Modern Economy, 2012, 3, 408-423 Published Online July 2012 (
Network Economies for the Internet
Hans W. Gottinger
STRATEC, Munich, Germany
Received April 8, 2012; revised April 23, 2012; accepted May 20, 2012
Most studies of resource allocation mechanisms have used a performance model of the resource, where the very concept
of the resource is defined in terms of measurable qualities of the service such as utilization, thruput, response time (de-
lay) and so on. Optimization of resource allocation is defined in terms of these measurable qualities. One novelty intro-
duced by the economic approach is to design a system which takes into account the diverse Quality of Service (QoS)
requirements of users, and therefore use multiobjective (utilities) optimization techniques to characterize and compute
optimum allocations. Economic (mechanism design) modelling of computer and communication resource sharing uses a
uniform paradigm described by two level modelling: QoS requirements as inputs into a performance model that is sub-
ject to economic optimization. In a first step, one transforms QoS requirements of users to a performance (example:
queueing service model). This model establishes quantifiable parameterization of resource allocation. For example, av-
erage delay QoS requirement, when based on a FIFO queueing model, is a function of resources, bandwidth and buffer,
and user traffic demands. These parameters are then used to establish an economic optimization model. The question of
whether the resource is a piece of hardware, a network link, a software resource such as a database or a server, or a vir-
tual network entity such as a TCP connection is not of primary importance. The first modeling transformation elimi-
nates the details and captures the relevant behaviors and the optimization parameters. We consider a decentralized
model of network and server economies , where we show efficient QoS provisioning and Pareto allocation of resources
(network and server resources) among agents and suppliers, which are either network routes or servers (content provid-
ers). We show how prices for resources are set at the suppliers based on the QoS demands from the agents.
Keywords: Internet; Network Economy; Mechanism Design; Distributed Economic System; Economic Agents
1. Introduction
With advances in computer and networking technology,
numerous heterogeneous computers can be intercon-
nected to provide a large collection of computing and
communication resources. These systems are used by a
growing and increasingly heterogeneous set of users
which are identified with the present Internet. A macro-
scopic view of distributed computer systems reveals the
complexity of the organization and management of the
resources and services they provide. The complexity
arises from the system size (e.g. no. of systems, no. of
users) and heterogeneity in applications (e.g. online
transaction processing, e-commerce, multimedia, intelli-
gent information search) and resources (CPU, memory,
I/O bandwidth, network bandwidth and buffers, etc.).
The complexity of resource allocation is further in-
creased by several factors. First, in many distributed sys-
tems, the resources are in fact owned by multiple or-
ganizations. Second, the satisfaction of users and the
performance of applications are determined by the si-
multaneous application of multiple resources. For exam-
ple, a multimedia server application requires I/O band-
width to retrieve content, CPU time to execute server
logic and protocols, and networking bandwidth to deliver
the content to clients. The performance of applications
may also be altered by trading resources. For example, a
multimedia server application may perform better by
releasing memory and acquiring higher CPU priority,
resulting in smaller buffers for I/O and networking but
improving the performance of the communication proto-
col execution.
Finally, in a large distributed system, the set of sys-
tems, users and applications is continuously changing. In
line with identifying the strategic factors of Internet en-
terprises, we address some of the issues of Quality of
Service (QoS) and pricing, and efficient allocation of
resources (computational resources) in networks and
We review and consider problems of Quality of Ser-
vice (QoS) provisioning, resource allocation and pricing
in computer networks and information systems. We con-
sider such complex systems as economies where multiple
classes of users (consumers) compete for resources and
opyright © 2012 SciRes. ME
services from suppliers: network providers and informa-
tion providers (servers). The resources under contention
are network bandwidth and buffers, server processing
rate and memory.
We model and solve problems using economic princi-
ples of market mechanism, where resources are priced by
suppliers based on demand, and users buy resources to
satisfy their Quality of Service (QoS) needs. We focus on
the issues of QoS provisioning, and the reasons in choos-
ing economic paradigms to solve some of the problems.
