Fair Network Resource Allocation and Link Pricing: A Numerical Study

Bouhtou, Mustapha; Diallo, Madiagne; Wynter, Laura

doi:10.1142/9789812775368_0003

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…In [17] they also proposed a pricing and resource allocation model to guarantee quality of service in a multi-service network. Bouhtou et al [4,5] introduced a framework to optimize telecommunication link prices using shadow pricing. Bouhtou et al [8,15] studied a bilevel model for pricing arcs in a network.…”

Section: Introductionmentioning

confidence: 99%

A continuous optimization model for a joint problem of pricing and resource allocation

Bouhtou

Erbs

2009

RAIRO-Oper. Res.

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This paper investigates the problem of maximizing the revenue of a telecommunications operator by simultaneously pricing point-to-point services and allocating bandwidth in its network, while facing competition. Customers are distributed into market segments, i.e., groups of customers with a similar preference for the services. This preference is expressed using utility functions, and customers choose between the offers of the operator and of the competition according to their utility. We model the problem as a leader-follower game between the operator and the customers. This kind of problem has classically been modeled as a bilevel program. A market segmentation is usually defined by a discrete distribution function of the total demand for a service; in this case, the problem can be modeled as a combinatorial optimization problem. In this paper, however, we motivate the use of a continuous distribution function and investigate the nonlinear continuous optimization problem obtained in this case. We analyze the mathematical properties of the problem, and in particular we give a necessary and sufficient condition for its convexity. We introduce methods to solve the problem and we provide encouraging numerical results on realistic telecommunications instances of the problem, showing that it can be solved efficiently.

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Section: Introductionmentioning

confidence: 99%

A continuous optimization model for a joint problem of pricing and resource allocation

Bouhtou

Erbs

2009

RAIRO-Oper. Res.

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“…Such a game is usually modeled as a bilevel mathematical program. Models of taxation using bilinear bilevel programs have been developed by Labbé et al [21,22], Brotcorne et al [7,8], and Bouhtou et al [2,3,5,6] for the pricing of arcs on networks (highway tolls, interconnection in telecommunications, etc.). Côté et al [9] studied the pricing of paths in a network in the context of the airline industry, with competition explicitly taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…An example of such a function is represented in Figure 1. We suppose here that the set of potential tariffs is ordered 3 . Intuitively what occurs may be explained as follows.…”

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confidence: 99%

Joint optimization of pricing and resource allocation in competitive telecommunications networks

Bouhtou¹,

Erbs²,

Minoux³

2007

Networks

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Yield management techniques have been used by companies in various competitive industrial contexts in order to keep a high level of revenue. With the opening of the telecommunications markets, operators are looking for ways of including competition in their decision process. By analyzing the customers' preferences, the market can be segmented into groups of similar preferences, and offers targeted to a particular market segment. In this paper, we study a problem of revenue management for a network operator offering services on end-to-end markets, while facing competition. We present a natural formulation for this problem that uses bilinear bilevel programming models, similar to those used in the airline industry [Côté et al., J Revenue Pricing Manage 2 (2003), 23-36]. However, such an approach leads to optimization problems that are very difficult to solve exactly on the large scale instances found in the telecommunications industry. To address difficulties solving large problems, we introduce a new alternative formulation for the problem, give a proof of NP-hardness, and propose solution methods related to this formulation. The first one is an exact method based on a branch-and-bound algorithm; then we propose two approximate methods, one based on Lagrangian relaxation, and one based on a concave approximation of the objective function to be maximized. Comparative results are given. We show that this approach is practically efficient and leads to exact solutions for instances of telecommunications networks of a size larger than previously possible.

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