Measuring the efficiency of decision making units

This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2600523.pdf

Rate control for communication networks: shadow prices, proportional fairness and stability

1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

/pdf/convex-bodies-the-brunn-minkowski-theory-3raynvod45.pdf

Convex bodies : the Brunn-Minkowski theory

Increasing Returns and Path Dependence in the Economy

Increasing risk: I. A definition

General competitive analysis , General competitive analysis , کتابخانه دانشگاه امام صادق(ع)

General competitive analysis

Our purpose is to survey the contributions that have been made to the theory of economic growth in the last twenty-five years and endeavour to place them in relation to one another. It will be clear that the survey cannot hope to cover all of growth economics. We have accordingly restricted ourselves in the following ways: (1) We take up the story with Harrod’s famous article of 1939 and make no attempt to cover writings before this date. The seriousness of this omission is evident when one recalls that this decision not only excludes the classical economists but also Wicksell, Marshall, Robertson and Cassel. (2) We restrict ourselves (except for occasional references) to the theoretical literature. Our central concern is with models of economic growth. The authors of these models have naturally had in mind as a rule that their work should contribute to an understanding of the way economies actually grow over time; but this approach to growth theory is none the less different from that which would be used if the immediate purpose was to provide the best available explanation of the variety of historical growth experiences.2 (3) While it has been found appropriate to give some summary of results in the theory of efficient accumulation, the problems of optimum saving and the development of backward countries have not been considered. (4) No discussion is presented of growth theory as applied to international trade.

The Theory of Economic Growth: A Survey

On the basis of theoretical considerations and on the evidence of real-world economies, Frank Hahn demonstrates in unequivocal terms that Monetarism offers an implausible solution to the most pervasive economic problems. He confronts the central issue of current economic theory by making the case that the growth of the money supply is not a necessary cause of inflation, as the Monetarists have assumed. And he contends that inflation is in any case not the overwhelming satanic force disrupting society and the economy that the strict Monetarists think it to be on theoretical grounds and so many others feel it to be in terms of practical economic realities. It is the tax systems, he points out, that are the real influence at work against the economies of the industrialized nations.Frank Hahn, one of Britain's most eminent economists, is Professor of Economics at Cambridge University and author of Equilibrium and Macroeconomics (MIT Press 1985).

Frank Hahn

Papers

General competitive analysis

The Theory of Economic Growth: A Survey

Money and inflation

The Theory of Interest Rates

The Stability of the Cournot Oligopoly Solution