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Decentralized throughput scheduling. (English) Zbl 1384.90052
Spirakis, Paul G. (ed.) et al., Algorithms and complexity. 8th international conference, CIAC 2013, Barcelona, Spain, May 22–24, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-38232-1/pbk). Lecture Notes in Computer Science 7878, 134-145 (2013).
Summary: Motivated by the organization of distributed service systems, we study models for throughput scheduling in a decentralized setting. In throughput scheduling, a set of jobs $$j$$ with values $$w _{j }$$, processing times $$p _{ij }$$ on machine $$i$$, release dates $$r _{j }$$ and deadlines $$d _{j }$$, is to be processed non-preemptively on a set of unrelated machines. The goal is to maximize the total value of jobs scheduled within their time window $$[r _{j },d _{j }]$$. While approximation algorithms with different performance guarantees exist for this and related models, we are interested in the situation where subsets of machines are governed by selfish players. We give a universal result that bounds the price of decentralization: Any local $$\alpha$$-approximation algorithm, $$\alpha \geq 1$$, yields Nash equilibria that are at most a factor ($$\alpha + 1$$) away from the global optimum, and this bound is tight. For identical machines, we improve this bound to $$\root\alpha\of e/(\root\alpha\of e-1)\approx (\alpha+1/2)$$, which is shown to be tight, too. The latter result is obtained by considering subgame perfect equilibria of a corresponding sequential game. We also address some variations of the problem.
For the entire collection see [Zbl 1263.68023].

##### MSC:
 90B35 Deterministic scheduling theory in operations research 68W25 Approximation algorithms 91A10 Noncooperative games
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