Improving the experience of using the public transportation system can
be done by estimating the arrival time of the bus and notifying the
passengers. Consequently, the accuracy of the estimation affects this
experience. As the number of buses, stations, and service areas increases,
the data collected in the cloud makes travel time estimation-related
data processing more challenging. Despite this challenge, a distributed
method for estimating the arrival time of the bus is considered in this
paper. Also, we present a way to decentralize data processing and distribute
it on each bus. Besides, using the Kalman filter and updating the
estimated values at short intervals improves the estimation error. Examination
of the degree of complexity shows that the proposed method
has significantly reduced the complexity in the cloud, which makes
the proposed method implementable in metropolitan areas. The implementation
results on a dataset show that the proposed method has a
good performance in terms of mean square error and root mean square.