Dissertations / Theses on the topic 'Pole assignment Mathematical models'

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis reviews, extends and applies to urban traffic analysis the entropy concept of Shannon and Luce's mathematical psychology in a fairly complex and mathematically demanding model of human decision making, if it is solved as a deeply nested structure of logit calculus. Recognising consumers' different preferences and the universal propensity to seek the best choice when going to some desired goal (k), a transparent mathematical program (MP) is developed: the equivalent of a nested multinomial logit model without its inherent computational difficulty. The MP model makes a statistical assessment of individual decisions based on a randomised (measurable) utility within a given choice structure: some path through a diagram (Rk, Dk), designed a priori, of a finite number of sequential choices. The Equivalence Theorem (ET) formalises the process and states a non-linear MP with linear constraints that maximises collective satisfaction: utility plus weighted entropy, where the weight (1/θn) is a behavioural parameter to be calibrated in each case, eg for the Perth CBD. An optimisation subject to feasible routes through the (Rk, Dk) network thus captures the rational behaviour of consumers on their individually different best-choice decision paths towards their respective goals (k). This theory has been applied to urban traffic assignment before: a Stochastic User Equi-librium (SUE). What sets this thesis apart is its focus on MP models that can be solved with standard Operations Research software (eg MINOS), models for which the ET is a conditio sine qua non. A brief list of SUE examples in the literature includes Fisk's logit SUE model in (impractically many) route flows. Dial's STOCH algorithm obviates path enumeration, yet is a logit multi-path assignment procedure, not an MP model; it is nei-ther destination oriented nor an optimisation towards a SUE. A revision of Dial's method is provided, named STOCH[k], that computes primal variables (node and link flows) and Lagrangian duals (the satisfaction difference n→k). Sheffi & Powell presented an unconstrained optimisation problem, but favoured a probit SUE, defying closed formulae and standard OR software. Their model corresponds to the (constrained) dual model here, yet the specifics of our primary MP model and its dual are possible only if one restricts himself to logit SUE models, including the ET, which is logit-specific. A real world application needs decomposition, and the Perth CBD example is iteratively solved by Partial Linearisation, switching from (measured) disutility minimisation to Sheffi & Powell's Method of Successive Averages near the optimum. The methodology is demonstrated on the Perth Central Business District (CBD). To that end, parameter Θ is calibrated on Main Roads' traffic count data over the years 1997/98 and 1998/99. The method is a revision of Liu & Fricker's simultaneous estimation of not only Θ but an appropriate trip matrix also. Our method handles the more difficult variable costs (congestion), incomplete data (missing observations) and observation errors (wrong data). Finally, again based on Main Roads' data (a sub-area trip matrix), a Perth CBD traffic assignment is computed, (a) as a logit SUE and - for comparison - (b) as a DUE (using the PARTAN method of Florian, Guélat and Spiess). The results are only superficially similar. In conclusion, the methodology has the potential to replace current DUE models and to deepen transport policy analysis, taking into account individual behaviour and a money-metric utility that quantifies 'social benefits', for instance in a cost-benefit-analysis.

[Truncated abstract] In an urban network, any change to the capacity of a road or an intersection will generally result in some traffic changing its route. In addition the presence of intersections creates the need for frequent stops. These stops increase the fuel consumption by anywhere between thirty to fifty percent as evidenced by published standardised vehicle fuel consumption figures for urban and for country driving. Other components of vehicle operating costs such as tyre and brake wear and time costs will also be increased by varying amounts. Yet almost all methods in use for economic evaluation of urban road projects use open road vehicle operating costs (sometimes factored to represent an average allowance for stopping at intersections) for one year or sometimes two years in the analysis period and then make assumptions about how the year by year road user benefits may change throughout the period in order to complete the analysis. This thesis will describe a system for estimating road user costs in an urban network that calculates intersection effects separately and then adds these effects to the travel costs of moving between intersections. Daily traffic estimates are used with a distribution of the flow rate throughout the twenty-four hours giving variable speed of travel according to the level of congestion at different times of the day. For each link, estimates of traffic flow at two points in time are used to estimate the year-by-year traffic flow throughout the analysis period by linear interpolation or extrapolation. The annual road user costs are then calculated from these estimates. Annual road user benefits are obtained by subtracting the annual road user costs for a modified network from the annual road user costs for an unmodified network. The change in the road network maintenance costs are estimated by applying an annual per lane maintenance cost to the change in lane-kilometres of road in the two networks. The Benefit Cost Ratio is calculated for three discount rates. An estimate of the likely range of error in the Benefit Cost Ratio is also calculated

