Understanding & Modeling Bus Transit Driver Availability

Document Type


Publication Date


Subject Area

mode - bus, organisation - management, organisation - workforce planning, place - north america


Extraboard management, Stochastic modeling, Risk-averse behavior, Bus driver scheduling, Tactical workforce planning


Bus transit agencies are required to hire extraboard (i.e. back-up) operators to account for unexpected absences. Incorrect sizing of extra driver workforce is problematic for a number of reasons. Overestimating the appropriate number of extraboard operators has financial implications while underestimating can lead to service disruption. It is therefore important that transit agencies properly manage extraboard operator staffing. A review of relevant literature showed that current models for extraboard management are generally agency-specific and that, in practice, extra driver assignments are usually based on the experience of the decision makers rather than the utilization of a mathematically sound modeling process. In this study, two mathematical programming models with probabilistic constraints were developed to determine daily optimal extraboard size for bus transit (driver availability and deployment) while incorporating reliability and risk measures in the decision making process. Two distinct solution approaches were proposed. The first approach used pLEP’s as the solution methodology and the second approach used second order stochastic dominance constraints. The models were tested using long-term data obtained from three Tri-County Metropolitan Transportation District of Oregon (TriMet) garage. The individual performance of both models under different cost assumptions was evaluated and then the actual historical assignments were compared with the optimal solutions obtained from these models. The results revealed possible improvements of extra driver size for one of the three garages studied. These models can be easily used in a computerized environment to assist agencies in efficient decision-making, which is also illustrated using a simulation procedure developed for comparison with observed driver assignment data.


Permission to link to this report has been given by Mineta National Transit Research Consortium, copyright remains with them. transweb.sjsu.edu/mntrc/index.html