# Pricing communication networks P11

Chia sẻ: Do Xon Xon | Ngày: | Loại File: PDF | Số trang:17

0
49
lượt xem
3

## Pricing communication networks P11

Mô tả tài liệu

Multicasting Một dịch vụ unicasting là một trong những yêu cầu mạng để cung cấp vận chuyển điểm-điểm giữa các nguồn chỉ là một thông tin và nhận một. Một dịch vụ multicasting mở rộng ý tưởng này bằng cách yêu cầu các mạng để cung cấp vận tải giữa một hoặc nhiều nguồn thông tin và một nhóm người nhận. Multicasting dịch vụ có thể được sử dụng cho teleconferencing phân phối phần mềm, và truyền dẫn của âm thanh và video. Một đặc tính quan trọng của một dịch vụ multicasting là nó có giá của nó phải là...

Chủ đề:

Bình luận(0)

Lưu

## Nội dung Text: Pricing communication networks P11

1. Pricing Communication Networks: Economics, Technology and Modelling. Costas Courcoubetis and Richard Weber Copyright  2003 John Wiley & Sons, Ltd. ISBN: 0-470-85130-9 Part D Special Topics
10. THE ECONOMIC PERSPECTIVE 271 11.5 The economic perspective 11.5.1 A Model for Allocating Multicast Bandwidth Let us extend the proportional fairness model of Section 10.2 to multicasting. Suppose a multicast group consists of a single source and a ﬁxed set of receivers and multicast tree. There is a single rate that is to be sent to all receivers and which can be adjusted by the sender. There is contention for bandwidth at each link of the multicast tree, since there are other connections that share the resources of the network with the multicast group. As before, we seek to use prices to regulate ﬂows and optimize the overall economic efﬁciency of the network. We discuss the similarities with the case of unicast ﬂows and indicate the new issues that arise. The multicasting problem differs from that of unicasting because many entities are involved, each of whom obtains a different value from the service and contributes to a common cost. Suppose the members of the multicast group agree to pick a representative, who is given full information about the utility functions of all the group members, and is delegated to make choices that maximize the net beneﬁt of the group as a whole. Faced with the prices that the network communicates through the ﬂow control signals, the representative will make a rational decision and choose the optimal rate for the sender to transmit. Given more authority, he could decide that some receivers ought temporarily to leave the group if they add more to the common cost than the extra utility they bring. Furthermore, he could decide, according to some pre-agreed fairness criteria, what contribution each receiver should make towards the total cost of the service. In practice, some of the members of the group, knowing how the cost will be shared, may have an incentives not to cooperate. They may feel they are in a stronger position to obtain a larger share of the overall net beneﬁt. Interestingly, it is the hidden information about utilities of the members of the group that makes the problem hard. In our unicast model we did not face such issues, since we assumed there was a single entity, the sender, who has full information and full control. We can make these clear with a model. Consider a model of a network in which there are sets of links and routes. Each route is associated with either a unicast user or a multicast group user and requires some subset of the links. The route associated with a multicast group is a tree of links rather than a path. A unicast user r has a utility for a ﬂow of rate xr along route r of u r .xr /. A multicast group r consists of a set of users, r1 ; : : : ; rnr , these being the sender and the receivers of the group. Each member r has its utility u r .xr / for a multicast ﬂow rate xr , and we P denote by u r D l u r .xr / the total utility of the group r. The unicast and multicast users have elastic utilities; that is, their utility is assumed to be increasing, strictly concave and continuously differentiable. Our aim is to maximize the social welfare subject to constraints on the capacities of the links. Similarly as in Chapter 10, we have the SYSTEM problem X SYSTEM : maximize u r .xr /; subject to Ax Ä C x½0 r where Ajr D 1 or 0 as j 2 r or j 62 r. We will use the terminology of user r to refer to a unicast user or to a multicast group associated with route r. Suppose user r may choose an amount to pay per unit time, wr . Then he receives a ﬂow xr D wr =½r , where ½r is a price per unit ﬂow on route r. The network chooses the price
11. 272 MULTICASTING ½r in such a way as to make the ﬂow feasible. The user’s problem is USERr : maximize u r .wr =½r / wr ; subject to wr ½ 0 If r is a multicast group, then the above is consistent with a delegate of the group choosing the rate of payment wr so as to sustain a rate xr D wr =½r that is optimal for the group. Suppose the network solves the problem nr X NETWORK : maximize wr log xr ; subject to Ax Ä C x½0 r D1 This is equivalent to allocating feasible ﬂows in a weighted proportionally fair way. As in Section 10.2, SYSTEM is solved when the USERr problems and NETWORK problems are solved simultaneously, with their solutions in equilibrium. That is, there exist f½r g, fxr g, fwr g such that xr D wr =½r and these are simultaneously solutions to SYSTEM, NETWORK and USERr , for all r. At this point, let us return to the multicast group r. We assumed that a delegate chooses the optimal rate xr for the group by solving the problem nr X maximize u r .xr / ½r xr (11.1) xr D1 where ½r is obtained by summing the prices for a unit of bandwidth over all links of the multicast tree. Here the delegate seeks to maximize the net beneﬁt of the group viewed as a coalition of agents, and this requires a complete knowledge of the utilities of the participants. This formulation raises the following important problems: ž How should the total net beneﬁt be shared among the participants? We could require participant r to pay the delegate Âr , so that er D u r Âr becomes his net beneﬁt. This internal payment mechanism must be agreed by all the group. A payment scheme is only stable if no participant has an incentive to leave the coalition because he feels unfairly charged. ž Under which conditions will the internal payment mechanism cover the total cost, i.e. P  Âr D ½r xr ? ž If a participant knows how his payment Âr` will be determined, does he have the incentive to declare his true utility u ri to the delegate, or will stating some other utility allow him to proﬁt by making a smaller payment? Note that to obtain the maximum proﬁt for the coalition as a whole the delegate must know the actual utilities. Otherwise, some participants may beneﬁt at the expense of others. Clearly there is a game here. A payment rule is incentive compatible if participants do best by declaring their true utilities, and so provide the information that is in the best interests of the group as a whole. ž Is there payment scheme that is both an incentive compatible and covers the total cost? Interestingly, there is not. One must sacriﬁce net beneﬁt to cover cost. In the next section we investigate the above questions in terms of a simple example. 11.5.2 The Problem of Sharing Common Cost The left of Figure 11.2 shows a multicast group consisting of two identical receivers with a price p D 1 per unit bandwidth on the shared link, and a price of 0 on each of the