Public transit agencies rely on disseminating accurate and reliable information to transit users to achieve higher service quality and attract more users. With the development of new technologies, the concept of providing users with reliable information about bus arrival times at bus stops has become increasingly attractive. Due to the fact that bus operation parameters and variables are highly stochastic, modeling prediction of bus travel and arrival times has become one of the many challenging tasks.

Stochastic time series and delay propagation models to predict bus arrival times using historical information were developed. Markov models were developed to predict propagation of bus delay to downstream bus stops based on heterogeneous conditions. The bus arrival times were predicted using a Markov model only and performance measures were obtained and a combined arrival time prediction model consisting of delay propagation and full autoregressive model was also developed. The inclusion of bus delay propagation into the bus arrival time prediction algorithm is an important contribution to the research efforts to predict bus arrival times. The research showed that Markov models can provide accurate bus arrival time predictions without increasing the need for a large number of bus operation variables, simulations and high polling frequency of the geographical bus location as used by other modeling approaches.