In this form a direct relationship can be seen between the scaling parameter µ and the travel cost. The only unknown parameter is a proportionality factor θ . Instead of calibrating each routeset, now the proportionality factor has to be calibrated. At first glance this might not seem to be an improvement. However, since θ is derived from travel cost variance the parameter can be linked to user classes, trip characteristics and link type. Further, the proportionality factor can be influenced in the model based on the level of information of travellers. This new approach is considered significantly more flexible for application and easier to apply to characteristics of model elements (network links, user classes, dynamic measures, etc.). However, additional research is needed to see to what extent this new method can be implemented for large scale modelling and to what extent it performs better than a scale parameter for each routeset. Elements that should be covered in that research are how multiple proportionality factors can be used to determine the scale parameter for one routeset.
From the literature referred to above we see that at present there is not a plausible and tractable way of including lane-changing in DTA models, yet we might ask: does this really matter? On the contrary, it might be argued that lane-changing behaviour is too unpredictable or too detailed a notion to be considered for planning models, and may not lead to an improved representation of traffic reality at the level of detail required for planning applications. The pioneers of DTA modelling would have faced similar concerns (of adding too much detail for planning models) when proposing alternatives to the established static equilibrium methods, especially given the difficulty in estimating time-sliced origin-destination matrices. However, the argument in favour of dynamic over static assignment is not that we necessarily always need the detail of dynamic models, but that we now know that static models are systematically biased in their treatment of congestion phenomena, even at the gross level. Adopting a similar spirit in our work, therefore, we have been motivated to consider DTA with lane- changing in order to see whether, at the gross level, there is a systematic effect at the gross-level compared with DTA without lane-changing. If such an effect exists, then there are several implications, even if at the present our understanding of dynamic lane-changing phenomena is relatively immature. For example, even if we are unsure about the specific behavioural mechanisms that underpin lane-changing, then if they have a gross-level impact we should at least consider
In the previous section it turned out to be convenient to merge the notion of an origin- destination movement and departure period into a single entity, referred to as a commodity. In the present section, on the other hand, a slight change of notation will considerably ease the presentation. In particular, we now suppose that all R routes across all origin-destination movements (but neglecting departure periods) are indexed r = 1,2,…,R, making the origin- destination movements implicit in the routes. We then write our commodity route flow rate vector u with the route and departure period explicit: thus, for each route and time period referred to in u we identify the corresponding route label r (in our new route labelling system) and departure time period label i, and will thus henceforth refer to the departure time specific route flow rates as ~ for u ir r = 1 , 2 ,..., R and i = 1,2,…,L. It will also be convenient to move between time defined on a continuous axis and time defined in terms of the discrete departure intervals. Thus we introduce the indicator function I ( t ) ( 0 ≤ t ≤ N δ ) which takes the value i if continuous time t refers to departure interval i (for i = 1,2,…,L).
There are several levels of planning in transportation research, as mentioned in Chapter 1. This research mainly deals with the operational planning level of transportation research. Strategic planning might come into scope when more long-term elements such as available vehicles or network changes are considered. On an operational planning level studies have been done on reducing travel times and transport costs for given sets of transport requests. Most studies consider the situation where the path choices influence the costs or even the possible paths for other traffic. In these cases the goal is to find some equilibrium, meaning a solution where it is not possible to improve the current situation. The equilibria in transport modelling are known as the principles of Wardrop .
In order to concentrate on wavelength assignment, the authors used fixed shortest path routing. They used a layered graph approach, where each layer of the physical topology represents a different wavelength. They used the Best Fit P-CAR Wavelength Assignment algorithm that takes lightpaths in random order and routes them on the layer which yields the lowest P-CAR after accommodating the lightpath. The P-CAR on each layer is calculated by finding the attack graph corresponding to that wavelength using a recursive algorithm and then finding its maximum degree incremented by one. They used the Best Fit Decreasing P-CAR Wavelength Assignment algorithm that sorts the lightpaths in decreasing order of their shortest paths and then proceeds as BF_PCAR_WA. They also used two additional approaches, First Fit Wavelength Assignment and First Fit Decreasing Wavelength Assignment) algorithms which place lightpaths on the first layers in random order or in decreasing order of their shortest paths. The authors claim that their proposed GRASP heuristics obtain significantly smaller PAR and SAR values in all test scenarios in comparison to FFD and the crosstalk-friendlier RP.
