in transit users’ preference for any of the other trip attributes from the two stations. Such findings suggest that a stronger contrast must exist between the operational and physical facilities offered at the terminals to witness a statistically significant influence of the facilities on transit users’ preference.
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Table 8 Fuzzy rules (sample set) for 300 data-points.
Table 10 Two sample t test results.
Scenario 1 Rule no. 1 2 3 4 . . . 37 38 39 40 41 42 43 44 45
IF IF IF IF . . .
[TWT1] [TWT1] [TWT1] [TWT1]
is is is is
[high] and [WT] is [low] THEN [ridership] is [B]. [moderate] and [WT] is [low] THEN ridership is [B]. [low] and [WT] is [low] THEN ridership is [B]. [moderate] and [WT] is [high] THEN ridership is [E].
Personal security IF [safety] is [high] and [WT] is [high] THEN ridership is [E]. IF [safety] is [moderate] and [WT] is [high] THEN ridership is [E]. IF [safety] is [low] and [WT] is [high] THEN ridership is [E]. IF [safety] is [high] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [moderate] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [low] and [WT] is [moderate] THEN ridership is [F]. IF [safety] is [high] and [WT] is [low] THEN ridership is [G]. IF [safety] is [moderate] and [WT] is [low] THEN ridership is [G]. IF [safety] is [low] and [WT] is [low] THEN ridership is [G].
Newmarket (mean)
Difference of mean values
pvalue
Transfer waiting time Transfer walking time Transfer delay time Comfort Safety and security
8.3 6.6
10.1 6.9
1.8 0.3
0.0091 0.5146
6.9 4.5 3.1
7.9 4.1 2.8
1.0 0.4 0.3
0.0239 0.2134 0.2258
Scenario
Fuzzy Output
Survey Data
Chi-squared/ p-value
Transfer waiting time
A
S1 S2 S1 S2 S1 S2
192 82 110 166 109 162
203 71 115 161 103 169
0.403/0.525
S1 S2 S1 S2 S1 S2
110 166 110 166 55 221
111 165 96 180 68 208
1.873/0.171
S1 S2 S1 S2 S1 S2
69 207 82 192 83 193
66 210 95 179 92 183
1.084/0.297
S1 S2 S1 S2 S1 S2
165 110 137 137 55 221
160 115 153 121 63 213
2.156/0.142
S1 S2 S1 S2 S1 S2
110 166 83 221 55 221
113 163 74 202 63 213
0.301/0.583
C Transfer walking time
A B C
Transfer delay time
A B C A B C A B C
Trip attribute
Case Scenario Prospect value
Fuzzy output
Survey data
Transfer waiting time
A B C A B
Case
B
Table 11 Comparison between fuzzy system output and CPT.
Transfer walking time
Trip Attribute
Safety
Britomart (mean)
Transfer waiting time (TWT1)
Table 9 Comparison between fuzzy system outputs and survey data.
Comfort
Trip Attribute
C Transfer delay time A B C Comfort
A B C
Safety
A B C
5. Discussion and comparison of CPT and fuzzy logic The main objective of the study is to determine the effects of uncertainty, in out-of-vehicle times during transfers, on transit users’ willingness to use transfer routes. Analysis of the survey data revealed that for all trip attributes, except for comfort, transit users’ exhibited greater preference for the scenario that was perceived to be ‘‘more conservative’’ despite a higher probability of shorter out-of-vehicle time in the ‘‘less
S1 S2 S1 S2 S1 S2
2.80 4.27 0.14 0.71 0.98 0.71
192 82 110 166 109 162
203 71 115 161 103 169
S1 S2 S1 S2 S1 S2
0.09 0.14 0.21 0.58 1.18 1.71
110 166 110 166 55 221
111 165 96 180 68 208
S1 S2 S1 S2 S1 S2
0.11 0.80 1.12 1.30 0.76 0.55
69 207 82 192 83 193
66 210 95 179 92 183
S1 S2 S1 S2 S1 S2
10.86 9.04 3.71 5.93 14.83 5.93
165 110 137 137 55 221
160 115 153 121 63 213
S1 S2 S1 S2 S1 S2
4.54 5.60 4.54 3.63 6.03 5.00
110 166 83 221 55 221
113 163 74 202 63 213
conservative’’ scenario. For comfort, transit users’ displayed risktaking characteristics when the waiting time for an available seat was less than 5 min. Such findings support the study by Eboli and Mazzulla (2012) which discussed that although comfort has been identified to be an important factor in service satisfaction, it is less important in the transit user’s decision process than other service factors. Results in Table 3 and Table 9 from the CPT and fuzzy logic model, respectively, illustrate that the two models are capable of representing transit users’ out-of-vehicle behaviour when making transfers. The cumulative prospect values were able to accurately reflect transit users’ preferences for the various transfer route scenarios. It was seen in most of the cases that as the difference between the cumulative prospect values for the two scenarios increased, the difference in the proportion of respondents’ preference also increased, with respondents favouring the higher cumulative prospect value scenario. Analysis also revealed no statistical evidence of significant difference between outputs from the fuzzy system developed and the survey data. Outputs of the fuzzy system were within 5% of the actual