Resource allocation in networks relate to computa-
tional models of networks, as developed in the works of
Radner , Mount and Reiter 2, Mount and Reiter 3,
Chap. 4, van Zandt 4 see also Gottinger 5, Chaps. 8,
9. Here they emanate from certain types of queueing
systems, Kleinrock 6, Wolff 7 on generalized net-
works. Network pricing could be looked at as a mecha-
nism design problem (Hurwicz and Reiter 8). More
specific mechanism design approaches for distributed
networks and grid-type systems are covered by Narahari
et al. 9 and Neumann et al. 10 see also Meinel and
Tison 1.
Massive complexity makes traditional approaches to
resource allocation impractical in modern distributed
systems such as the Internet. Traditional approaches
attempt to optimize some system-wide measure of per-
formance (e.g. overall average response time, thruput etc.).
Optimization is performed either by a centralized algo-
rithm with complete information, or by a decentralized
consensus based algorithm.
The current and future complexity of resource alloca-
tion problems described makes it impossible to define an
acceptable system-wide performance metric. What single,
system-wide performance metric adequately reflects the
performance objectives of multimedia server and an
online transaction processing system? Centralized or
consensus based algorithms are impractical in dynamic
systems owned by multiple organizations. Resource al-
location complexity due to decentralizations and hetero-
geneity is also present in economic systems. In general,
modern economies allocate resources in systems whose
complexity overwhelms any algorithm or technique de-
veloped for computer systems. As in economic mecha-
nism design we focus on the similarities between com-
plex distributed systems and economies. Competitive
economic models could provide algorithms and tools for
allocating resources in distributed computer systems
(Deng and Graham 2) in particular Ackermann et al.
3, Chen et al. 4, Iong et al. 5. The tools used are
algorithmic mechanism design, dynamic game theory,
complexity and computational equilibrium.
There is another motivation that has come about due to
the commercialization of the Internet. The debate has
begun in the area of multiple QoS levels and pricing.
How should pricing be introduced to provide many ser-
vice levels in the Internet? Should pricing be based on
access cost or should it be based on usage and QoS re-
ceived by the end user? Will usage based pricing help the
Internet economy grow, and help in accounting and im-
prove the efficiency of the Internet, and make users
benefit much more? Similar issues are being investigated
in the ATM networking community. We address some of
the issues of QoS and pricing, and efficient allocation of
resources (computational resources) in networks and
2. Internet Resources
The evolution of Internet pricing poses interesting re-
source allocation problems. Flat-rate pricing has been a
key condition that allowed the Internet to expand very
fast. In the initial stages of the Internet flat rate pricing
has been more prevalent in the US than in Europe which
partially explains higher user diffusion rates in the US
than in (most of) Europe or Japan among private users.
But as the net has grown in size and complexity, not
discounting engineering advances in network (manage-
ment) technologies, it is becoming more obvious that
other pricing schemes being able to cope with severe
congestion and deadlock should come forward. New
pricing schemes should not only be able to cope with a
growing Internet traffic but also be able to foster applica-
tion development and deployment vital to service pro-
viders. Usage-based pricing of this new kind should
make the internet attractive to many new users. Casual
users will find it more affordable, while business users
will find a more stable environment.
Without an incentive to economize on usage, conges-
tion and higher exposure to security breaches could be-
come quite serious. The problem is more serious for data
networks like the Internet than for other congestible
transportation network resources because of the tremen-
dously wide range of usage rates. A single user at a
modern workstation can send a few bytes of email or put
a load of hundreds Mbps on the network, for example, by
downloading videos demanding as much as 1 Mbps. In
the 1990s the maximum thruput on given backbones used
to be only 45 Mbps, so it it was clear that even a few
users with relatively inexpensive equipment could block
the network. There was witness of these problems after
American Online (AOL) introduced a flat fee for its
internet services and experienced a massive and persis-
tent breakdown with disgruntled customers. A natural
response by shifting resources to expand technology will
be expensive and not a satisfactory solution in the long
run. Aside from breakthrough technological advances
such as broadband that could mitigate but not eliminate
the problem many proposals rely on voluntary efforts to
Copyright © 2012 SciRes. ME
control congestion. Many participants in congestion dis-
cussions suggest that peer pressure and user ethics will
be sufficient to control congestion costs. But as Mac Kie-
Mason and Varian  suggest we essentially have to
deal with a problem like “the tragedy of the commons”,
that is overgrazing the commons, e.g. by overusing a
generally accessible communication network. A few pro-
posals would require users to indicate the priority they
want each of the sessions to receive, and for routers to be
programmed to maintain multiple queues for each prior-
ity class. The success of such schemes would depend on
the users’ discipline to stick to the assigning of appropri-
ate priorities to some of their traffic. On the other hand,
priority scheduling flies in the face of “network neutral-
ity” requested, that is, that all internet traffic should be
delivered at the same speed and reliability. There are no
effective sanction and incentive schemes that would con-
trol such traffic, and therefore such a scheme is liable to
be ineffective. This is why alternative pricing schemes
have gained foremost attention and various approaches
and models have been discussed in the network commu-
nity (Shenker 7; Wang et al. 8).