First the paper considers, in sections 2-4, two simple dynamical [flow + green-time] models involving route flows and signal green-times in which the signal adjustments seek to ensure that consequent natural travellers’ re -routeing decisions make the best utilisation of the capacity available on a given road network. In these two models (which we call “the general model” and “the special m odel”) signal setting changes actively encourage congestion -reducing route-swaps in the future; both models maximise network capacity under natural conditions. The capacity maximising effect arises because both models utilise the P 0 signal control policy. This policy has been studied previously (see
XVHDWUDI¿FVLPXODWRUWRUHSOLFDWHWKHWUDI¿F±ÀRZG\- namics, critical for meaningful strategies for operating. 7KHFULWLFDOFRQVWUDLQWVWKDWGHVFULEHWUDI¿FÀRZSURS- agation and spatial-temporal interactions, such as the SDWKOLQNLQFLGHQFHUHODWLRQVKLSVÀRZFRQVHUYDWLRQDQG vehicular movements are addressed through simulation instead of analytical [Han et al. 2010]. This is because DQDO\WLFDOUHSUHVHQWDWLRQVRIWUDI¿FÀRZWKDWDGHTXDWHO\ UHSOLFDWH WUDI¿F WKHRUHWLF UHODWLRQVKLS DQG \LHOG ZHOO behaved mathematical formulations are currently un- available. Simulation provides the convenient tool for modelling complex dynamic phenomena thus overcom- LQJ WKH GLI¿FXOWLHV ZKLFK DUH DVVRFLDWHG ZLWK WKH XVH of analytical mathematical formulations [Mitaskis et al. 2011]. A key issue with simulation based method is that theoretical insights cannot be analytically derived as the FRPSOH[WUDI¿FLQWHUDFWLRQVDUHPRGHOOHGXVLQJVLPXOD- tions. But due to their better reliability vis-à-vis realistic WUDI¿FPRGHOOLQJVLPXODWLRQEDVHGPRGHOVKDYHJDLQHG greater acceptability in the context of red world deploy- ment [Mahasammi et al. 1998].
Now, as noted earlier, we shall assume that the link is homogeneous and the actual bottleneck is at the downstream node. If there are other constraints within the considered link such as lane-drops, we should split the link into several sub-links with constant capacity and corresponding sub-nodes between them. Furthermore, we also assume that traffic along a link is characterized by two regimes (i.e. either free-flow or congested), which are then considered in two cases as defined below. Due to the importance of this feature in our modeling approach, we have named it the Two-regime Transmission Model, or TTM for short. The idea of modelling a link as two traffic regimes has been applied in Bliemer (2007). However, Bliemer (2007) did not model the spatial and time dynamics of the density or flow along the link in detail, whereas our model allows for describing the dynamics of density along the link. Depending on how traffic flows into and flows out of the link, the length of each regime is determined. Instead of describing the dynamics of traffic on links through many cells with an equal length as in the CTM, TTM takes into account the changes in the density between each regime and the propagation wave speeds of each regime. With these assumptions, we are only interested in the jam formation and the propagation of the upfront jam under a certain boundary condition (when and where a traffic jam occurs). To this end, we will show that the traffic dynamics at a certain location in the link can be determined by the upstream boundary conditions in the free-flow situations and/or by the downstream boundary conditions in the congested situations.
Accurate depiction of existing traffic states is essential to devise effective real-time traffic management strategies using Intelligent Transportation Systems (ITS). Existing applications of DynamicTrafficAssignment (DTA) methods are mainly based on either the prediction from macroscopic traffic flow models or measurements from the sensors and do not take advantage of the traffic state estimation techniques, which produce estimate of the traffic states which has less uncertainty than the prediction or measurement alone. On the other hand, research studies which highlight estimation of real-time traffic state are focused only on traffic state estimation and have not utilized the estimated traffic state for DTA applications. In this paper we propose a framework which utilizes real-time traffic state estimate to optimize network performance during an incident through traveller information system. The estimate of real-time traffic states is obtained by combining the prediction of traffic density using Cell Transmission Model (CTM) and the measurements from the traffic sensors in Extended Kalman Filter (EKF) recursive algorithm. The estimated traffic state is used for predicting travel times on alternative routes in a small traffic network and the predicted travel times are communicated to the commuters by a variable message sign (VMS). In numerical experiments on a two-route network, the proposed estimation and information method is seen to significantly improve travel times and network performance during a traffic incident.
