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comes smaller than the application transmission rate. For delay-adaptive audio and video
applications, the utility function curves can look like that in Figure 2.1(c).
Another class of real-time applications is represented by rate-adaptive applications.
These applications do not require hard bandwidth guarantees and hence they can adapt
their transmission rate in response to network congestion. The utility function for rate-
adaptive applications has the shape shown in Figure 2.1(d).
Pricing
The pricing can represent an important component of bandwidth utility functions [2, 26].
Dynamic pricing mechanisms can take advantage of application adaptivity to increase
network availability, revenue, and user-perceived utility [2].
In a network with QoS support, pricing of network services based on the level of service,
usage, and congestion provides an incentive for applications to adapt their sending rates
according to network conditions. Increasing the price during congestion gives the applica-
tion an incentive to back-off its sending rate and at the same time allows an application
with more stringent bandwidth and QoS requirements to maintain a high quality by paying
more.
A number of pricing schemes are used in the Internet today like access-rate-dependent
charge, volume-dependent charge, or the combination of the both. These charging schemes
are described in [26].
2.2 Dynamic Bandwidth Allocation Algorithms
2.2.1 Max-Min Fair Allocation Algorithms
Several algorithms have been proposed to allocate network resources fairly among com-
peting connections. A max-min fair allocation algorithm is introduced in [13] to allocate
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