A. Ceder et al. / Transport Policy 27 (2013) 112–122
response. Therefore, while the cumulative prospect value is able to provide an indication of transit users’ preference, fuzzy logic is capable of providing the proportion of transit users preferring a transfer route. Table 11 provides a comparison between the outputs of the fuzzy system, the cumulative prospect values and the actual survey responses for each transfer route scenarios for the complete data set (300 data-points). The cumulative prospect values included in the comparison had RP of 9.0 min for transfer waiting time, RP of 6.5 min for transfer walking time, RP of 7.5 min for transfer delay time, RP of 4.5 min for comfort and RP of 3.0 min for personal safety. As can be seen, both models are capable of representing the survey data. The fuzzy logic model represented the survey data more closely than the CPT model. Therefore, transit users’ out-of-vehicle travel behaviour can be modelled using either CPT or fuzzy logic. It should be noted that the cumulative prospect values are strongly dependent on the reference point and the outputs of the fuzzy system are strongly dependent on the membership functions and fuzzy rules. Development of the fuzzy system was a more iterative process than the one undertaken for CPT.
6. Conclusion It has been well established in literature that issues with the quality of PT services such as reliability issues, lack of information on connections and personal safety at transfer location contributed towards transit users’ feeling anxious (McCord et al., 2006; Cheng, 2010). Such factors were shown to cause out-of-vehicle times to be perceived as being more onerous than in-vehicle time by transit users (Iseki and Taylor, 2009). The present study provides researchers and practitioners with a better understanding of transit users’ decision to use transfer routes based on the degree of uncertainty which exist in out-of-vehicle times. A user preference survey was conducted in Auckland, New Zealand. The survey data was modelled by two commonly used cognitive models: cumulative prospect theory (CPT) and fuzzy logic. Results showed that for all trip attributes, except for comfort, transit users’ exhibited greater preference for the scenario that was perceived to be ‘‘more conservative’’ (less difference in range of out-of-vehicle times) despite a higher probability of shorter out-of-vehicle time in the ‘‘less conservative’’ scenario. Transit users’ perceived the attractive transfer route to be one that has a lower variability in out-of-vehicle times. Such findings suggest that policy makers and PT operators are required to focus on methods of reducing the uncertainty in outof-vehicle times. In other words, increasing the consistency in out-of-vehicle times will increase attractiveness of transfer routes thus enabling a more efficient and integrated PT network to result in enlargement of ridership. Analysis of transit users’ perception of trip attributes, given their current station, revealed statistical evidence for difference in two trip attributes, transfer waiting time and vehicle delay. Transit users who were accustomed to better out-of-vehicle facilities had a lower tolerance for uncertainty in transfer waiting times and delays. A comparison of the two models revealed that transit users’ willingness to use transfer routes based on their perception of outof-vehicle times can be modelled using either CPT or fuzzy logic; both models are capable of representing transit users’ route choice. However, while CPT provides an indication of transit users’ preference for a transfer route, fuzzy logic is capable of providing a closer approximation of the proportion of transit users preferring a transfer route. It should be noted that development of fuzzy system is a more iterative process than the one required for CPT.
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