Adopting a continuous-time representation of the system, on the other hand, seems more appealing from the point of view that in the real world, time is typically considered to be continuous; surely, then, the discrete time system is only an approximation? This can be a somewhat misleading line of thought, however, due to the difficulty in dealing with the two different time-scales over which within-day traffic interactions occur, and between-day updating of travel choices occurs. A continuous-time model which could deal with both would indeed be attractive, but rather complex due to the lagged effect of daily experiences on subsequent decisions. Virtually all models considered in the literature are not so complex, and do not separate these scales, meaning that it is more difficult to understand which real-world phenomena these models are aiming to capture. It seems that a more plausible explanation for the continuous-time approaches we have reviewed here is that they are intended as smooth approximations to an underlying discrete day-to-day adjustment process. These approximations themselves may not have any direct real-world interpretation; rather their value is in the light they shed on the underlying discrete-time world. In particular, as discussed in section 3.5, it is possible to use stability analysis of a continuous-time model to infer stability properties of a related discrete-time model, in a consistent way with results obtained by directly analyzing the discrete-time model. On the other hand continuous-time models need discretization to be solved, thus this kind of models are less relevant from the solution point-of-view.
Roadworks are perhaps the most controversial topic in transport professional field. On one hand, they are a necessity to assure the current and future functionality of the traffic network, while on the other, they are seen as a major disturbance by road users with concerns for excessive travel time delays. The impact of roadworks is usually analysed at a local level however the network-wide effects are crucial to ensure reliable travel times. Moreover the analysis usually focusses on private cars and the reliability impact on public transport services are too important to ignore. This paper investigates the impact of roadworks undertaken on a given road link over wider parts of the network and assesses travel time reliability for both cars and buses. This research involves setting up of a con- ventional network assignment model to arrive at the routechoice of drivers as a result of the roadworks and then integrates the outcomes with a microsimulation model to generate space-time trajectories to arrive at travel times of individual vehicles. We adopted a reli- ability measure from the literature to compute travel time reliability of a given type of vehicle by unique origin-destination (O-D) pair combinations and also more generally to provide a wider picture at an aggregated network level. The method was tested on a real life network in England, and travel time reliability results were analysed both at the network scale and significant O-D pair level for private cars and bus routes.
Mesoscopic models are at the intermediate level between micro and macro models. Mesoscopic models represent individual vehicle motion based on macroscopic traffic relationships (ex., speed-density function), but not their interactions (2). Since mesoscopic models keep recording the travel experience of each individual vehicle, they are normally used as an evaluation tool for traveler information systems. Mesoscopic models integrated with DynamicTrafficAssignment (DTA) (3, 4) have become popular tools for traffic analysts to perform such applications (i.e., capacity enhancement strategy assessment) on large-scale transportation networks because of thier ability to allocate individual vehicle within the network to their destination based on factors that affect their routechoice. Over the last three decades, the focus of DTA research has been on the demand characterization side, such as incorporating dynamic time-dependent demand, stochastic departure times, and multiple user classes.
To address the inconsistency issue for real- time DTA, Peeta and Zhou (2002) developed a hybrid framework combining offline and real-time strategies to deal with two solution- related issues: (i) factoring the randomness in the O-D demand and/or network supply conditions, and (ii) enhancing the computational performance. The offline component uses historical O-D demand data to determine a robust initial solution, which is then updated dynamically in real-time based on unfolding O-D demand and incidents. The computationally intensive components are addressed offline to generate a robust initial solution that allows for efficient real-time updates, thereby enhancing the computational performance. Peeta and Yu (Peeta and Yu, 2004, 2005; Yu and Peeta, 2011) proposed and numerically analyzed a model that combines quantitative and qualitative variables in a single framework to more robustly predict travelers’ en-routeroutechoice behavior under information provision. Later, Peeta and Yu (2006) combined their routechoice model for network loading and a consistency-seeking model that updates driver behavior class fractions in real-time, called a behavior based consistency-seeking model (BBCS). BBCS captures the heterogeneous driver class fractions in real-time using the observed link traffic counts (Peeta and Yu, 2006). Although BBCS improves the solution quality, the computational effort is still significant relative to real-time deployment needs.
comparable simulation scenarios. In this simulation study, the approach ’simple fastest routes without any heuristics’ caused unbalanced traffic and resulted in an overall con- gested road network. Considering turn costs and distribut- ing vehicles among alternative routes by using the ’Choice Routing’ algorithm resulted in more balanced traffic. By using this approach, bottlenecks were avoided and, thus, no congestion occurred in the simulated scenario. However, this approach was not able to achieve a user equilibrium which represents a traffic distribution close to reality. To approx- imate the user equilibrium, we applied several iterations of a simple dynamictrafficassignment method. First, the ini- tial routes were calculated by the ’simple fastest routes’ ap- proach. Here, many iterations were required until a user equilibrium was reached. In a second experiment, we used initial routes pre-calculated by ’Choice Routing’ before an iterative trafficassignment approach was applied. Now, we were able to approximate the user equilibrium with less it- erations.
