The dynamics of formation and dissipation of queues at isolated signalized intersections are investigated by analyzing the vehicle conservation equation along the street. Solution of the conservation equation is obtained by the method of characteristics for general initial and boundary conditions, and the effect of the control variables (cycle length, green and red intervals) and system parameters (arrival rates, capacity) on the length of the queue is examined. The theoretical results are obtained by examining the dynamics of the shock waves which are formed because of the intermitted service of traffic by the signal. These results include analytical criteria for the development of saturated or unsaturated situations, analytical expressions for the maximum queue length and limits on the control variables so that the queues remain bounded. The basic findings of this study can be employed for the solution of the traffic signal optimal control problem.