Abstract
Multicasting provides an efficient method of transmitting data in real time applications from one source to many users. The source sends one copy of a message to its users and this copy is replicated only at the branching points of a multicast tree. Real life examples of such multicast applications are audio/video broadcasting, teleconferencing, distributed databases, financial information, electronic newspapers, weather maps and experimental data. Conventional multicast studies the problem in which the rate received by all the users of the same multicast group is constant. The inherent problem with such a formulation is that a constant rate will overwhelm the slow receivers while starving the fast ones. Multi-rate multicast transmissions can be used to address this problem by allowing a receiver to obtain data at a rate that satisfies its requirements.
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Notes
- 1.
Since in this chapter we present decentralized resource allocation mechanisms in equilibrium form, it is reasonable to assume that during the play of the game at each link \( l \in \mathbf{{L}} \), each user of link \( l \) learns the set of the other users competing for bandwidth at \( l \).
- 2.
The price per unit of bandwidth paid collectively by each multicast group at a link \(l\) is equal to the sum of the prices paid by the members’ of the group who use the link \(l\).
- 3.
For technical reasons (cf. Theorem 5) we choose \(\Upsilon \) to be arbitrary and large but finite.
- 4.
Therefore, when A and B (both) hold, then \(\frac{1\{A\}1\{B\}}{1-1\{A\}1\{B\}}\approx \frac{1}{0^+}\) is well defined and it becomes a large number.
- 5.
The situation where \((j,G_i)\) is the only user of group \(G_i\) with the maximum demand at link \(l\) is discussed in other cases (e.g. Case D (Part DII)), where it is shown again that the price user \((j,G_i)\) pays per unit of bandwidth at link \(l\) is not controlled by him.
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Kakhbod, A. (2013). Multi-Rate Multicast Service Provisioning. In: Resource Allocation in Decentralized Systems with Strategic Agents. Springer Theses. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6319-1_5
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