Delay Resistant Single Track Train Timetables

Robustness is an important parameter in the planning of railway systems.Robustness of a railway system is the influence-ability of the system by disturbances.Small disturbances can cause large delays for non-robust railway systems.The thesis discusses the improvements of railway's timetable robustness at the design stage.Based on the evaluation time of the robustness,different robustness measures can be classified as:ex-ante and ex-post measures.Ex-ante measures are very much helpful for planners at the design stage.A limited number of the ex-ante approaches are available for the robustness measurement of the train timetables.First part of the thesis introduces measures to quantify and improve the robustness of the train timetables at the design stage.The thesis presents the modeling and application of an ex-ante robustness measure for single track railways,known as the Critical Robustness Measure(CRM).Efficiency of the CRM is presented by comparing with the available ex-ante robustness measures i.e.,number of trains per hour per section,total amount of runtime margin for each individual train,sum of shortest headway reciprocals,weighted average distance,marginal runtime difference,robustness in critical points and margin along the longest path.Computational results show that all components of margin are not useful in robustness of a timetable.Furthermore,the robustness is not a statically quantifiable quantity rather it changes with time and depends on the way of the train's interactions.Furthermore,to improve the robustness of a train timetable the thesis presents a model and heuristic technique to find the better position to allocate the limited amount of time margins(buffers and running time supplements)in a timetable.The goal of reallocation of the available time margins is to adjust an existing timetable to minimize the sum of train delays at the event of the operational disturbances and thus increase the robustness of the timetable.The thesis treats the train timetable as a Directed Arc Graph(DAG)with aggregation concept.The basic concept of aggregation is the combination of a sizeable portion of the network into a single node of the graph.The thesis proposes a time margin reallocation heuristic technique known as Critical Time Margins Allocation(CTMA),and simulates and evaluates the modified timetable under different disturbance situations.The thesis implements the technique on a hypothetical small railway network and a practical timetable with a single line for the track segment from Rawalpindi to Lalamusa,Pakistan.In addition,random disturbance instances are generated to further verify the effectiveness of CTMA.The results show that the timetable obtained from the CTMA modification reduces the total delay by an average of 3.25%for the small fictive railway network,and 5.18%for large real world data set,when it is tested in different random disturbed scenarios.The results suggest that adding time supplements to a timetable in the appropriate positions can reduce the delay propagation.The last part of the thesis models the train scheduling problem of a single track railway network with main concern to minimize total operational cost and delays with relation to position of sidings.The range of possible meet places poses a challenge for the planners to determine the minimum investment in the infrastructure to facilitate the meet plans while maintaining the specified level of service.Main concern in the problem is to find the optimum position of sidings on the railway network to minimize the total operating cost and total delay(including conflict delays).The problem explores the impact of number and position of sidings on timetable for a single track railway network.Sensitivity analysis is conducted by changing the number of sidings and trains to quantify the relatedness between the number of sidings and train conflict delays.Some of sidings which do not have any impact on scheduling of the network are mentioned by analysis.Sensitivity analysis of actual schedule of Pakistan Railways(Rawalpindi to Lalamusa)shows that 4 positions of sidings i.e.,Kaliamawan,Sohawa,Ratial and Kalagujran have negligible effect on the schedule.The technique can be used to determine the investments in terms of location and number of sidings because conflict related delays has direct relationship with number and position of sidings.