Abstract
We study the static pricing problem for a network service provider in a loss system with a tree structure. In the network, multiple classes share a common inbound link and then have dedicated outbound links. The motivation is from a company that sells phone cards and needs to price calls to different destinations. We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.
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Notes
In this last case, N 2<N but it is large enough to fall in the complete-sharing case. That is why the two prices are identical.
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Research supported in part by the Center of eBusiness at MIT, ONR Contracts N00014-95-1-0232 and N00014-01-1-0146, and by NSF Contracts DMI-9732795, DMI-0085683 and DMI-0245352.
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Caro, F., Simchi-Levi, D. Optimal static pricing for a tree network. Ann Oper Res 196, 137–152 (2012). https://doi.org/10.1007/s10479-012-1115-4
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DOI: https://doi.org/10.1007/s10479-012-1115-4