The responses of vehicles to the changes in traffic situations inevitably have delays in observing an event and implementing a control command,which often causes fatal accidents.So far,the methods for handling delays are empirical and cannot be mathematically proven.To eliminate the accidents caused by such delays,in this paper,we develop mathematically prov-able methods to handle these delays.Specifically,we use networked discrete event systems to model the process of driving vehicles and present a supervisory controller for handling delay situations.The method developed in this paper could serve as a new start for modeling and controlling the responsive behaviors of self-driving vehicles in the future.