2.1. Quality of Service (QoS)
With the Internet we observe a single quality of service
(QoS): “best effort packet service”. Packets are trans-
ported first come, first-served with no guarantee of suc-
cess. Some packets may experience severe delays, while
others may be dropped and never arrive. Different kinds
of data place different demands on network services
(Shenker et al. 7) Email and file transfer requires 100
percent accuracy, but can easily tolerate delay. Real-time
voice broadcasts require much higher bandwidth than file
transfers, and can tolerate minor delays but they can’t
tolerate significant distortion. Real-time video broadcasts
have very low tolerance for delay and distortion. Because
of these different requirements, network allocation algo-
rithms should be designed to treat different types of traf-
fic differently but the user must truthfully indicate which
type of traffic he/she is preferring, and this would only
happen through incentive compatible pricing schemes.
Network pricing could be looked at as a mechanism
design problem. The user can indicate the “type” of trans-
mission and the workstation in turn reports this type to
the network. To ensure truthful revelation of preferences,
the reporting and billing mechanism must be incentive
2.2. Pricing Congestion
The social cost of congestion is a result of the existence
of network externalities. Charging for incremental capac-
ity requires usage information. We need a measure of the
user’s demand during the expected peak period of usage
over some period, to determine the share of the incre-
mental capacity requirement. In principle, it might seem
that a reasonable approach would be to charge a premium
price for usage during the pre-determined peak periods (a
positive price if the base usage price is zero), as is
rountinely done for electricity pricing (Wilson 9).
However, in terms of internet usage, peak demand peri-
ods are much less predictable than for other utility ser-
vices. Since the use of computers would allow to sched-
ule some activities during off-peak hours, in addition to
different time zones around the globe, we face the prob-
lem of shifting peaks. By identifying social costs for
network externalities the suggestion by MacKie-Mason
 was directed toward a scheme for internalizing this
cost as to impose a congestion price that is determined by
a real-time Vickrey auction. The scheme requires that
packets should be prioritized based on the value that the
user puts on getting the packet through quickly. To do
this, each user assigns his/her packets a bid measuring
his/her willingness-to-pay (indicating effective demand)
for immediate servicing. At congested routers, packets
are prioritized based on bids. In line with the design of a
Vickrey auction, in order to make the scheme incentive
compatible, users are not charged the price they bid, but
rather are charged the bid of the lowest priority packet
that is admitted to the network. It is well-known that this
mechanism provides the right incentives for truthful
revelation (Nisan and Ronen 20). Such a scheme has a
number of desirable characteristics. In particular, not
only do those users with the highest cost of delay get
served first, but the prices also send the right signals for
capacity expansion in a competitive market for network
services. If all of the congestion revenues are reinvested
in new capacity, then capacity will be expanded to the
point where its marginal value is equal to its marginal
3. Quality of Service Parameters
3.1. Internet Communication Technologies:
The Internet and Asynchronous Transfer Mode (ATM)
have strongly positioned themselves for defining the fu-
ture information infrastructure. The Internet is success-
fully operating one of the popular information systems,
the World Wide Web (WWW), which suggests that the
information highway is forming on the Internet. However,
such a highway is limited in the provision of advanced
multimedia services such as those with guaranteed qual-
ity of service (QoS). Guaranteed services are easier to
support the ATM technology. Its capability far exceeds
that of the current Internet, and it is expected to be used
as the backbone technology for the future information
infrastructure. ATM proposes a new communications
Copyright © 2012 SciRes. ME
paradigm. ATM allows integration of different types of
services such as digital voice, video and data in a single
network consisting of high speed links and switches. It
supports a Broadband Integrated Services Digital Net-
work (B-ISDN), so that ATM and B-ISDN are some-
times used interchangeably, where ATM is referred to as
the technology and B-ISDN as the underlying technical
standard. ATM allows efficient utilization of network
resources, and simplifies the network switching facilities
compared to other proposed techniques in that it will
only require one type of switching fabric (packet switch).
