Approximate Optimality with Bounded Regret in Dynamic Matching Models

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Proves that, under paired arrivals and a single critical bottleneck, a constructed H-max-weight with threshold policy achieves asymptotic optimality with bounded regret versus a workload relaxation; analysis uses a one-dimensional workload relaxation and reflected-Brownian diffusion to pick the threshold, compares to MaxWeight and FCFS, and shows numeric gains on an N–N example. Assumptions: linear holding costs, knowledge of the bottleneck, connectivity and technical continuity; useful if the model’s paired-arrival and heavy-traffic limits match the application.

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" chapters (13)

1. 0:00Intro
2. 2:31Outline
3. 4:58Matching in Health-care
4. 6:24Dynamic Matching Model: FCFS
5. 12:31Dynamic Bipartite Matching Model
6. 17:25Dynamic Matching Model: Stability
7. 19:24Dynamic Matching Model: Approximate Optimality
8. 20:03Necessary stability conditions
9. 23:23Optimization
10. 27:11Workload Dynamics
11. 30:52Asymptotic optimality
12. 36:32Example
13. 37:21Final remarks