After much delay, the last paper Sida and I wrote together came out last week in Transportation Research Part C.   Growing out of the last chapter of Sida’s PhD dissertation, the first draft of the paper was completed before he went back to China in the summer of 2020, at the height of COVID19 pandemic.   In part, the long delay was due to Sida’s transition to his new job at Beijing Jiaotong University.   I am glad he pressed on despite the early setbacks and eventually published the paper  in a descent journal.  Here is the abstract for those who wonder what is an integrated bus-bike system.

Abstract: This paper examines the design of a transit system that integrates a fixed-route bus service and a bike-sharing service. Bike availability – the average probability that a traveller can find a bike at a dock – is modelled as an analytical function of bike utilization rate, which depends on travel demand, bike usage and bike fleet size. The proposed system also recognizes the greater flexibility provided by biking. Specifically, a traveller can choose between the closest bus stop and a more distant stop for access, egress or both. Whether the closest stop is a better choice depends on the relative position of the traveller’s origin and destination, as well as system design parameters. This interdependence complicates the estimation of average system cost, which is conditional on route choice. Using a stylized analysis approach, we construct the optimal design problem as a mixed integer program with a small number of decision variables. Results from our numerical experiments show the integrated bus-bike system promises a modest but consistent improvement over several benchmark systems, especially in poorer cities with lower demand density. We find a large share of travellers, more than 20% in nearly all cases tested, opt not to use the nearest bus stop in an optimally designed system. The system also tends to maintain a high level of bike availability: the probability of finding a bike rarely drops below 90% except in very poor cities.