The goal of this research is to develop a heuristic traffic assignment method to simulate the traffic flow of a transportation network at a real-time speed. The existing assignment methods are reviewed and a heuristic path-recording assignment method is proposed. Using the new heuristic assignment method, trips are loaded onto the network in a probabilistic approach for the first iteration; paths are recorded, and path impedance is computed as the basis for further assignment iteration. The real-time traffic assignment model developed with the new assignment method is called HEUPRAE. The difference in link traffic between this new assignment and Dial's multipath assignment ranges from 10 to 25 percent. Saving in computer time is about 55 percent. The proposed heuristic path-recording assignment is believed to be an efficient and reliable method. Successful development of this heuristic assignment method helps solve those transportation problems which need assignment results at a real-time speed, and for which the assignment process lasts a couple of hours. Evacuation planning and operation are well suited to the application of this real-time heuristic assignment method. Evacuation planning and operations are major activities in emergency management. Evacuation planning instructs people where to go, which route to take, and the time needed to accomplish an evacuation. Evacuation operations help the execution of an evacuation plan in response to the changing nature of a disaster. The Integrated Evacuation Decision Support System (IEDSS) is a computer system which employs the evacuation planning model, MASSVAC2, and the evacuation operation model, HEUPRAE, to deal with evacuations. The IEDSS uses computer graphics to prepare input and interpret output. It helps a decision maker analyze the evacuation system, review evacuation plans, and issue an evacuation order at a proper time. Users of the IEDSS can work on evacuation problems in a friendly interactive visual environment. The application of the IEDSS to the hurricane and flood problems for the city of Virginia Beach shows how IEDSS is practically implemented. It proves the usefulness of the IEDSS in coping with disasters.
Ph. D.

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Erera, Alan L.; Committee Member: Ergun, Ozlem; Committee Member: Savelsbergh, Martin; Committee Member: Tetali, Prasad; Committee Member: White III, Chelsea C.. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This thesis considers three physician scheduling problems in health care systems. Specifically, we focus on improvements to current physician scheduling practices through the use of mathematical modeling. In the first part of the thesis, we present a physician shift scheduling problem focusing on maximizing continuity of care (i.e., ensuring that patients are familiar with their treating physicians, and vice versa). We develop an objective scoring method for measuring the continuity of a physician schedule and combine it with a mixed integer programming model. We apply our methods to the problem faced in the pediatric intensive care unit at Children's Healthcare of Atlanta at Egleston, and show that our schedule generation approach outperforms manual methods for schedule construction, both with regards to solution time and continuity. The next topic presented in this thesis focuses on two scheduling problems: (i) the assignment of residents to rotations over a one-year period, and given that assignment, (ii) the scheduling of residents' night and weekend shifts. We present an integer programming model for the assignment of residents to rotations such that residents of the same type receive similar educational experiences. We allow for flexible input of parameters and varying groups of residents and rotations without needing to alter the model constraints. We present a simple model for scheduling 1st-year residents to night and weekend shifts. We apply these approaches to problems faced in the Department of Surgery Residency Program at Emory University School of Medicine. Rotation assignment is made more efficient through automated schedule generation, and the shift scheduling model allows us to highlight infeasibilities that occur when shift lengths exceed a certain value, and we discuss the impact of duty hour restrictions under limitations of current scheduling practices. The final topic of this thesis focuses on the assignment of physicians to various tasks while promoting equity of assignments and maximizing space utilization. We present an integer programming model to solve this problem, and we apply this model to the physician scheduling problem faced in the Department of Gynecology and Obstetrics at Emory University Hospital and generate high quality solutions very quickly.

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering. University of the Witwatersrand, Johannesburg, 2016
Given a flight schedule with fixed departure times and cost, solving the fleet assignment problem assists airlines to find the minimum cost or maximum revenue assignment of aircraft types to flights. The result is that each flight is covered exactly once by an aircraft and the assignment can be flown using the available number of aircraft of each fleet type. This research proposes a novel, non-linear integer programming fleet assignment model which differs from the linear time-space multi-commodity network fleet assignment model which is commonly used in industry. The performance of the proposed model with respect to the amount of time it takes to create a flight schedule is measured. Similarly, the performance of the time-space multicommodity fleet assignment model is also measured. The objective function from both mathematical models is then compared and results reported. Due to the non-linearity of the proposed model, a genetic algorithm (GA) is used to find a solution. The time taken by the GA is slow. The objective function value, however, is the same as that obtained using the time-space multi-commodity network flow model. The proposed mathematical model has advantages in that the solution is easier to interpret. It also simultaneously solves fleet assignment as well as individual aircraft routing. The result may therefore aid in integrating more airline planning decisions such as maintenance routing.
MT2017

