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)


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.


Cost Function Utility Function Fair Share Equilibrium Allocation Quadratic Cost Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Damon Mosk-Aoyama
    • 1
  • Tim Roughgarden
    • 1
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA

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