We consider a queuing model with applications to electric vehicle (EV) charging systems in smart grids. We adopt a scheme where an Electric Service Company (ESCo) broadcasts a one bit signal to EVs, possibly indicating ‘on-peak’ periods during which electricity cost is high. EVs randomly suspend/resume charging based on the signal. To model the dynamics of EVs we propose an M/M/∞ queue with random interruptions, and analyze the dynamics using time-scale decomposition. There exists a trade-off: one may postpone charging activity to ‘off-peak’ periods during which electricity cost is cheaper, however this incurs extra delay in completion of charging. Using our model we characterize achievable trade-offs between the mean cost and delay perceived by users. Next we consider a scenario where EVs respond to the signal based on the individual loads. Simulation results show that peak electricity demand can be reduced if EVs carrying higher loads are less sensitive to the signal.