Ng Cho Yiu.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 70-74).
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgement --- p.iii
Preface --- p.x
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Multiple Access --- p.1
Chapter 1.1.1 --- Time Division Multiple Access --- p.2
Chapter 1.1.2 --- Frequency Division Multiple Access --- p.3
Chapter 1.1.3 --- Code Division Multiple Access --- p.3
Chapter 1.1.4 --- Hybrid Multiple Access Scheme --- p.4
Chapter 1.2 --- Goal Programming --- p.5
Chapter 2 --- Previous Works in Channel Assignment --- p.10
Chapter 2.1 --- Voice Service Network --- p.10
Chapter 2.2 --- Data Network --- p.11
Chapter 2.2.1 --- Throughput Optimization --- p.13
Chapter 2.2.2 --- Channel Assignment Schemes with QoS Consideration --- p.14
Chapter 3 --- General Channel Assignment Scheme --- p.16
Chapter 3.1 --- Baseline Model --- p.17
Chapter 3.2 --- Goal Ranking --- p.22
Chapter 3.3 --- Model Transformation --- p.22
Chapter 3.4 --- Proposed Algorithms --- p.23
Chapter 3.4.1 --- Channel Swapping Algorithm --- p.24
Chapter 3.4.2 --- Best-First-Assign Algorithm --- p.26
Chapter 4 --- Special Case Algorithms --- p.28
Chapter 4.1 --- Single Order of Selection Diversity --- p.28
Chapter 4.1.1 --- System Model --- p.29
Chapter 4.1.2 --- Proposed Algorithm --- p.30
Chapter 4.1.3 --- Extension of Algorithm --- p.31
Chapter 4.2 --- Single Channel Assignment --- p.32
Chapter 4.2.1 --- System Model --- p.33
Chapter 4.2.2 --- Proposed Algorithms --- p.34
Chapter 5 --- Performance Evaluation --- p.37
Chapter 5.1 --- General Channel Assignment and Single Channel Assignment --- p.37
Chapter 5.1.1 --- System Model --- p.38
Chapter 5.1.2 --- Lower Bound of Weighted Sum of Unsatisfactory Function --- p.40
Chapter 5.1.3 --- Performance Evaluation I --- p.41
Chapter 5.1.4 --- Discussion --- p.44
Chapter 5.1.5 --- Performance Evaluation II --- p.44
Chapter 5.2 --- Single Order of Selection Diversity Algorithm --- p.47
Chapter 5.2.1 --- System Model --- p.47
Chapter 5.2.2 --- Performance Evaluation I --- p.49
Chapter 5.2.3 --- Performance Evaluation II --- p.53
Chapter 6 --- Conclusion and Future Works --- p.58
Chapter 6.1 --- Conclusion --- p.58
Chapter 6.2 --- Future Works --- p.60
Chapter 6.2.1 --- Multi-cell Channel Assignment --- p.60
Chapter 6.2.2 --- Theoretical Studies --- p.62
Chapter 6.2.3 --- Adaptive Algorithms --- p.62
Chapter 6.2.4 --- Assignment of Non-orthogonal Channels --- p.63
Chapter A --- Proof of Proposition 3.1 --- p.64
Chapter B --- Proof of Proposition 4.1 --- p.66
Chapter C --- Assignment Problem --- p.68
Bibliography --- p.74

