Thực tế rằng có tồn tại ap để làm cho khả năng này sau từ thực tế rằng p là NN Lagrange nhân mà chúng ta có thể giải quyết tối ưu hóa vấn đề hạn chế P (xem Phụ lục A). N Hãy xi. p / giá trị tối đa hóa của xi (), thể hiện như là một chức năng của trang giá Chúng tôi kêu gọi xi. | 20 PRICING AND COMMUNICATIONS NETWORKS The fact that there exists a p to make this possible follows from the fact that p is the Lagrangian multiplier with which we can solve the constrained optimization problem P see Appendix A . Let xi p be the maximizing value of xi in expressed as a function of the price p. We call xi p user i s demand function. It is the amount of bandwidth he would wish to purchase if the price per unit bandwidth were p. Under our assumptions on ui Xi p decreases as p increases. Let us suppose that at a price of 0 the customers would in aggregate wish to purchase more than C and when p is sufficiently large they would wish to purchase less that C. It follows that as p increases from 0 the total amount of bandwidth that the customers wish to purchase namely Pi xi p decreases from a value exceeding C towards 0 and at some value say p p we have Pi xi p C. By setting the price at p the operator ensures that the total bandwidth purchased exactly exhausts the supply and that it is allocated amongst users in a way that maximizes the total benefit to the society of customers taken as a whole. This solution to problem P has a number of desirable properties. First the network need not know the utility functions of the users. Secondly the decisions are taken in a decentralized way each user rationally choosing the best possible amount of bandwidth to buy. Thirdly since the price is chosen so that demand equals capacity the network technology s sharing policy does not intervene. Users decide the sharing amongst themselves with price serving as a catalyst. Hence price works as a kind of flow control mechanism to shape the demand. The operator may or may not be happy with this solution. He has obtained a total revenue equal to pC which of course equals p Pixi p . Customer i is left with a user surplus of ui xi p pXi p . The total value to society of the Athens-London link has been maximized and then divided amongst the operator and customers. However it
