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We study the design of state dependent control for a closed queueing network model, inspired by shared transportation systems such as ridesharing. In particular, we focus on the design of assignment policies, wherein the platform can choose which supply unit to dispatch to meet an incoming customer request. The supply unit subsequently becomes available at the destination after dropping the customer. We consider the proportion of dropped demand in steady state as the performance measure. We propose a family of simple and explicit state dependent policies called Scaled MaxWeight (SMW) policies and prove that under the complete resource pooling (CRP) condition (analogous to a strict version of Hall's condition for bipartite matchings), any SMW policy induces an exponential decay of demand-dropping probability as the number of supply units scales to infinity. Furthermore, we show that there is an SMW policy that achieves the optimal exponent among all assignment policies, and analytically specify this policy in terms of the matrix of customer-request arrival rates. The optimal SMW policy protects structurally under-supplied locations.
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Blind Dynamic Resource Allocation in Closed Networks via Mirror Backpressure
We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with a finite, fixed number of supply units that circulate in the system. Demand arrives stochastically, and serving a demand unit (customer) causes a supply unit to relocate from the “origin” to the “destination” of the customer. The key challenge is to manage the distribution of supply in the network. We consider general controls including customer entry control, pricing, and assignment. Motivating applications include shared transportation platforms and scrip systems. Inspired by the mirror descent algorithm for optimization and the backpressure policy for network control, we introduce a rich family of mirror backpressure (MBP) control policies. The MBP policies are simple and practical and crucially do not need any statistical knowledge of the demand (customer) arrival rates (these rates are permitted to vary in time). Under mild conditions, we propose MBP policies that are provably near optimal. Specifically, our policies lose at most [Formula: see text] payoff per customer relative to the optimal policy that knows the demand arrival rates, where K is the number of supply units, T is the total number of customers over the time horizon, and η is the demand process’ average rate of change per customer arrival. An adaptation of MBP is found to perform well in numerical experiments based on data from NYC Cab. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Funding: Y. Kanoria was supported by the National Science Foundation’s Division of Civil, Mechanical, and Manufacturing Innovation [Grant CMMI-1653477]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4934 .
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- Award ID(s):
- 1653477
- PAR ID:
- 10471807
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Management Science
- ISSN:
- 0025-1909
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/mnsc.2023.4934