Kwan, Cheuk Lam.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.
Includes bibliographical references (p. 115-118).
Abstract also in Chinese.
Chapter 1 --- Introduction --- p.9
Chapter 1.1 --- The Gate Assignment Problem --- p.9
Chapter 1.2 --- Contributions --- p.10
Chapter 1.3 --- Formulation of Gate Assignment Problem --- p.11
Chapter 1.4 --- Organization of Thesis --- p.13
Chapter 2 --- Literature Review --- p.15
Chapter 2.1 --- Introduction --- p.15
Chapter 2.2 --- Formulations of Gate Assignment Problems --- p.15
Chapter 2.2.1 --- Static Gate Assignment Model --- p.16
Chapter 2.2.1.1 --- Total Passenger Walking Distance --- p.17
Chapter 2.2.1.2 --- Waiting Time --- p.20
Chapter 2.2.1.3 --- Unassigned Flights --- p.21
Chapter 2.2.2 --- Stochastic and Robust Gate Assignment Model --- p.22
Chapter 2.2.2.1 --- Idle Time --- p.22
Chapter 2.2.2.2 --- Buffer Time --- p.23
Chapter 2.2.2.3 --- Flight Delays --- p.23
Chapter 2.2.2.4 --- Gate Conflicts --- p.24
Chapter 2.3 --- Solution Methodologies --- p.25
Chapter 2.3.1 --- Expert System Approaches --- p.25
Chapter 2.3.2 --- Optimization --- p.27
Chapter 2.3.2.1 --- Exact Methods --- p.27
Chapter 2.3.2.2 --- Heuristic Approaches --- p.28
Chapter 2.3.2.3 --- Meta-Heuristics Approaches --- p.29
Chapter 2.3.2.4 --- Tabu Search and Path Relinking --- p.31
Chapter 2.4 --- Current Practice of Gate Assignment Problems --- p.32
Chapter 2.5 --- Summary --- p.32
Chapter 3 --- Tabu Search --- p.34
Chapter 3.1 --- Introduction --- p.34
Chapter 3.2 --- Mathematical Model --- p.34
Chapter 3.3 --- Principles of Tabu Search --- p.36
Chapter 3.4 --- Neighborhood Structures --- p.38
Chapter 3.4.1 --- Insert Move --- p.38
Chapter 3.4.2 --- Exchange Move --- p.39
Chapter 3.5 --- Short Term Memory Structure --- p.41
Chapter 3.6 --- Aspiration Criterion --- p.42
Chapter 3.7 --- Intensification and Diversification Strategies --- p.43
Chapter 3.8 --- Tabu Search Framework --- p.45
Chapter 3.8.1 --- Initial Solution --- p.45
Chapter 3.8.2 --- Tabu Search Algorithm --- p.46
Chapter 3.9 --- Computational Studies --- p.52
Chapter 3.9.1 --- Parameters Tuning --- p.52
Chapter 3.9.1.1 --- Fine-tuning a Tabu Search Algorithm with Statistical Tests --- p.53
Chapter 3.9.1.2 --- Tabu Tenure --- p.54
Chapter 3.9.1.3 --- Move Selection Strategies --- p.56
Chapter 3.9.1.4 --- Frequency of Exchange Moves --- p.59
Chapter 3.9.2 --- Comparison the Fine-tuned TS with original TS --- p.62
Chapter 3.10 --- Conclusions --- p.63
Chapter 4 --- Path Relinking --- p.65
Chapter 4.1 --- Introduction --- p.65
Chapter 4.2 --- Principles of Path Relinking --- p.65
Chapter 4.2.1 --- Example of Path Relinking --- p.66
Chapter 4.3 --- Reference Set --- p.68
Chapter 4.3.1 --- Two-Reference-Set Implementation --- p.71
Chapter 4.3.1.1 --- Random Exchange Gate Move --- p.72
Chapter 4.4 --- Initial and Guiding Solution --- p.73
Chapter 4.5 --- Path-Building Process --- p.74
Chapter 4.6 --- Tabu Search Framework with Path Relinking --- p.78
Chapter 4.6.1 --- Computational Complexities --- p.82
Chapter 4.7 --- Computational Studies --- p.82
Chapter 4.7.1 --- Best Configuration for Path Relinking --- p.83
Chapter 4.7.1.1 --- Reference Set Strategies and Initial and Guiding Criteria --- p.83
Chapter 4.7.1.2 --- Frequency of Path Relinking --- p.86
Chapter 4.7.1.3 --- Size of Volatile Reference Set --- p.87
Chapter 4.7.1.4 --- Size of Non-volatile Reference Set --- p.89
Chapter 4.7.2 --- Comparisons with Other Algorithms --- p.94
Chapter 5 --- Case Study --- p.98
Chapter 5.1 --- Introduction --- p.98
Chapter 5.2 --- Airport Background --- p.98
Chapter 5.2.1 --- Layout of ICN --- p.98
Chapter 5.3 --- Data Preparation --- p.99
Chapter 5.3.1 --- Passenger Data --- p.103
Chapter 5.4 --- Computational Studies --- p.104
Chapter 5.4.1 --- Experiments without Airline Preference --- p.104
Chapter 5.4.2 --- Experiments with Airline Preference --- p.106
Chapter 5.4.2.1 --- Formulation --- p.106
Chapter 5.4.2.2 --- Results --- p.108
Chapter 5.5 --- Conclusion --- p.111
Chapter 6 --- Conclusion --- p.112
Chapter 6.1 --- Summary of Achievement --- p.112
Chapter 6.2 --- Future Developments --- p.113
Bibliography --- p.115
Appendix --- p.119
Chapter 1. --- Friedman´ةs Test --- p.119
Chapter 2. --- Wilcoxon's Signed Rank Test for Paired Observation --- p.120
Chapter 3. --- Hybrid Simulated Annealing with Tabu Search Approach --- p.121
Chapter 4. --- Arrival Flight Data of Incheon International Airport --- p.122
Chapter 5. --- Departure Flight Data of Incheon International Airport --- p.139

