Sharing the Cost of a Multicast Transmission in Visual Studio .NET Make Code 39 Full ASCII in Visual Studio .NET Sharing the Cost of a Multicast Transmission

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14.2.2 Sharing the Cost of a Multicast Transmission using none toprint none on web,windows application Microsoft .NET Multicast none for none is an Internet packet-transmission mode that delivers a single packet to multiple receivers. It is accomplished by setting up a shared delivery tree that spans all the receivers; packets sent down this tree are replicated at branch points so that no more than one copy of each packet traverses each link. Because it is far more ef cient than traditional unicast transmission (in which packets are sent only to a single destination), multicast is particularly appropriate for distributing popular real-time content, such as movies, to a large number of receivers.

Internet content distribution both provides bene ts and incurs cost, which we can model as follows. We assume that there are agents, located at various places in the network, who would derive some utility from receiving the content and that a cost is incurred each time the content is transmitted over a network link. The policy question is how these costs and bene ts should be distributed; more speci cally, which agents should receive the content, and how much should each agent pay To de ne the problem more precisely, we consider a user population P residing at a set of network nodes N that are connected by bidirectional network links L.

The multicast ow emanates from a source node o N; given any set of receivers S P , the transmission ows through a multicast tree T (S) L rooted at o that spans the nodes at which users in S reside. We make the natural assumption that routing is monotonic, i.e.

, that S1 S2 T (S1 ) T (S2 ). Each link l L has an associated cost c(l) 0 that is known by the nodes on each end, and each user i assigns a utility value ui to receiving the transmission. The total cost C(S) of reaching a set S of receivers is given by C(S) = l T (S) c(l), and the net welfare NW (S) of delivering content to this set of receivers is given by NW (S) = i S ui C(S).

A cost-sharing mechanism determines which users receive the multicast transmission and how much each receiver is charged. We let pi 0 denote how much user i. distributed algorithmic mechanism design is charged none none and i denote whether user i receives the transmission; i = 1 if the user receives the multicast transmission, and i = 0 otherwise. The mechanism M is then a pair of functions M(u) = ( (u), p(u)). It is important to note that both the inputs and the outputs of these functions are distributed throughout the network; that is, each user inputs his ui from his network location, and the outputs i (u) and pi (u) must be delivered to him at that location.

The practicality of deploying the mechanism on the Internet depends on the feasibility of computing the functions (u) and p(u) and distributing the results. In our model, it is the agents who are sel sh. The routers (represented by tree nodes), links, and other network-infrastructural components are obedient.

The costsharing algorithm does not know the individual utilities, and so users could lie about them, but once they are reported to the network infrastructure (e.g., by sending them to the nearest router), the algorithms for computing (u) and p(u) can be reliably executed by the network.

Thus, our interest here is in network complexity, not computational manipulation. Given the sel sh nature of agents, the mechanism should be strategyproof, i.e.

, revealing ui truthfully should be a dominant strategy. There are two other desirable features one would want in a cost-sharing mechanism: budget balance (the sum of the charges pi covers the total cost of transmitting the content) and ef ciency (the total welfare is maximized). The classic result of Laffont and Green, as reviewed in 9, implies that no strategyproof mechanism with quasilinear utilities can achieve both budget balance and ef ciency2 ; we therefore consider two separate mechanisms, one that achieves budget balance and one that achieves ef ciency.

To achieve ef ciency, we consider a VCG mechanism called marginal cost (MC). Let denote the largest set that maximizes NW (S) (this is uniquely de ned), and let NW = S NW (S); similarly, NW i is the maximum value over all S of NW (S i). Then the MC mechanism chooses the receiver set S and sets payments pi = i ui NW + NW i .

For budget balance, we choose the Shapley Value (SH) mechanism. The mechanism shares the cost of each link equally among all the agents downstream of that link; an agent i is downstream of a link l if l T ({i}). To determine which agents receive the transmission, we rst start with S = P and compute the charges.

We then eliminate any agent for which the charge exceeds the agent s utility (i.e., pi > ui ) and recursively prune the receiver set until all agents within the set have utilities greater than or equal to their charge.

The cross-monotonic nature of these charges (an agent is never charged less after another agent leaves the receiver set) guarantees that the resulting set is well de ned, independent of the order in which agents are eliminated. To see why the ordering does not matter, consider the following. We say that an elimination (or pruning) is legal if the node to be removed is charged more than its utility; an elimination ordering is legal if each individual pruning is legal.

We note that, if an agent i is charged more than his utility when the set S of agents remains, then this continues to hold when any subset of S remains (because cross-monotonicity requires. More preci sely, the Laffont Green result reviewed in 9 shows that the only strategyproof, welfaremaximizing mechanisms with quasi-linear utilities are the VCG mechanisms, which are known not to be budget-balanced. Myerson and Satterthwaite have shown a more general result about the impossibility of achieving ef cient and budget-balanced allocations with rational agents; see 9 for details..

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