Modellingtraffic consists roughly of four steps, this is known as the ‘four-step model’. The first step is ‘trip generation’. It determines the frequency of trips that are going in and out of zones as a function of socio-economic data. For example, a zone containing a lot of shops will generate many trips going into that zone. The second step is ‘trip distribution’. It matches origins and destinations, in such a way that it determines how much travellers will be travelling from a specific origin to a specific destination. Thus a trip matrix is obtained. Often a gravity model is used in this step, based on the fact that masses attract each other: the bigger the mass (higher frequency of trips) and the smaller the distance between the masses (smaller distance between origins and destinations), the bigger the attraction (more trips are made). The third step is ‘modal split’, where the trips are assigned to different modes, for example cars, bicycles or public transport. The fourth and final step is the trafficassignment. It determines which routes will be chosen by travellers, given their origins and destinations. In this step the travellers are ‘placed’ on the network, and a resulting load on every road is obtained. This last step, known as the TrafficAssignment Problem (TAP), is the subject of this study.
journey planners do not currently consider bus travel time which may vary with the time of the day due to recurrent road congestion. The current journey planners also do not take into account queuing time at stops and stations due to passenger congestion on the transit network. From an assignment perspective, this may lead to passengers changing their route and mode choice, time of departure and sometimes even their final destination, and while this is a major problem in large cities’ public transport networks, there does not seem to be any broad agreement in the literature on how this phenomenon should be modelled.
The technique of simulation modelling provides solutions to complex trafficassignment problems such as the doubly dynamictrafficassignment described in this paper through a fairly simple and transparent process. For transport modellers applying such models, the practical counterpart to deterministic equilibrium is the stationary state of the stochastic processes, and in this paper correlograms were analysed as a way of detecting the stationarity. Properties of link travel time models including FIFO compliance were illustrated. In the future, affirmative tests of stationarity of the stochastic processes such as the ones involving spectral density functions will be investigated. Further useful experiments could also be performed to investigate the impact of alternative travel time functions (e.g. higher order than linear) on the autocorrelation functions. ACKNOWLEDGEMENT
The concept of transportation has been around ever since men settled down and founded homes. In the beginning little was going on. However, since the twentieth century, the transportation sector has seen a dramatic increase in number of vehicles and turnover. As there are literally billions of euros spent in traffic, this sector has become more and more important which resulted in the increase of importance of traffic models. A set of these models are the macroscopic dynamictrafficassignment (MDTA) models. These models were developed somewhere halfway the twentieth century in order to have scientific methods for attacking the problem of organizing road traffic so that the full benefits of the increased mobility can be enjoyed at the lowest cost in human life and capital [LW55]. These models were originally developed for use on highways. With the ascending of the computer however they were soon used on suburban roads and recently even on urban roads. A large difference between highways and (sub)urban roads which has to be dealt with, is the presence of junctions. Macro dynamictrafficassignment models should therefore take into account the effects of junctions on traffic flows. This leads to the first goal of this thesis; to formulate a global theory of how to take into account the effects of junctions in macroscopic dynamictrafficassignment models. The second goal of this research is the development of an algorithm which deals with junctions in MaDAM and can be implemented in its code. MaDAM stands for Macroscopic DynamicAssignment Model and is the MDTA used and developed by Omnitrans International.
The first group of cycle planners are ones which are covering travelling around the city. An example which could be used is the Vancouver cycle planner (Cycling Route Planner, 2007). The user has a possibility to set his preferences, such as priority usage of cyclist facilities instead of major roads, shortest path, least elevation gain path, least traffic pollution or mostly vegetated path. Then the planner finds ideal path which is based on these preferences and display the path on the map with overall information about it along with directions. Another even more detail approach is used in the OPT for health – route planner for San Francisco (OPT for Health, 2010). Cyclists are not the only target group but possibility to adjust the searching for ideal route is here even more complex. The user is allowed to set values for each attribute which is considered (e.g. most bicycle friendly, major road, traffic access restricted…). This setting is supposed to lead to improvement of searched path. On the other hand there are other types of cycle planners which are trying to be still complex even with limited amount of adjustable preferences such as San Francisco Bicycle trip planner (2009). In this planner the user can choose only from three types of paths – shortest, balanced or biker friendly and setting of maximum grade.