Dynamic Vehicle Routing for Translating Demands: Stability Analysis and Receding-Horizon Policies
Author(s)Bopardikar, Shaunak D.; Smith, Stephen; Bullo, Francesco; Hespanha, Joao P.
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We introduce a problem in which demands arrive stochastically on a line segment, and upon arrival, move with a fixed velocity perpendicular to the segment. We design a receding horizon service policy for a vehicle with speed greater than that of the demands, based on the translational minimum Hamiltonian path (TMHP). We consider Poisson demand arrivals, uniformly distributed along the segment. For a fixed segment width and fixed vehicle speed, the problem is governed by two parameters; the demand speed and the arrival rate. We establish a necessary condition on the arrival rate in terms of the demand speed for the existence of any stabilizing policy. We derive a sufficient condition on the arrival rate in terms of the demand speed that ensures stability of the TMHP-based policy. When the demand speed tends to the vehicle speed, every stabilizing policy must service the demands in the first-come-first-served (FCFS) order; and the TMHP-based policy becomes equivalent to the FCFS policy which minimizes the expected time before a demand is serviced. When the demand speed tends to zero, the sufficient condition on the arrival rate for stability of the TMHP-based policy is within a constant factor of the necessary condition for stability of any policy. Finally, when the arrival rate tends to zero for a fixed demand speed, the TMHP-based policy becomes equivalent to the FCFS policy which minimizes the expected time before a demand is serviced. We numerically validate our analysis and empirically characterize the region in the parameter space for which the TMHP-based policy is stable.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers
Bopardikar, S.D. et al. “Dynamic Vehicle Routing for Translating Demands: Stability Analysis and Receding-Horizon Policies.” Automatic Control, IEEE Transactions On 55.11 (2010) : 2554-2569. © 2011 IEEE.
Final published version
INSPEC Accession Number: 11623534