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Steven H. Low. Equilibrium allocation and pricing of variable resources among user-suppliers. Performance Evaluation, 34(4), December 1998.

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Optimization Flow Control, I: Basic Algorithm and - Convergence Steven Low (1999)   (104 citations)  Self-citation (Low)   (Correct)

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Steven H. Low. Equilibrium allocation and pricing of variable resources among user-suppliers. Performance Evaluation, 34(4), December 1998.


Equilibrium Bandwidth and Buffer Allocations for Elastic Traffics - Low (2000)   (4 citations)  Self-citation (Low)   (Correct)

....is removed and user n chooses its allocation to solve: M2: max (x;y)0 un (E(xR yB) var(xR yB) Gamma(px qy) In both M1 and M2 the allocations (x n ; yn ) are restricted to be nonnegative. A variant of M1 where the nonnegativity constraint on (x n ; yn ) is removed is treated in [12]. It models users (resellers) who can both buy and sell bandwidth and buffers among themselves through the network. The nonnegativity constraint here turns out to destroy the simple structure of the process and greatly complicates the analysis. Let X i = P n x ni (respectively, X i = P n x ....

....where it is optimal for every investor to diversify [24] 10] 17] 9] The security models there however have an important difference: investors are allowed to hold short positions, i.e. x n ; yn ) can be negative as well as positive. The case that allows negative allocations is treated in [12]. The nonnegativity constraint in our model complicates greatly the equilibrium analysis. We now illustrate the results with a numerical example. Example 2: Dynamics of Model M1 In this example, there are N = 4 users whose utility functions are un ( v) Gamma log 2 v n where n = n. ....

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Steven H. Low. Equilibrium allocation and pricing of variable resources among user-suppliers. Performance Evaluation, 34(4):207--225, December 1998.


Optimization Flow Control, I: Basic Algorithm and Convergence - Low, Lapsley (1999)   (104 citations)  Self-citation (Low)   (Correct)

....purchase them to maximize their own benefits. The interpretation is that a source that desires only fixed bandwidth in the model would subscribe to CBR in practice and a source that desires both fixed and variable bandwidth would subscribe to ABR with a minimum cell rate guarantee. We show in [24], 25] that at equilibrium, where all sources are at their optimality and demand equals supply, every source desires a strictly positive amount of variable bandwidth. This observation provides perhaps another motivation for end to end flow control, for reactive flow control, where sources ....

Steven H. Low. Equilibrium allocation and pricing of variable resources among user-suppliers. Performance Evaluation, 34(4), December 1998.


Pricing Network Services - Shu, Varaiya (2003)   (6 citations)  (Correct)

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S. H. Low, "Equilibrium Allocation and Pricing of Variable Resources Among User-Suppliers," Performance Evaluation, vol. 34, no. 4, pp. 207--25, 1998.

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