562 research outputs found
Non-clairvoyant Scheduling Games
In a scheduling game, each player owns a job and chooses a machine to execute
it. While the social cost is the maximal load over all machines (makespan), the
cost (disutility) of each player is the completion time of its own job. In the
game, players may follow selfish strategies to optimize their cost and
therefore their behaviors do not necessarily lead the game to an equilibrium.
Even in the case there is an equilibrium, its makespan might be much larger
than the social optimum, and this inefficiency is measured by the price of
anarchy -- the worst ratio between the makespan of an equilibrium and the
optimum. Coordination mechanisms aim to reduce the price of anarchy by
designing scheduling policies that specify how jobs assigned to a same machine
are to be scheduled. Typically these policies define the schedule according to
the processing times as announced by the jobs. One could wonder if there are
policies that do not require this knowledge, and still provide a good price of
anarchy. This would make the processing times be private information and avoid
the problem of truthfulness. In this paper we study these so-called
non-clairvoyant policies. In particular, we study the RANDOM policy that
schedules the jobs in a random order without preemption, and the EQUI policy
that schedules the jobs in parallel using time-multiplexing, assigning each job
an equal fraction of CPU time
The Price of Anarchy for Minsum Related Machine Scheduling
We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e-1). This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature
Games and Mechanism Design in Machine Scheduling – An Introduction
In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;
A Distributed Demand-Side Management Framework for the Smart Grid
This paper proposes a fully distributed Demand-Side Management system for
Smart Grid infrastructures, especially tailored to reduce the peak demand of
residential users. In particular, we use a dynamic pricing strategy, where
energy tariffs are function of the overall power demand of customers. We
consider two practical cases: (1) a fully distributed approach, where each
appliance decides autonomously its own scheduling, and (2) a hybrid approach,
where each user must schedule all his appliances. We analyze numerically these
two approaches, showing that they are characterized practically by the same
performance level in all the considered grid scenarios. We model the proposed
system using a non-cooperative game theoretical approach, and demonstrate that
our game is a generalized ordinal potential one under general conditions.
Furthermore, we propose a simple yet effective best response strategy that is
proved to converge in a few steps to a pure Nash Equilibrium, thus
demonstrating the robustness of the power scheduling plan obtained without any
central coordination of the operator or the customers. Numerical results,
obtained using real load profiles and appliance models, show that the
system-wide peak absorption achieved in a completely distributed fashion can be
reduced up to 55%, thus decreasing the capital expenditure (CAPEX) necessary to
meet the growing energy demand
Coordinating selfish players in scheduling games
We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the makespan. It was raised as an open question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. Next we introduce multi-job players that control a set of jobs, with the aim of minimizing the sum of the completion times of theirs jobs. In this setting, previous mechanisms designed for players with single jobs are inadequate, e.g., having large price of anarchy, or not guaranteeing pure Nash equilibria. To meet this challenge, we design three mechanisms that induce pure Nash equilibria while guaranteeing relatively small price of anarchy.
Then we consider multi-job players where each player\u27s objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players\u27 costs. We first prove that if machines order jobs according to Smith-rule, then the coordination ratio is at most 4, moreover this is best possible among non-preemptive policies. Then we design a preemptive policy, em externality that has coordination ratio 2.618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. An interesting consequence of our results is that an local optima of for the jump neighborhood can be found in polynomial time and is within a factor of 2.618 of the optimal solution.Wir betrachten Koordinationsmechanismen um n Jobs auf m Maschinen mit individuellen Bearbeitungszeiten zu verteilen. Ziel dabei ist es den Makespan zu minimieren. Es war eine offene Frage, ob es möglich ist einen preämptiven Koordinationsmechanismus zu entwickeln, der einen konstanten Price of Anarchy hat. Wir beantworten diese Frage im negativen Sinne. Als nächstes führen wir Multi-Job-Spieler ein, die eine Menge von Jobs kontrollieren können, mit dem Ziel die Summe der Fertigstellungszeiten ihrer Jobs zu minimieren. In diesem Szenario sind bekannte Mechanismen, die für Ein-Job-Spieler entworfen worden sind, nicht gut genug, und haben beispielsweise einen hohen Price of Anarchy oder können kein reines Nash Gleichgewicht garantieren. Wir entwickeln drei Mechanismen die jeweils ein reines Nash Gleichgewicht besitzen, und einen relativ kleinen Price of Anarchy haben.
Zusätzlich betrachten wir Multi-Job-Spieler, mit dem Ziel jeweils die gewichtete Summe der Fertigstellungszeiten ihrer Jobs zu minimieren, während die Gesamtkosten die Summe der Kosten der Spieler sind. Wir zeigen zuerst, dass das Koordinationsverhältnis höchstens ist, wenn die Maschinen die Jobs nach der Smith-Regel sortieren, was bei nicht-preämptiven Verfahren optimal ist. Danach entwickeln wir ein preämptives Verfahren, Externality, welches ein Koordinationsverhältnis von 2.618 hat, und ergänzen dieses Ergebniss indem wir beweisen, dass dieses Verhältnis optimal ist, auch für den Fall, dass wir Randomisierung oder volle Information erlauben. Eine interessante Folge unserer Ergebnisse ist, dass ein -lokales Optimum von für die Jump-Neighborhood in Polynomialzeit gefunden werden kann, und innerhalb eines Faktors von 2.618 von der optimalen Lösung ist
Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms
We reconsider the well-studied Selfish Routing game with affine latency
functions. The Price of Anarchy for this class of games takes maximum value
4/3; this maximum is attained already for a simple network of two parallel
links, known as Pigou's network. We improve upon the value 4/3 by means of
Coordination Mechanisms.
We increase the latency functions of the edges in the network, i.e., if
is the latency function of an edge , we replace it by
with for all . Then an
adversary fixes a demand rate as input. The engineered Price of Anarchy of the
mechanism is defined as the worst-case ratio of the Nash social cost in the
modified network over the optimal social cost in the original network.
Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified
network for rate and \Copt(r) denotes the cost of the optimal flow in the
original network for the same rate then [\ePoA = \max_{r \ge 0}
\frac{\CM(r)}{\Copt(r)}.]
We first exhibit a simple coordination mechanism that achieves for any
network of parallel links an engineered Price of Anarchy strictly less than
4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25.
Then, for the case of two parallel links, we describe an optimal mechanism; its
engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201
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