Complete Resource Pooling (CRP)
CRP: workload is one-dimensional and non-negative.
Solution of the Brownian control problem “keep all of the work in the buffer i* with the smallest ratio of holding cost to workload contribution , and only allow server idling when the whole system is empty.
How should one interpret this solution?
Parallel server system: P=0
Harrison-Lopez ‘00:
- CRP iff all servers communicate via basic activities
- proposed discrete review policy (proof of asymptotic optimality – special two server case: Harrison ’98)
W. ‘00 (see also Squillante, Xia, Yao, Zhang ‘00):
- CRP iff server-buffer graph with edges given by basic activities is a tree
- proposed threshold policy (continuous review)
Bell-W. ‘01
- Proof that threshold policy of W. ‘00 is asymptotically optimal (two server (AAP) & multiserver (in prep.))
General network with CRP:
- S. Kumar ‘99: proposed discrete review policy (example)
- Ata, Harrison, Kumar ’01 (in prep.): discrete review policy and proof of asymptotic optimality
- Bramson-W. (in prep.): proposed threshold policy (continuous review)