We introduce and study a general version of the fractional online knapsack problem with multiple knapsacks, heterogeneous constraints on which items can be assigned to which knapsack, and rate-limiting constraints on the assignment of items to knapsacks. This problem generalizes variations of the knapsack problem and of the one-way trading problem that have previously been treated separately, and additionally finds application to the real-time control of electric vehicle (EV) charging. We introduce a new algorithm that achieves a competitive ratio within an additive factor of one of the best achievable competitive ratios for the general problem and matches or improves upon the best-known competitive ratio for special cases in the knapsack and one-way trading literatures. Moreover, our analysis provides a novel approach to online algorithm design based on an instance-dependent primal-dual analysis that connects the identification of worst-case instances to the design of algorithms. Finally, we illustrate the proposed algorithm via trace-based experiments of EV charging.
By employing local renewable energy sources and power generation units while connected to the central grid, microgrid can usher in great benefits in terms of cost efficiency, power reliability, and environmental awareness. Economic dispatching is a central problem in microgrid operation, which aims at effectively scheduling various energy sources to minimize the operating cost while satisfying the electricity demand. Designing intelligent economic dispatching strategies for microgrids, however, is drastically different from that for conventional central grids, due to two unique challenges. First, the demand and renewable generation uncertainty emphasizes the need for online algorithms. Second, the widely-adopted peakbased pricing scheme brings out the need for new peak-aware strategy design. In this paper, we tackle these critical challenges and devise peak-aware online economic dispatching algorithms. We prove that our deterministic and randomized algorithms achieve the best possible competitive ratios 2−β and e/(e−1+β) in the fast responding generator scenario, where β ∈ [0, 1] is the ratio between the minimum grid spot price and the localgeneration price. By extensive empirical evaluations using realworld traces, we show that our online algorithms achieve near offline-optimal performance. In a representative scenario, our algorithm achieves 17.5% and 9.24% cost reduction as compared to the case without local generation units and the case using peak-oblivious algorithms, respectively.
NOTATIONSThis section lists the main notations used in this paper. e(t) The net electricity demand at time t in KWh. u(t) The amount of energy generated by local generators at time t in KWh. v(t) The amount of energy purchased from electricity grid at time t in KWh. p e (t) The spot price of the electricity from grid at time t in $/KWh. p min e Minimum spot price of the electricity from grid, min t p e (t). p gThe unit cost of the electricity by local generators in $/KWh. β Ratio between p min e and p g .
This paper tackles online scheduling of electric vehicles (EVs) in an adaptive charging network (ACN) with local and global peak constraints. Given the aggregate charging demand of the EVs and the peak constraints of the ACN, it might be infeasible to fully charge all the EVs according to their charging demand. Two alternatives in such resource-limited scenarios are to maximize the social welfare by partially charging the EVs (fractional model) or selecting a subset of EVs and fully charge them (integral model). The technical challenge is the need for online solution design since in practical scenarios the scheduler has no or limited information of future arrivals in a time-coupled underlying problem. For the fractional model, we devise both offline and online algorithms. We prove that the offline algorithm is optimal. Using competitive ratio as the performance measure, we prove the online algorithm achieves a competitive ratio of 2. The integral model, however, is more challenging since the underlying problem is strongly NP-hard due to 0/1 selection criteria of EVs. Hence, efficient solution design is challenging even in offline setting. For offline setting, we devise a low-complexity primal-dual scheduling algorithm that achieves a bounded approximation ratio. Built upon the offline approximate algorithm, we propose an online algorithm and analyze its competitive ratio in special cases. Extensive trace-driven experimental results show that the performance of the proposed online algorithms is close to the offline optimum, and outperform the existing solutions.
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