Although the expected travel time is an important factor affecting the travellers’ **route** **choice**, as proved by the numerical example, many studies have found that the reliability of travel time due to non-recurrent congestion can be even more important. Indeed a “wrong” **choice** of **route** or mode can result in a significant delay, which may have severe consequences for the traveller (e.g. late arrival at the workplace). Equally, some groups of travellers may be particularly adverse to discomfort on board due to overcrowding (e.g. elderly travellers, parents travelling with your children …) and decide to change their **route** and/or departure time according to network conditions. As such, future developments will concentrate in the inclusion of these factors in a multi- class **route** **choice** **model** coupled with departure time **choice** **model** in public transport networks.

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Two final remarks will be made in this review. Smith (1984) considered a dynamical system formulation of day-to-day **route** **choice**, in terms of **route** flows. Drivers were assumed to switch between routes according to the difference in **route** travel costs; Smith showed that such a system converged to a stable equilibrium under the usual assumptions. Mahmassani and co- workers (1991) have proposed a **route** **choice** **model** which appears to be particularly suited to modelling day-to-day evolution. In fact, Cascetta et al (1991a) suggest the possible use of Mahmassani's **model** within their stochastic process framework; as far as the author is aware, this is a possibility presently being investigated by Mahmassani. The **route** **choice** **model** is derived from the premise that drivers base their decisions on minimum perceived travel time differences, or thresholds. This is known as `boundedly rational' behaviour, with a boundedly rational user equilibrium occurring when every driver is satisfied with his current **choice** of **route** (eg there is no alternative **route** which is perceived more than the threshold percentage quicker than the current **choice**). The **model** also makes sense in non-equilibrium contexts. The threshold values may vary across the population, according to driver characteristics and the propensity to switch; thus, a kind of habit effect is achieved.

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Although Discrete **choice** models provide parsimony and an elegant econometric generalization of drivers’ behavior, they do not include an explicit behavioral abstraction of the effect of the real-time information provided by ATIS. Capturing this effect on drivers within the framework of discrete **choice** models requires additional behavioral assumptions. Previous attempts to address the effect of partial information on drivers’ behavior focus on three main approaches. Under one approach, the information affects the error term in the routes’ utilities functions thus providing information implied less error in the system (e.g. Watling & Van Vuren, 1993 and see review by Bonsall, 2000). Another approach is to reduce system error by gaining more knowledge through reinforced learning. For example, Horowitz (1984) described a simple **route** **choice** **model** over time whereby decisions are based on the weighted average of previous travel decisions’ utilities.

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Some researchers have introduced the stochastic **route** **choice** **model**, which is one source of demand variation, with or without the demand uncertainty into network equilibrium models (11)- (15). Inouye (16) adapted an original Probit stochastic equilibrium **model** for evaluating travel time reliability by interpreting the error terms associated with the travel cost as the source of variation. Clark & Watling (17) proposed a stochastic network **model** assuming stochastic demand as well as stochastic **route** **choice** and defined an approach to approximate the probability density function (pdf) of the total travel time. The pdf of the total travel time within the network is then used to calculate the total travel time reliability which is defined as a probability of the total travel time to be less than a specified value.

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One major disadvantage of our approach is that we compare the results of our **route** **choice** variants with only one dataset. We use the data of Enschede to measure the reality of our variants, but it is possible that we get other results if we use data of other cities. In Enschede, congestions do not occur often, therefore we do not know if the same results hold for a congestion situation. Further, we test our **route** **choice** variants for short trips, but it is generally agreed that **route** decisions for long trips are different from **route** decisions for short trips. Therefore our results also do not have to hold for long trips. We get a more general result at the last test, by testing on multiple OD’s, but we still have to deal with the fact that the travelers in Enschede could make other **route** choices than travelers in other regions. Another disadvantage of our research approach is that our measure, reality, is based on an outcome of more processes than the **route** **choice** step. The **route** choices resulting from a transport **model** are a result of the network in the **model**, the travel time functions, the origin destination matrix estimation, the loading method, and the **route** **choice** **model**. Errors in other steps than the **route** **choice** modeling influence the result of our tests. Therefore we do not know if our results also hold for other loading methods, or for instance in other networks. Of course, we cannot test with all possible loading methods to investigate all possible influences of the loading methods, but we use different loading methods to get a good sense of the possible influences of the loading method. In the Enschede tests we assign all vehicles in a 15 minutes interval according to the same probability distribution. We choose to aggregate the vehicles in a 15 minute interval, because there is not much traffic, and it is hard to assign 1 vehicle for 30% to one **route** and for 70% to another **route**. The aggregation of the vehicles influences the results of the tests, we expect that the shortest **route** principle is more accurate if the shortest **route** is calculated in smaller time intervals. In Chapter 3 we mentioned two other shortcomings of our research approach. We do not investigate other utility functions than the travel time, predicted travel time and combinations of distance and travel time. Also we do not investigate **choice** set generation methods, although we know that the **choice** set and the utility function strongly influence the **route** **choice** results. An investigation of these two elements is beyond the scope of this master thesis project.

