Transit systems with flexible operation can help improve mobility by adapting to the changing demand with more personalized services, especially in areas where traditional fixed transit operations may be insufficient. Different operation policies vary in suitability depending on the system settings such as demand density, passenger time value, operation time value, passenger walking speed, and other factors. Operation policies should be compared in the same system setting to determine the one yielding the best system performance. This paper modelled the four most commonly adopted operational strategies in community transit systems analytically using the continuous approximation method: fixed transit service with fixed route, stops, and headway; on-demand dispatch transit service with fixed route, stops and demand-driven flexible headway; stop-on-call transit service with fixed route, demand-driven flexible stops and headway; demand responsive transit service with demand-driven flexible route, stops and headway. Both random and planned arrival of passengers at their destination are considered to estimate the waiting time. Analytical models are formulated to minimize the average cost per passenger subject to vehicle capacity and fleet size constraints. Passengers will be rejected when the system capacity is reached, and penalties will be applied accordingly. The operation policy with a minimum average cost per passenger is preferred. Closed-form solutions are obtained for the models. Numerical analysis demonstrates how the range of demand density in the service area influences the selection of the best operating policy. The impact of system configurations on the overall performance of the four policies is also illustrated. This work marks the initial step toward developing a decision-making tool for evaluating the performance of fixed and flexible public transit schemes.