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An generalised approach for simulating relative offset of traffic signals in an urban traffic network is presented. It is shown that is is possible to optimize relative offset settings of signals for various criteria. A general criterion is proposed by which either delays, stops, fuel consumption, or carbon monoxide can be selected by a proper choice of constants. When these criteria are minimized, it was found that the best criterion to be selected for offset setting is the minimization of fuel consumption, since this in turn nearly minimizes the delays, stops, and carbon monoxide emission, and it has the effect of minimizing stops at low saturation and minimizing delays as the degree of saturation increases. Further analysis of the criterion function has shown that the functions minimized are uneven around their optimum offset value and in each case an early switching is favored. The expression to determine optimum offset is updated to calculated optimum offsets that minimizes fuel consumption or carbon monoxide emission.