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As previously mentioned, the motivation for which it is worth studying compliance with information is strictly relat- ed to network effects. In some cases [8, 10], it has been proven that a high level of compliance is required in order for ATIS to be effective. However, the relationship between compliance and reliability of information (with reference to different kinds of information) has often been argued but not in all cases proven. According to widely used definitions, we state herein that the information is reliable when the esti- mates made by the ATIS are consistent with the travel times the travellers have actually experienced once at destination. This is determined by a combination of forecasting methods from the ATIS side, variability in travel times from the network side and travellers ’ experiences. The result is that compliance is not always expected to be high. This difficulty is exacerbated in the case of congested networks by the so- called anticipatory **route** guidance problem (ARG problem, e.g. [16, 24]). In order to obtain reliable information, the suggestions, based on the estimates of the predicted state of traffic conditions, should consider travellers’ reactions to the information itself. These reactions are however dependent on the actual compliance, and thus even in forecasting models that account for travellers’ reactions 100 % reliability is not expected to be met if compliance behaviour is not fully captured. These complex interactions defend our interest in compliance but are excluded from our experiment, since it is much more useful for studying the respondents ’ behaviour to treat reliability as an external parameter. In particular, reli- ability is the main design parameter of our experiment, since the effects of different reliability levels on compliance with information is one of the main interests in this work.

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It is pertinent to ask under what conditions will there exist solutions to the SUE(2) **model** proposed in (3.9), and under what conditions will there be a unique solution. The existence question is quite straightforward to answer, using tools similar to those used by Smith (1979) for deterministic user equilibrium and Cantarella & Cascetta (1995) for conventional SUE. Basically, if all the functions involvedi.e. the **choice** probability function p u u ( 1 , 2 ) and the modified cost-flow functions given by (3.8) are continuous, then Brouwer’s fixed point theorem (Baiocchi & Capelo, 1984) will ensure the existence of at least one solution to the fixed point problem (3.9), since the mapping implied by the right hand side of (3.9) is to a closed, bounded, convex set. In order for the modified cost-flow functions to be continuous, it is clearly sufficient that the original cost-flow functions are twice continuously differentiable throughout their range. The uniqueness question needs a little more thought. In the introduction of the SUE(2) problem (expressions (3.7)-(3.9)), it was notationally convenient to express the problem purely in terms of the flow mean and variance on **route** 1. However, let us now assume the functions h 1 and h 2 given by (3.8) are instead replaced by functions of ( 1 , 1 ) and ( 2 , 2 ) , respectively the flow rate mean and variance on routes 1 and 2, i.e.

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been proved. For example, it has been shown that, for any steady feasible demand within a special flow **model**, if the general day to day re-routeing **model** is combined with the general day to day green-time response **model** then under natural conditions any (flow, green-time) solution trajectory cannot leave the region of supply-feasible (flow, green-time) pairs and costs are bounded. It has been shown that throughput is maximised in the following sense. Given any constant feasible demand; this demand is met as any routeing / green-time trajectory evolves (following either the general or the special dynamical **model**). The paper has then considered simple “pressure driven” responsive control policies, with explicit signal cycles of fixed duration. A possible approach to responsive control within a within-day dynamic network, allowing for variable **route** choices has been very briefly outlined. It has finally been shown that modified Varaiya (2013) and Le at al (2013) pressure-driven responsive controls may not maximise network capacity when **route** choices are variable, by considering a very simple one junction network. There are many opportunities for further work in the directions discussed in this paper. For example it would be interesting to understand whether P 0

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algorithm with a macroscopic traffic flow **model** for freeway traffic state estimation. Park and Lee (2004) used a Bayesian technique to estimate travel speed for a link of an urban arterial using data from a dual loop detector. Gang, Jiang, and Cai (2007) presented a traffic state estimation scheme based on the Cell Transmission **Model** (CTM) and Kalman filter for a single urban arterial street under signal control. Liu et al. (2012) proposed a travel time estimation approach for a long corridor with signalized intersections based on probe vehicle data. Long et al. (2008) developed a **model** based on the CTM for congestion propagation and bottleneck identification in an urban traffic network. They also estimated average journey velocity for vehicles in the network. Long et al. (2011) applied CTM for simulating traffic jams caused due to an incident in an urban network. They assumed that both traffic flow parameters and the duration of the incident were known during the incident and used a CTM alone for traffic prediction. Zhang, Nai and Qian (2013) compared travel-time computed using three different traffic flow models that could be used for predicting network traffic namely the point queue **model**, the spatial queue **model** and the CTM, and concluded that the CTM is better than the other two models for predicting travel times especially when queue spillback prevails. Sumalee et al. (2011) and Zhong et al. (2011) proposed a Stochastic CTM for network traffic flow prediction, the stochasticity intended to address uncertainties in both traffic demand and capacity supplied by the network.

