We study the design of state-dependent controls for a closed queueing network model inspired by shared transportation systems. We focus on the assignment policy, where the platform can choose which nearby vehicle to assign to an incoming customer; if no units are available nearby, the request is dropped. The vehicle becomes available at the destination after dropping the customer. We study how to minimize the proportion of dropped requests in steady state.
We propose a family of simple state-dependent policies called Scaled MaxWeight (SMW) policies that dynamically manage the geographical distribution of supply. We prove that under the complete resource pooling (CRP) condition (analogous to the condition in Hall's marriage theorem), each SMW policy leads to exponential decay of demand-dropping probability as the number of supply units scales to infinity. Further, there is an SMW policy that achieves the *optimal* exponent among all assignment policies, by maintaining high supply levels near structurally under-supplied locations.
Joint work with Sid Banerjee and Pengyu Qian. The paper is available here
Back to the workshop page