Competitive Charging Station Pricing for Plug-in Electric Vehicles

This paper considers the problem of charging station pricing and plug-in electric vehicles (PEVs) station selection. When a PEV needs to be charged, it selects a charging station by considering the charging prices, waiting times, and travel distances. Each charging station optimizes its charging price based on the prediction of the PEVs' charging station selection decisions and the other station's pricing decision, in order to maximize its profit. To obtain insights of such a highly coupled system, we consider a one-dimensional system with two competing charging stations and Poisson arriving PEVs. We propose a multi-leader-multi-follower Stackelberg game model, in which the charging stations (leaders) announce their charging prices in Stage I, and the PEVs (followers) make their charging station selections in Stage II. We show that there always exists a unique charging station selection equilibrium in Stage II, and such equilibrium depends on the charging stations' service capacities and the price difference between them. We then characterize the sufficient conditions for the existence and uniqueness of the pricing equilibrium in Stage I. We also develop a low complexity algorithm that efficiently computes the pricing equilibrium and the subgame perfect equilibrium of the two-stage Stackelberg game.Comment: 15 pages, 21 figure

Empirical metallicity-dependent calibrations of effective temperature against colours for dwarfs and giants based on interferometric data

We present empirical metallicity-dependent calibrations of effective temperature against colours for dwarfs of luminosity classes IV and V and for giants of luminosity classes II and III, based on a collection from the literature of about two hundred nearby stars with direct effective temperature measurements of better than 2.5 per cent. The calibrations are valid for an effective temperature range 3,100 - 10,000 K for dwarfs of spectral types M5 to A0 and 3,100 - 5,700 K for giants of spectral types K5 to G5. A total of twenty-one colours for dwarfs and eighteen colours for giants of bands of four photometric systems, i.e. the Johnson ($UBVR_{\rm J}I_{\rm J}JHK$), the Cousins ($R_{\rm C}I_{\rm C}$), the Sloan Digital Sky Survey (SDSS, $gr$) and the Two Micron All Sky Survey (2MASS, $JHK_{\rm s}$), have been calibrated. Restricted by the metallicity range of the current sample, the calibrations are mainly applicable for disk stars ([Fe/H]$\,\gtrsim\,-1.0$). The normalized percentage residuals of the calibrations are typically 2.0 and 1.5 per cent for dwarfs and giants, respectively. Some systematic discrepancies at various levels are found between the current scales and those available in the literature (e.g. those based on the infrared flux method IRFM or spectroscopy). Based on the current calibrations, we have re-determined the colours of the Sun. We have also investigated the systematic errors in effective temperatures yielded by the current on-going large scale low- to intermediate-resolution stellar spectroscopic surveys. We show that the calibration of colour ($g-K_{\rm s}$) presented in the current work provides an invaluable tool for the estimation of stellar effective temperature for those on-going or upcoming surveys.Comment: 28 pages, 19 figures, 8 tables, accepted for publication in MNRA