Approximating the Performance of a “Last Mile” Transportation System

The Last Mile Problem refers to the provision of travel service from the nearest public transportation node to a home or office. We study the supply side of this problem in a stochastic setting, with batch demands resulting from the arrival of groups of passengers who request last-mile service at urban rail stations or bus stops. Closed-form approximations are derived for the performance of Last Mile Transportations Systems (LMTS) as a function of the fundamental design parameters of such systems. An initial set of results is obtained for the case wherein a fleet of vehicles of unit capacity provides the Last-Mile service, and each delivery route consists of a simple round trip between the rail station or bus stop and a single passenger’s destination. These results are then extended to the general case in which the capacity of a vehicle is a small number (up to 20). It is shown through comparisons with simulation results that the approximations perform consistently well for a broad and realistic range of input values and conditions. These expressions can therefore be used for the preliminary planning and design of an LMTS, especially for determining approximate resource requirements, such as the number of vehicles/servers needed to achieve some prespecified level of service, as measured by the expected waiting time until a passenger is picked up from the station or delivered to her destination.