| In our daily life, we generally expect the transport system to be efficient, safe, and reliable. However, there exist several sources of uncertainties in the transportation system both on demand and supply sides. With a constant growth in economic activities most urban transport networks currently operate at or beyond their capacities leaving very small tolerant capacities to cope with the uncertainties. As a result, the unreliability in transport system has gradually become one of the major problems. The potential sources of uncertainty may range from natural disasters at one extreme to recurrent events like congestion and road maintenance works at the other. With all these uncertain environments, the travellers and network planners face a serious challenge in evaluating, planning, and managing the transport network against these uncertainties.
In order to cope with these problems, one needs to understand several aspects of the effect of uncertainties related to the network operation, short and long term planning, evaluation of network reliability, and travellers' behaviours under certain condition. The significance and timeliness of this topic has brought together a group of transport researchers and practitioners to address the reliability of transport system. The International Symposium on Transport Network Reliability (INSTR) has been established since 2001 (organized in Kyoto) to serve this purpose. Following the success of the first symposium, the symposium has been held every three years since then. The latest symposium (the Third INSTR) was held in the Hague, the Netherland in 2007 which was chaired by Prof. Henk van Zuylen, Delft University of Technology. This special issue is one of the fruitful outcomes from this symposium.
The issue aims to select some significant papers from the conference which report on the state-of-the-art of the evaluation and enhancement of transport network reliability using network equilibrium based approach. Seven papers are finally selected to be included in this special issue. The focuses of the papers range from basic analytical development of the static equilibrium model to the future view on the extension to the dynamic case.
The first paper by Sumalee and Watling proposes the efficient partition-based method to evaluate the transport network from the view point of travel time reliability after the disasters. The algorithm will dissect and classify the network states into reliable, unreliable, and un-determined partitions. By postulating the monotone property of the reliability function, each reliable and/or unreliable state can be used to determine a number of other reliable and/or unreliable states without evaluating all of them with an equilibrium assignment procedure. It also proposes the cause-based failure framework for representing dependent link degradation probabilities. The algorithm and framework proposed are tested with a medium size test network to illustrate the performance of the algorithm.
The second paper by Zhou and Chen proposes different stochastic network equilibrium assignment frameworks under demand uncertainty. The traditional user equilibrium model, the demand driven travel time reliability-based user equilibrium model, and the α-reliable mean-excess travel time user equilibrium model are compared and evaluated under uncertain travel demand. The numerical experiment to a small network highlights the limitation of the traditional UE model and the advantage of the assignment models considering both reliability and unreliability of travel time.
The third paper by Shao et al proposes a travel time reliability-based traffic assignment model to investigate the rain effects on risk-taking behaviours of different road users in networks with day-to-day demand fluctuations and variations in travel time. In view of the rain effects, road users' perception errors on travel time and risk-taking behaviour on path choices are incorporated in the proposed model with the use of a logit-based stochastic user equilibrium framework. A numerical example is illustrated for assessment of the rain effects on road networks with uncertainty.
The forth paper by Shimamoto et al proposes an algorithm to specify the critical lines and stations of a transit network by considering the number of passengers failing to board and attempting to evaluate its impact on service quality and safety risks. A station size dependent satisfaction function is proposed, and the value of the function for each station is calculated by the transit assignment model considering the capacity constraints. The method is applied to the London's underground network with a number of scenarios to identify critical stations in the network under the unexpected delays.
The fifth paper by Li et al addresses the optimal toll design problem to improve the network reliability. The bi-level optimisation problem to determine the optimal toll level is formulated to minimise the weighted sum of average travel time and variance under user equilibrium constraints. The proposed model is applied to a small network to evaluate the proposed method.
The sixth paper by Iryo performs a theoretical analysis of instability in a departure time choice problem. It examines the stability of a dynamic user equilibrium problem with the bottleneck model and departure time choice. A mechanism of day-to-day change of traveller's behaviour and a function showing dissimilarities between different equilibrium points are defined. The day-to-day change of the dissimilarity function is mathematically examined with approximations. A numerical test is carried out to verify the result and illustrate the non-converging behaviour of the system.
The last paper in this special issue by Hoogendoorn, et al proposes a robust optimal control framework of a traffic network taking into account the uncertainty in predicted traffic condition and system performance. The problem is formulated as a stochastic dynamic program in which the rolling horizon approach is adopted to define the control strategy. The main objective of the problem is to control the traffic inflow to minimize the expected total travel cost during the control period. Two simple examples show the applications and benefits of the proposed model in addressing uncertainties by using traffic management system.
The guest editors do believe that the area of transport network reliability is still an emerging research field, and hope that this special issue may contribute to the developing of this interesting and important topic. We would like to acknowledge Prof. van Zuylen and his colleagues at Delft University of Technology for organising the Third INSTR, Prof. Chan Wirasinghe and Prof. William H. K. Lam for their support during the preparation stage of this special issue, and authors and reviewers who have contributed to this special issue.
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