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This paper considers a network problem in charging infrastructure for electric vehicles (EVs). It generally takes a longer time to charge the empty battery of an EV than refueling of gasoline vehicles. It is not easy to actually reduce the waiting time for charging. However, if charging is done during shopping or eating, the charging time is no longer the waiting time. Of course, we may sometimes have to wait a longer time to charge batteries than shopping time to prevent running out of the batteries during the next drive. This means that we have a trade off between the extra waiting time and possibility to run out of battery. In this paper, we theoretically consider properties of this trade off and theoretically analyze characteristics of the extra waiting time needed to guarantee that an EV does not run out of battery in a drive. We discuss effects of some factors such as density of charging stations, the number of outlets in each station, the number of waiting cars, and so on.