The Power of Migration for Online Slack Scheduling

We investigate the power of migration in online scheduling for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. Once we decide to accept a job, we have to complete it before its deadline d that satisfies d >= (1+epsilon)p + r, where p is the processing time, r the submission time and the slack epsilon > 0 a system parameter. Typically, the hard case arises for small slack epsilon << 1, i.e. for near-tight deadlines. Without migration, a greedy acceptance policy is known to be an optimal deterministic online algorithm with a competitive factor of (1+epsilon)/epsilon (DasGupta and Palis, APPROX 2000). Our first contribution is to show that migrations do not improve the competitive ratio of the greedy acceptance policy, i.e. the competitive ratio remains (1+epsilon)/epsilon for any number of machines. Our main contribution is a deterministic online algorithm with almost tight competitive ratio on any number of machines. For a single machine, the competitive factor matches the optimal bound of (1+epsilon)/epsilon of the greedy acceptance policy. The competitive ratio improves with an increasing number of machines. It approaches (1+epsilon) ln((1+epsilon)/epsilon) as the number of machines converges to infinity. This is an exponential improvement over the greedy acceptance policy for small epsilon. Moreover, we show a matching lower bound on the competitive ratio for deterministic algorithms on any number of machines

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;

New utilization criteria for online scheduling

In the classical scheduling problems, it has been assumed that complete knowledge of the problem was available when it was to be solved. However, scheduling problems in the real world face the possibility of the lack of the knowledge. Uncertainties frequently encountered in scheduling environments include the appearance of new jobs and unknown processing times. In this work, we take into account these realistic issues. This thesis deals with the problem of non-preemptive scheduling independent jobs on m identical parallel machines. In our online model, the jobs are submitted over time non-clairvoyantly. Therefore, the processing times of the jobs are unknown until they complete. Further, we assume that the ratio of weight to processing time is equal for all jobs, that is, all jobs have the same priorities. The jobs are assigned to the machines in a nondelay fashion. Our main scheduling objective is to maximize the utilization of the system. We show that the commonly used makespan criterion usually cannot reflect the true utilization of this kind of online scheduling problems. For this reason, it is very important to find another criterion capable of evaluating system utilization. Therefore, we introduce two new alternative criteria that more accurately capture the utilization of the machines. Moreover, we derive competitive factors for both criteria. Those competitive factors are tight for one criterion and almost tight for the other. Finally, we present an experimental investigation to evaluate the performance of the nondelay online algorithm with respect to our criteria. The experimental results show the confirmation of our theoretical results

Efficiency and fairness in ambulance planning

Mei, R.D. van der [Promotor]Bhulai, S. [Promotor

Generalized Incremental Mechanisms for Scheduling Games

We study the problem of devising truthful mechanisms for cooperative cost sharing games that realize (approximate) budget balance and social cost. Recent negative results show that group-strategyproof mechanisms can only achieve very poor approximation guarantees for several fundamental cost sharing games. Driven by these limitations, we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness. Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently introduced the broad class of weakly group-strategyproof acyclic mechanisms and show that several primal-dual approximation algorithms naturally give rise to such mechanisms with attractive approximation guarantees. In this paper, we provide a simple yet powerful approach that enables us to turn any r-approximation algorithm into a r-budget balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving weakly group-strategyproof mechanisms for several fundamental scheduling problems that outperform the best possible approximation guarantees of Moulin mechanisms. The mechanisms that we develop for completion time scheduling problems are the first mechanisms that achieve constant budget balance and social cost approximation factors. Interestingly, our mechanisms belong to the class of generalized incremental mechanisms proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]