In public transportation providing the fast transport service is the main concern to satisfy thernpassenger demand. The bus service accessibility in response to the passenger demandrnis deferent from route to route. This deference resulted in short passengers waiting time for highrnfrequency and long passengers waiting time for the route of low bus service frequency. Thernlong passengers waiting time is one of the measure of poor public transit service quality. In thisrnthesis mathematical modeling was developed based on the dynamic passengers demand and busrnservice operational constraint to optimize passengers waiting time at bus terminals of AddisrnAbaba city in case of Anbessa bus transport using the data collected during literature review,rninterview, field study and secondary data collected from ACBSE. Mixed Integer Non-LinearrnPrograming MINLP and Mixed Integer Linear Programing MILP model were developed forrnstatic and dynamic passenger demand. The dynamic passenger demand was solved as MixedrnInteger Linear Programing MILP model by discretizing the bus planning horizon into smallrntime (in minutes) to linearize and make the model tractable to solve it using software. LINGOrnsoftware was used to solve the model. The result was evaluated with bus headway, busrnfrequency and bus capacity. The evaluation shows that the overall average bus departure timernreduction is 39.62% and 37.74% for DAF or rigid Bishoftu bus and articulated bus respectively.rnThe improved average frequency for DAF or rigid and articulate bus is 62.44% and 60.67%rnof actual bus rnfrequency. The rntotal average passengers waiting rntime rnfor rnthe DAF and Bishoftu bus was 8.03% more than the passengers waiting time for articulated bus.rnThe overall average passengers waiting time reduction is 39.62% and 37.74% for DAF orrnrigid Bishoftu bus and articulated bus respectively, through the proposed mathematicalrnoptimization models.