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An extended classical time allocation model with travel time reliability constraint is proposed in this study. The valuation function of travel time savings is deduced, and the relationship between the value of travel time savings and other social environment variables, especially the waiting time and service level, is revealed. Meanwhile, the change of the value of travel time savings with the waiting time and the service level is investigated through a comparative static analysis method. Analytical results show that the change of the value of travel time savings with the service level is dependent on the inverse of the cumulative distribution function. By contrast, the value of travel time savings tends to decrease with the increase in waiting time. The findings further imply that adopting the optimal head start can relieve the waiting time of urban commuters, thereby minimizing their generalized travel cost. Moreover, the values of service headway and reliability are analyzed, which can improve the quality of service toward either frequency or reliability improvements to reduce the cost for the society.

Analytical Model for the Change of Travel Time Savings With Waiting Time and Service Level