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An important consideration for traffic signal control is that traffic arrivals are not deterministic. The effect of stochastic arrivals is mainly handled by introducing stochastic terms in delay formulas. Although convenient, this approach is somewhat indirect. Moreover, when the degree of saturation is high, the system becomes transient; it is questionable whether a static or time-invariant result in the form of a delay formula is applicable. In this paper, instead of relying on steady state or equilibrium probability measures, the transient effect is captured by analyzing the state of the system from cycle to cycle based on a probabilistic treatment of overflow in an event tree. This approach can be used to analyze an existing timing plan or to design a timing plan that satisfies a certain clearance reliability requirement. Some numerical results are included to demonstrate this approach.