Online Mechanism Design for Scheduling Non-Preemptive Jobs under Uncertain Supply and Demand

ABSTRACT We design new algorithms for the problem of allocating uncertain, flexible, and multi-unit demand online given uncertain supply, in order to maximise social welfare. The algorithms can be seen as extensions of the expectation and consensus algorithms from the domain of online scheduling. The problem is especially relevant to the future smart grid, where uncertain output from renewable generators and conventional supply need to be integrated and matched to flexible, non-preemptive demand. To deal with uncertain supply and demand, the algorithms generate multiple scenarios which can then be solved offline. Furthermore, we use a novel method of reweighting the scenarios based on their likelihood whenever new information about supply becomes available. An additional improvement allows the selection of multiple non-preemptive jobs at the same time. Finally, our main contribution is a novel online mechanism based on these extensions, where it is in the agents' best interest to truthfully reveal their preferences. The experimental evaluation of the extended algorithms and different variants of the mechanism show that both achieve more than 85% of the offline optimal economic efficiency. Importantly, the mechanism yields comparable efficiency, while, in contrast to the algorithms, it allows for strategic agents

Average-case Approximation Ratio of Scheduling without Payments

Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem [Nisan and Ronen 1999]. One version of this problem which includes a verification component is studied by [Koutsoupias 2014]. It was shown that the problem has a tight approximation ratio bound of (n+1)/2 for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given in [Koutsoupias 2014] is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio, and indicates that the optimal mechanism for the problem actually works well on average, although in the worst-case the expected cost of the mechanism is Theta(n) times that of the optimal cost

A deterministic truthful PTAS for scheduling related machines

Scheduling on related machines ($Q||C_{\max}$) is one of the most important problems in the field of Algorithmic Mechanism Design. Each machine is controlled by a selfish agent and her valuation can be expressed via a single parameter, her {\em speed}. In contrast to other similar problems, Archer and Tardos \cite{AT01} showed that an algorithm that minimizes the makespan can be truthfully implemented, although in exponential time. On the other hand, if we leave out the game-theoretic issues, the complexity of the problem has been completely settled -- the problem is strongly NP-hard, while there exists a PTAS \cite{HS88,ES04}. This problem is the most well studied in single-parameter algorithmic mechanism design. It gives an excellent ground to explore the boundary between truthfulness and efficient computation. Since the work of Archer and Tardos, quite a lot of deterministic and randomized mechanisms have been suggested. Recently, a breakthrough result \cite{DDDR08} showed that a randomized truthful PTAS exists. On the other hand, for the deterministic case, the best known approximation factor is 2.8 \cite{Kov05,Kov07}. It has been a major open question whether there exists a deterministic truthful PTAS, or whether truthfulness has an essential, negative impact on the computational complexity of the problem. In this paper we give a definitive answer to this important question by providing a truthful {\em deterministic} PTAS

Integrating Consumer Flexibility in Smart Grid and Mobility Systems - An Online Optimization and Online Mechanism Design Approach

Consumer flexibility may provide an important lever to align supply and demand in service systems. However, harnessing dispersed flexibility endowments in the presence of self-interested agents requires appropriate incentive structures. This thesis quantifies the potential value of consumers\u27 flexibility in smart grid and mobility systems. In order to include incentives, online optimization approaches are augmented with methods from online mechanism design

Truthful Mechanisms For Real-Time System Scheduling In Competitive Environments

In a non-competitive environment, sporadic real-time task scheduling on a single processor is well understood. In this thesis, we consider a competitive environment comprising several real-time tasks vying for execution upon a shared single processor. Each task obtains a value if the processor successfully schedules all its jobs. Our objective is to select a feasible subset of these tasks to maximize the sum of values of selected tasks. We consider both dynamic-priority and static-priority scheduling algorithms. There are algorithms for solving these problems in non-competitive settings. However, we consider these problems in an economic setting in which each task is owned by a selfish agent. Each agent reports the characteristics of her own task to the processor owner. The processor owner uses a mechanism to allocate the processor to a subset of agents and to determine the payment of each agent. Since agents are selfish, they may try to manipulate the mechanism to obtain the processor. We are interested in truthful mechanisms in which it is always in agents\u27 best interest to report the true characteristics of their tasks. We design exact and approximate truthful mechanisms for this competitive environment and study their performance

Minimizing Maximum Flow Time on Related Machines via Dynamic Posted Pricing

We consider a setting where selfish agents want to schedule jobs on related machines. The agent submitting a job picks a server that minimizes a linear combination of the server price and the resulting response time for that job on the selected server. The manager\u27s task is to maintain server prices to (approximately) optimize the maximum response time, which is a measure of social good. We show that the existence of a pricing scheme with certain competitiveness is equivalent to the existence of a monotone immediate-dispatch algorithm. Our main result is a monotone immediate-dispatch algorithm that is O(1)-competitive with respect to the maximum response time