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Roadworks are inevitable activity on any road network, and the analysis usually focuses on the local impact surrounding the location. However, this paper considers the affects at a larger scale over the entire traffic network and analyses the travel time reliability impact on private cars and buses. In the literature, roadworks fall under irregular condition-depen- dent variation that affects the travel time distribution, hence, any change in the distribution will affect the reliability value. Thus, this paper adopted a probability measure for quan- tifying the travel time reliability and proposed a joint **model**- ling procedure using conventional assignment and microsimulation models to evaluate the proposed roadwork diversion schemes. The conventional assignment **model** al- lows modifying the network for each proposed diversion

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For only a few people is transport an end in itself. Most need to travel to be able to perform a certain activity, e.g. work, education or shopping. Since activities are carried out at different locations, people tend to make trips between these locations. This results in mobility and has its effect on daily society life. This chapter gives an introduction to the study presented in this report on dynamic traffic assignment **route** **choice** modelling. Paragraph 1.1 gives a short introduction on the growing mobility that partly forms the research motive pointed out in paragraph 1.2. In paragraph 1.3 the research objective and questions are presented. Paragraphs 1.4 and 1.5 describe the context of the study and scope of research respectively. This chapter concludes in paragraph 1.6 by giving an outline of the report contents.

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BikeAnjo: A group of biking fanatics founded in 2010 that helps new people to ride a bike, as well as organising cycling trips around the city of S˜ao Paulo. With the use of BikeAnjo a large variety of cyclists can be reached, since both experienced and inexperienced cyclists will be part of this community. It is expected that deviations of the mean speeds will be high, but the average speed tends to be a good representation since there will be cyclists from both sides of the spectrum. However, as stated by Stinson & Bhat (2004), there is a differ- ence in **route** **choice** factors between different levels of experience. Inexperienced cyclists tend to give more value to factor related to separation from cars, while experienced cyclists are more sensitive to factors related to travel time.

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As can be seen, equal aggregated values and relative aggregated values correlate about the same with the global preference. The average correlation coefficients for equal weights and relative weights are about the same and these correlation coefficients are high. While the correlation coefficients for equal weights are high, it is not clear if the aggregated values on the basis of relative weights produce high correlation coefficients or if these correlation coefficients are high because the correlation coefficients for equal weights are high already. It is possible that the quality of the relative weights depends partly on the correlational structure of the data. The beta aggregated values have much higher correlation coefficients with the global preference than the other two methods. The correlation between aggregated values based on beta weights and the global preference is high. So if a **route** is much preferred by a subject, the aggregated value for that **route**, based on the beta weights, will be high too. The beta weights seem to produce more valid aggregated values then relative weights do. There are only small differences between the three countries and the two travel modes.

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Traditionally, travel behavior modeling has been based on the axioms of expected utility (Bernoulli, 1738; Von-Neumann & Morgenstern, 1944; Luce & Raiffa, 1957). Random utility based discrete-**choice** models or RUM provide an econometric interpretation of expected utility theory. This approach is still regarded as the official workhorse for most travel related behavioral modeling. RUM have been developed considerably in the past three decades and specifically for **route**-**choice** modeling. Chronologically speaking, the classic Multinomial Logit **Model** (Daganzo & Sheffi, 1977) was the first to be applied followed by the C-logit **model** (Cascetta et al., 1996), the IAP logit (Cascetta & Papola, 1998) and Path-Size Logit (Ben-Akiva & Bierlaire, 1999). Following the presentation of the General Extreme Value theorem (McFadden, 1978) more flexible modeling structures were developed including: Nested Logit (Ben Akiva & Lerman, 1985); Cross-Nested Logit (Vovsha, 1997); General- Nested Logit (Wen & Koppelman, 2001) and Paired-Combinatorial Logit (Chu, 1989; Koppelman & Wen, 2000). These GEV-based models were applied to **route**-**choice** models with an adaptation of GNL and PCL (Prashker & Bekhor, 1998; Gliebe et al., 1999; Bekhor & Prashker, 2001) and a GNL based Link Nested Logit (Vovsha & Bekhor, 1998). In the last decade, a major breakthrough in modeling capabilities was achieved by the introduction of the Mixed Logit or Logit Kernel **model** (Ben Akiva & Bolduc, 1996; Bhat, 1998; Bhat, 2000; McFadden & Train, 2000). Several studies have recently adapted Mixed Logit in the context of **route**-**choice** modeling: (Bekhor et al., 2002; Srinivasan & Mahamassani, 2003; Jou et al., 2007). A detailed review of such RUM-based **route**-**choice** models is provided by (Prashker & Bekhor, 2004).

