ICALP 2009: Automata, Languages and Programming pp 546-557

# Worst-Case Efficiency Analysis of Queueing Disciplines

• Damon Mosk-Aoyama
• Tim Roughgarden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5556)

## Abstract

Consider n users vying for shares of a divisible good. Every user i wants as much of the good as possible but has diminishing returns, meaning that its utility U i (x i ) for x i  ≥ 0 units of the good is a nonnegative, nondecreasing, continuously differentiable concave function of x i . The good can be produced in any amount, but producing $$X = \sum_{i=1}^n x_i$$ units of it incurs a cost C(X) for a given nondecreasing and convex function C that satisfies C(0) = 0. Cost might represent monetary cost, but other interesting interpretations are also possible. For example, x i could represent the amount of traffic (measured in packets, say) that user i injects into a queue in a given time window, and C(X) could denote aggregate delay (X ·c(X), where c(X) is the average per-unit delay). An altruistic designer who knows the utility functions of the users and who can dictate the allocation x = (x 1,...,x n ) can easily choose the allocation that maximizes the welfare $$W(x) = \sum_{i=1}^n U_i(x_i) - C(X)$$, where $$X = \sum_{i=1}^n x_i$$, since this is a simple convex optimization problem.

## Keywords

Cost Function Utility Function Fair Share Equilibrium Allocation Quadratic Cost Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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