  In the paper, we consider delay-optimal charging scheduling of the electric
vehicles (EVs) at a charging station with multiple charge points. The charging
station is equipped with renewable energy generation devices and can also buy
energy from power grid. The uncertainty of the EV arrival, the intermittence of
the renewable energy, and the variation of the grid power price are taken into
account and described as independent Markov processes. Meanwhile, the charging
energy for each EV is random. The goal is to minimize the mean waiting time of
EVs under the long term constraint on the cost. We propose queue mapping to
convert the EV queue to the charge demand queue and prove the equivalence
between the minimization of the two queues' average length. Then we focus on
the minimization for the average length of the charge demand queue under long
term cost constraint. We propose a framework of Markov decision process (MDP)
to investigate this scheduling problem. The system state includes the charge
demand queue length, the charge demand arrival, the energy level in the storage
battery of the renewable energy, the renewable energy arrival, and the grid
power price. Additionally the number of charging demands and the allocated
energy from the storage battery compose the two-dimensional policy. We derive
two necessary conditions of the optimal policy. Moreover, we discuss the
reduction of the two-dimensional policy to be the number of charging demands
only. We give the sets of system states for which charging no demand and
charging as many demands as possible are optimal, respectively. Finally we
investigate the proposed radical policy and conservative policy numerically.
