Delay Percentile Contracts Sample Clauses

Delay Percentile Contracts. In this subsection we assume that contract customers are operating under a delay percentile contract. We derive the optimal policy for the firm, under the assumptions of heavy-traffic steady-state, as described in the previous section. We then present a regular-traffic policy that we argue should asymptotically converge to the optimal heavy-traffic policy. The implications of these results are discussed. Under the previously described assumptions, in the case of a delay percentile contract, hˆ(w) = w and gˆ(w) = Iw≤Dˆ , where Dˆ is the acceptable delay in the contract scaled appropriately so that gˆπ (W˜ n∗ ) = gπ(Wn∗ ). Thus, under conventional heavy-traffic scalings Dˆ = D/√n∗. Under ▇▇▇▇▇▇-▇▇▇▇▇ scalings Dˆ = √ND, where N = Nn∗ is the number of servers in the non-scaled system when the delay D is contracted. To see this, note that under ▇▇▇▇▇▇-▇▇▇▇▇, while the queue length grows as √n, the time for n servers to serve these customers decreases as 1/√n. Under conventional scalings both the queue length and delay grow in proportion to √n. Therefore, the given scalings for contracted delay provide the appropriate scaled delays for the corresponding systems. By definition, hˆπ (W˜ n∗ ) = hπ(Wn∗ ). Further,