The relation 
(Equation 1) between the resource consumption
and user satisfaction factors
can be complex and interdependent due to resource sharing.
For instance, the user satisfaction component is dependent on the jitter
encountered by the receiving client, which may be a result of
insufficient resources in the pipeline from the disk to the client buffer.
Examples of user satisfaction functions:
(1) 
(2) 
where x represents the resource utilization.
A QoS metric must capture how far we are from an optimal resource
allocation. In the presence of conflicting requirements, we use an
economic (pricing)framework to represent the near-optimal resource allocation.
An economic paradigm is essential when quality must be ensured
in a system with shared resources.
The metric (weighted cost-satisfaction ratio) is a function that
determines the degree of equilibrium of the system, for example the
supply-demand equilibrium in economics.
The cost-satisfaction ratio can be used to generate the desired
trading profile to satisfy the service provider goal of operating in
an equilibrium region.
Users of a multimedia system view QoS differently. Without proper pricing mechanisms, users will always request the best available quality and this will result in misuse of the shared resources. In the presence of pricing, the user satisfaction depends not only on QoS parameters, such as EED, jitter or synchronization skew, but also on pricing structures for QoS. Pricing models can be simple and completely static (as with telephone pricing) where a service does not adapt to variations in demand and a user cannot specify multiple levels of QoS. Such models have no incentive for proper usage and hence are inappropriate for our purposes. Complex models of pricing include bidding mechanisms where a server constantly and continuously negotiates for the best price. Studies indicate that fixed-rate pricing policies perform substantially worse than volume-based pricing policies for Internet traffic [9]. Economic models for network provisioning have been studied in [21]. A market-system approach to improve QoS on the Internet involves negotiating and establishing price and quality contracts based on economic principles [9]. Pricing schemes that charge more for peak time usage discourage non-critical requests when the system and network are overloaded. Scaling video applications that permit degradation in picture quality, frame loss coupled with monetary incentives [10], indicate increased user benefit and lower request blocking.
The objective of the billing process that draws a relationship between
US and RC is to improve QoS and performance by integrating economic issues
with technical issues.
Following the results of the empirical study, we would like to
design our billing model based on the class of service; i.e.,
the QoS level.
For each QoS class described in the workload model, we try to determine
a relation between price and resource usage that in turn determines a billing
mechanism for that class.
Let 
be the ordered set of available QoS
levels, 
.
This set partitions the users into QoS equivalence classes
according to quality, price and resource requirements.
Hence, each QoS class has 3 attributes ( 
) where:
(1) 
represents the price range, and quantifies the price that user
i must pay for access.
(2) 
represents the QoS desired by the user; 
.
(3) 
represents the system resource consumption for user i's requests,
i.e.,the resource share attributed to the request by user i.
The billing mechanism determines the price ( ) of service
based on (quality desired) and (resource consumed).
Note that these factors incorporate the two components of the QoS metric,
representing the user satisfaction(US) and representing
the resource consumption(RC).
The billing model must accommodate two optimizing criteria from two
perspectives:
maximizing profit to the
service provider while supplying the negotiated QoS to the user.
This can be translated as a need to provide a balance between price
and QoS 
of information, represented as a benefit
function, 
.
The user i specifies resource requirements to maximize benefit ( ),
i.e. the best QoS for the least price. The user goal is stated as:
The service provider specifies resource requirements and availability to maximize profit. The service provider goal is stated as:
where could be a constraint vector that specifies the resources
assigned and price charged.
The pricing model adopted is critical to solving this optimization problem.
In general, a pricing model, that determines , must include:
(1) the cost of resource consumption,
(2) a static startup cost (L), i.e. that of admission control, negotiation,
resource reservation and connection setup and
(3) a profit factor (K) that quantifies the surcharge introduced by
the service provider.
Hence, Price is expressed as follows:
where determines the resource consumption needed to
satisfy the user satisfaction criteria.
In the case of video, the resource consumption( ) for the service is a
function and is likely to depend on a number of factors such as:
(a) Quality of Service Level( ),
(b) Resource Availability ( 
),
(c) Duration of the Request ( 
), and
(d) demand for information (Dem) based on popularity of data and
time of request.
