• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.5
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• pp.1569-1586
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• 2015

This paper considers the optimal cell association and resource allocation for load balancing in a heterogeneous cellular network subject to user's quality-of-service (QoS) constraints. We adopt the proportional fairness (PF) utility maximization formulation which also accommodates the QoS constraints in terms of minimum rate requirements. With equal resource allocation this joint optimization problem is either infeasible or requires relaxation that yields a solution which is difficult to implement. Nevertheless, we show that this joint optimization problem can be effectively solved without any priori assumption on resource allocation and yields a cell association scheme which enforces single BS association for each user. We re-formulated the joint optimization problem as a network-wide resource allocation problem with cardinality constraints. A reweighted heuristic l₁-norm regularization method is used to obtain a sparse solution to the re-formulated problem. The cell association scheme is then derived from the sparsity pattern of the solution, which guarantees a single BS association for each user. Compared with the previously proposed method based on equal resource allocation, the proposed framework results in a feasible cell association scheme and yields a robust solution on resource allocation that satisfies the QoS constraints. Our simulations illustrate the impact of user's minimum rate requirements on cell association and demonstrate that the proposed approach achieves load balancing and enforces single BS association for users.

• Journal of Korean Society of Transportation
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• v.18 no.2
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• pp.91-101
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• 2000

The optimal congestion charge in transportation economics corresponds to the solution to the welfare maximization Problem for users of a certain road link where congestion takes Place. This congestion charge is in nature the optimal Price of the transportation facility, which is derived by the Partial equilibrium analysis on that facility. Therefore it is not certain that this congestion charge can maximize the well-being of all the users of the total transportation network, since the analysis does not count the impact of the congestion charge on traffic volumes of other links. This study suggests an alternative approach to estimate the optimal congestion charge. The key difference of this study from Previous ones is to derive the solution through the general equilibrium analysis on a market where several transportation facilities as well as Private goods are available to consumers. This approach shows a set of solutions a little different from the Previous one, which are explained below. The optimal congestion charge is derived for two different cases. One is the situation of which the congestion charge is levied on every transportation facility In this case, the optimal solution of each facility should equate the marginal utility of every user to the marginal cost of the corresponding facility. This analysis result in general equilibrium coincides with the Previous analysis result in partial equilibrium. However this result cannot apply to another case of which the charge is imposed only on a certain transportation facility. In this case, the optimal charge on a certain transportation facility should be less than the optimal congestion charge of partial equilibrium analysis.