Paris Metro Pricing (PMP) is a simple multi-class flat-rate pricing scheme already practiced by transport systems, specifically by the Paris Metro at one time. The name is coined after Andrew Odlyzko proposed it for the Internet as a simple way to provide differentiated services. Subsequently, there were several analytical studies of this promising idea. The central issue of these studies is whether PMP is viable, namely, whether it will produce more profit for the service provider, or whether it will achieve more social welfare. The previous studies considered similar models, but arrived at different conclusions. In this paper, we point out that the key is how the users react to the congestion externality of the underlying system. We derive sufficient conditions of congestion functions that can guarantee the viability of PMP, and provide the relevant physical meanings of these conditions.

Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generations. Two recent trends in microgrids are the integration of local renewable energy sources (such as wind farms) and the use of co-generation (i.e., to supply both electricity and heat). However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids. Traditional generation scheduling paradigms rely on perfect prediction of future electricity supply and demand. They are no longer applicable to microgrids with unpredictable renewable energy supply and with co-generation (that needs to consider both electricity and heat demand). In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation. Based on the insights from the structure of the offline optimal solution, we propose a class of competitive online algorithms, called CHASE (Competitive Heuristic Algorithm for Scheduling Energy-generation), that track the offline optimal in an online fashion. Under typical settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms, and the ratio is no larger than a small constant 3. We also extend our algorithms to intelligently leverage on limited prediction of the future, such as near-term demand or wind forecast. By extensive empirical evaluations using real-world traces, we show that our proposed algorithms can achieve near offline-optimal performance. In a representative scenario, CHASE leads to around * The first two authors are in alphabetical order.20% cost reduction with no future look-ahead, and the cost reduction increases with the future look-ahead window.

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In the literature, asymptotic studies of multi-hop wireless network capacity often consider only centralized and deterministic TDMA (time-division multi-access) coordination schemes. There have been fewer studies of the asymptotic capacity of large-scale wireless networks based on CSMA (carriersensing multi-access), which schedules transmissions in a distributed and random manner. With the rapid and widespread adoption of CSMA technology, a critical question is that whether CSMA networks can be as scalable as TDMA networks. To answer this question and explore the capacity of CSMA networks, we first formulate the models of CSMA protocols to take into account the unique CSMA characteristics not captured by existing interference models in the literature. These CSMA models determine the feasible states, and consequently the capacity of CSMA networks. We then study the throughput efficiency of CSMA scheduling as compared to TDMA. Finally, we tune the CSMA parameters so as to maximize the throughput to the optimal order. As a result, we show that CSMA can achieve throughput as Ω( 1 √ n ), the same order as optimal centralized TDMA, on uniform random networks. Our CSMA scheme makes use of an efficient backbone-peripheral routing scheme and a careful design of dual carrier-sensing and dual channel scheme. We also address the implementation issues of our CSMA scheme.