Modeling Bus Capacity for Bus Stops Using Queuing Theory and Diffusion Approximation

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, infrastructure - stop, operations - capacity, planning - methods, planning - service quality


Bus, service quality, line capacity, bus stop


For bus service quality and line capacity, one critical influencing factor is bus stop capacity. This paper proposes a bus capacity estimation method incorporating diffusion approximation and queuing theory for individual bus stops. A concurrent queuing system between public transportation vehicles and passengers can be used to describe the scenario of a bus stop. For most of the queuing systems, the explicit distributions of basic characteristics (e.g., waiting time, queue length, and busy period) are difficult to obtain. Therefore, the diffusion approximation method was introduced to deal with this theoretical gap in this study. In this method, a continuous diffusion process was applied to estimate the discrete queuing process. The proposed model was validated using relevant data from seven bus stops. As a comparison, two common methods—Highway Capacity Manual (HCM) formula and M/M/S queuing model (i.e., Poisson arrivals, exponential distribution for bus service time, and S number of berths)—were used to estimate the capacity of the bus stop. The mean absolute percentage error (MAPE) of the diffusion approximation method is 7.12%, while the MAPEs of the HCM method and M/M/S queuing model are 16.53% and 10.23%, respectively. Therefore, the proposed model is more accurate and reliable than the others. In addition, the influences of traffic intensity, bus arrival rate, coefficient of variation of bus arrival headway, service time, coefficient of variation of service time, and the number of bus berths on the capacity of bus stops are explored by sensitivity analyses.


Permission to publish the abstract has been given by SAGE, copyright remains with them.