Driving cycles are used to understand the driving pattern of vehicles and in estimating their emissions. Although several studies exist on driving cycles worldwide, few studies have focused on developing driving cycles for intra-city buses in heterogeneous traffic conditions. In this study, driving cycles for intra-city buses were developed using real-world GPS data collected during peak and off-peak periods in Chennai city, India. The methodology for the construction of the candidate cycle was based on k-means clustering and one-step Markov modelling. For Markov chain modelling, a transition matrix is constructed which is a probability matrix based on one step succession. To understand the effect of duration of the driving cycle, the candidate cycles were developed for different durations ranging from 400 seconds to 2800 seconds. Further, the average error for each duration of the candidate cycles was determined. The duration which corresponds to the least average error was chosen for developing the final driving cycle. Three driving cycles - corresponding to morning peak hour, off-peak hour, and evening peak hour - were developed. Finally, the developed cycles were compared with the existing local and international cycles. The developed driving cycle was found to be significantly different from the existing cycles for buses.