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Following the network analysis process outlined in Chapter 6, a trip count was ascertained for each CAST zone, providing an indication of how many trips can be expected to pass through each zone, regardless of the mode of transport. Figure 7.5.1 illustrates that those areas with the highest number of potential trips passing through them are unsurprisingly mostly located in close proximity to significant arterial routes, as these often represent the most direct **route** between two points on a network. In saying this however, there are also a number of areas where there is expected to be a substantial number of trips passing through areas where there is minimal cycle infrastructure, a number of which are located on the western side of the city (Figure 7.5.2). There are also a number of areas with medium to high trip density and minimal cycle infrastructure (highlighted in red in Figure 7.6.1), arguably representing zones where accessibility could be easily improved through minor extensions to the current proposed major cycleways network. It is important to once again point out that a large number of the city’s key growth areas are located on the western side of the city, as can be seen in rest of the results presented in this chapter. Improving access to cycle infrastructure between key residential growth and employment zones would not only help to expand the overall levels of accessibility throughout the city, but also contribute to the city centre and surrounding areas being more accessible to the key growth areas by alternative modes of transport; in consequence contributing to the overarching goal of making the city more liveable and sustainable.

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In this paper, we propose a novel approach to **model** **route** **choice** behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume fur- ther that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indiffer- ence curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least neg- ative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi- objective user equilibrium (TSmaxBUE) condition. That is, for each O-D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O-D pair.

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The current **model** is implemented in Matlab. This environment is very well suited for **model** development and testing, however, it is slow. Therefore, in Matlab it is not possible to use ex- tended optimization schemes. To be able to calibrate the **model** thoroughly and to apply it for analysis and online guidance generation, translation to a fast language is necessary. Furthermore, efficiency improvements in the programming code are needed to improve the computation speed. In the case study, a limited number of iterations is used in the optimization algorithm. With this limited optimization the algorithm is not able to find good solutions for every period and every scenario. Therefore, it is not possible to conclude on the effect of guidance. With the chosen **model** settings, one **model** run takes at least 4 days at the computers available at Witteveen+Bos. With a fast computer the same run can currently be performed in less than 1 day. For calibration and online implementation this should at least be reduced to one hour (for a complete morning peak). Traffic propagation

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In the first repetition, one out of three ve- hicles has never been involved. The second ve- hicle has also passed a **route** about four times more than the other car, which indicates uneven division of loads between vehicles. In the sec- ond case, similarly to the first case, one vehicle has been idle and two other vehicles have passed a distance a little close to each other; however, they also have infeasible state. The third state performed better than the other two; however, its infeasible result cannot be ignored because the passed distance and the load carried are sig- nificantly different between vehicles. In order to yield better results, it should be optimized through MOPSO algorithm.

We **model** line planning with **route** **choice** (LPRC) as a bilevel optimization problem with a line planning problem on the upper level and passenger **route** **choice** problems on the lower level. We use two different techniques to transfer the bilevel optimization problem into a single-level (mixed-)integer linear problem ((M)IP). For both transformations, binary variables and ’big-M- constraints’ need to be added, which lead to an increase in computation time compared to the problem formulation with **route** assignment instead of **route** **choice**. However, it turns out that in practical situations, most of the additional constraints are unnecessary. For this reason, we develop a constraint-generation approach, which iteratively adds the set of constraints to the formulation which are violated by the current solution.

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Several issues can be raised about these costs the first of which is that, apart from driver training, they all fall on the local authority. This raises the question of whether to include them in the **model** since whilst they will not directly affect the bus operators’ costs they will impact upon the generalised cost of the passengers’ trips via those passengers’ valuation of quality attributes and the higher the number of passengers per bus, the slower the service and the higher the cost. The second issue that has to be determined is what the relative cost of passenger infrastructure provided for a QBP is compared with a non-QBP **route**. That is to say would bus shelters be provided on non-QBP routes and if so how much less do they cost as compared with a high specification QBP bus shelter. At the moment our preferred position would be to use the cost of passenger infrastructure as an input into a cost benefit analysis rather than as a **model** input. This issue also highlights the need to take into consideration the costs of any road infrastructure, such as bus lane and bus priority measures. Again none of these costs are allocated to the bus operators, yet the bus operators benefit via the quality of service bestowed upon their passengers together with any cost savings arising from improved vehicle speeds. At the moment we would recommend that these costs be treated like passenger infrastructure costs, in that they be assessed in a cost benefit framework alongside the outputs of the **model**. To do this it is necessary that any additional road infrastructure costs that are attributable to a QBP be identified.

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