Researchers in multiple areas have shown that characterizing and accounting for the uncertainty inherent in decision support models is critical for developing more efficient planning and operational strategies. This is particularly applicable for the transportation engineering domain as most strategic decisions involve a significant investment of money and resources across multiple stakeholders and has a considerable impact on the society. Moreover, most inputs to transportation models such as travel demand depend on a number of social, economic and political factors and cannot be predicted with certainty. Therefore, in recent times there has been an increasing emphasis being placed on identifying and quantifying this uncertainty and developing models which account for the same. This dissertation contributes to the growing body of literature in tackling uncertainty in transportation models by developing methodologies which address the uncertainty in input parameters in traffic assignment models. One of the primary sources of uncertainty in traffic assignment models is uncertainty in origin destination demand. This uncertainty can be classified into long term and short term demand uncertainty. Accounting for long term demand uncertainty is vital when traffic assignment models are used to make planning decisions like where to add capacity. This dissertation quantifies the impact of long term demand uncertainty by assigning multi-variate probability distributions to the demand. In order to arrive at accurate estimates of the expected future system performance, several statistical sampling techniques are then compared through extensive numerical testing to determine the most "efficient" sampling techniques for network assignment models. Two applications of assignment models, network design and network pricing are studied to illustrate the importance of considering long term demand uncertainty in transportation networks. Short term demand uncertainty such as the day-to-day variation in demand affect traffic assignment models when used to make operational decisions like tolling. This dissertation presents a novel new definition of equilibrium when the short term demand is assumed to follow a probability distribution. Various properties of the equilibrium such as existence, uniqueness and presence of a mathematical programming formulation are investigated. Apart from demand uncertainty, operating capacity in real world networks can also vary from day to day depending on various factors like weather conditions and incidents. With increasing deployment of Intelligent Transportation Systems, users get information about the impact of capacity or the state of the roads through various dissemination devices like dynamic message signs. This dissertation presents a new equilibrium formulation termed user equilibrium with recourse to model information provision and capacity uncertainty, where users learn the state or capacity of the link when they arrive at the upstream node of that link. Depending on the information received about the state of the upstream links, users make different route choice decisions. In this work, the capacity of the links in the network is assumed to follow a discrete probability distribution. A mathematical programming formulation of the user equilibrium with recourse model is presented along with solution algorithm. This model can be extended to analytically model network flows under information provision where the arcs have different cost functional form depending on the state of the arc. The corresponding system optimal with recourse model is also presented where the objective is minimize the total system cost. The network design problem where users are routed according to the user equilibrium with recourse principle is studied. The focus of this study is to show that planning decisions for networks users have access to information is significantly different from the no-information scenario.
text

Braess' paradox is a counter-intuitive phenomenon which can occur in congesting networks. It refers to those cases where the introduction of a new link in the network results in the total travel time on the network increasing. The dissertation starts by introducing the traffic assignment problem and the concept of equilibrium in traffic assignment. The concept of equilibrium is based on Wardrop's first principle that all travellers will attempt to minimize their own travel time regardless of the effect on others. A literature review includes details of a number of papers that have been published investigating theoretical aspects of the paradox. There is also a brief description of Game Theory and the Nash Equilibrium. It has been shown that the equilibrium assignment is an example of Nash Equilibrium. The majority of work that has been published deals with networks where the delay functions that are used to compute the travel times on the links of the network do not include explicit representation of the capacity of the links. In this dissertation a network that is similar in form to the one first presented by Braess was constructed with the difference being that the well-known BPR function was used in the delay functions. This network was used to show that a number of findings that had been presented previously using simpler functions also applied to this network. It was shown that when it occurs, Braess' paradox only occurs over a range of values at relatively low levels of congestion. Real-world networks were then investigated and it was found that similar results occurred to those found in the simpler test networks that are often used in discussions of the paradox. Two methodologies of eliminating the paradox were investigated and the results are presented.
Decision Sciences
M.Sc.