A strategic timing of arrivals to a linear slowdown processor sharing system

Liron Ravner, Moshe Haviv, Hai L. Vu

Research output: Contribution to journalArticlepeer-review


We consider a discrete population of users with homogeneous service demand who need to decide when to arrive to a system in which the service rate deteriorates linearly with the number of users in the system. The users have heterogeneous desired departure times from the system, and their goal is to minimise a weighted sum of the travel time and square deviation from the desired departure times. Users join the system sequentially, according to the order of their desired departure times. We model this scenario as a non-cooperative game in which each user selects his actual arrival time. We present explicit equilibria solutions for a two-user example, namely the Subgame Perfect and Cournot Nash equilibria and show that multiple equilibria may exist. We further explain why a general solution for any number of users is computationally challenging. The difficulty lies in the fact that the objective functions are piecewise-convex, i.e., non-smooth and non-convex. As a result, the minimisation of the costs relies on checking all arrival and departure order permutations, which is exponentially large with respect to the population size. Instead we propose an iterated best-response algorithm which can be efficiently studied numerically. Finally, we compare the equilibrium arrival profiles to a socially optimal solution and discuss the implications.

Original languageEnglish
Pages (from-to)496-504
Number of pages9
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - 1 Dec 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


  • Arrival time game
  • Linear slowdown
  • Piecewise-convex programming
  • Processor sharing
  • Sequential timing game

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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