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Network Utility Maximization (NUM) Theory
Published in Liansheng Tan, Resource Allocation and Performance Optimization in Communication Networks and the Internet, 2017
In microeconomic theory, an indifference curve [135] is a graph showing different bundles of goods between which a consumer is indifferent in terms of utility. That is, at each point on the curve, the consumer has no preference for one bundle over another. One can equivalently refer to each point on the indifference curve as outputting the same degree of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles [136].
A day-to-day dynamic evolution model and pricing scheme with bi-objective user equilibrium
Published in Transportmetrica B: Transport Dynamics, 2021
Xiaoyu Ma, Wei Xu, Caihua Chen
Here is a nonlinear function strictly increasing with toll and determined by the indifference curve of travel time and toll. The indifference curve is a concept from economics, which is a graph showing all the combinations of two commodities that give a consumer equal satisfaction and utility. In this study, the indifference curve is applied to represent the combinations of time and toll. That is, along a given indifference curve, though each point represents a different combination of time and toll, all of them bring the same level of utility to the travelers. For example, on the indifference curve given in Figure 1, let point A represent a path with and , and point B a path with and . Then, for the travelers owning this indifference curve, path A and path B are equally attractive to them. Wang and Ehrgott (2013) have showed that given a monotone function (i.e. given an indifference curve), the above optimization problem (2) is strictly convex and its optimal solution is a BUE solution.