This simplifies the network management process (Acker-
mann et al. 3). The basic operation of ATM, and gen-
erally of packet-switched networks, is based on statistical
multiplexing. In order to provide QoS, the packets need
to be served by certain scheduling (service) disciplines.
Resource allocation algorithms depend heavily on the
scheduling mechanism deployed. The scheduling is to be
done at the entrance of the network as well as the
switching points. The term “cell” designates the fixed-
size packet in ATM networks. ATM allows variable bit
rate sources to be statistically multiplexed. Statistical
multiplexing produces more efficient usage of the chan-
nel at the cost of possible congestion at the buffers of an
ATM switch. When the congestion persists, buffer over-
flow occurs, and cells are discarded (or packets are
dropped). Therefore, resources (i.e. bandwidth and buffer
space) need to be carefully allocated to meet the cell loss
and the delay requirements of the user. The delay and the
cell loss probability that the user wishes the network to
guarantee are referred to as the QoS parameters. Overall,
QoS is usually defined in terms of cell loss probability,
delay bounds and other delay and drop-off parameters.
How can one provide such QoS with guarantees? The
general approach is to have an admission or performance
algorithm that takes into account the traffic characteris-
tics of the source and assigns suitable amounts of re-
sources to the new connection during channel establish-
ment. The admission algorithm is responsible for calcu-
lating the bandwidth and buffer space necessary to meet
the QoS requirements specified by the user. The algo-
rithm depends on how the traffic is characterized and the
service disciplines supported by the switches.
Although the Internet is capable of transporting all
types of digital information, it is difficult to modify the
existing Internet to support some features that are vital
for real time communications. One important feature to
be supported is the provision of performance guarantees.
The Internet uses the Internet Protocol (IP), in which
each packet is forwarded independently of the others.
The Internet is a connectionless network where any
source can send packets any time at speeds that are nei-
ther monitored nor negotiated. Congestion is bound to
happen in this type of network. If congestion is to be
avoided and real-time services are to be supported, then a
negotiation (through pricing or rationing) between the
user and the network is necessary. ATM is a connec-
tion-oriented network that supports this feature. A virtual
channel is established, and resources are reserved to pro-
vide QoS prior to data transfer. This is referred to as
channel establishment.
3.2. Traffic in B-ISDN
In a B-ISDN environment high-bandwidth applications
such as video, voice and data are likely to take advantage
of compression. Different applications have different
performance requirements, and the mechanisms to con-
trol congestion should be different for each class of traf-
fic. Classification of these traffic types is essential in
providing efficient services. There are two fundamental
classes of traffic in B-ISDN: real-time and non real-time
(best effort) traffic. The majority of applications on the
Internet currently are non-real-time ones (Paxon 21)
based on TCP/IP. TCP/IP is being preserved with an
ATM technology (Chao 22). The Internet can support
data traffic well but not real-time traffic due to the limi-
tations in the functionality of the protocols. B-ISDN
needs to support both non-real-time and real-time traffic
with QoS guarantees. Most data traffic requires low cell
loss, but is insensitive to delays and other QoS parame-
ters. Applications such as Telnet require a real-time re-
sponse and should therefore be considered real-time ap-
plications, the same applies to Voice of Internet Protocol
(VOIP). Video is delay-sensitive and, unlike Telnet, re-
quires high bandwidth. High throughput and low delay
are required of the ATM switches for the network to
support video services to the clients. This puts a con-
straint on the ATM switch design in that switching
should be done in hardware and the buffer sizes should
be kept reasonably small to prevent long delays. On the
other hand, best effort traffic tends to be bursty, and its
traffic characteristics are hard to predict. This puts an-
other, opposite constraint on an ATM switch, which re-
quires large buffers at the switching point, further com-
plicating its design.
3.3. Congestion Control
Statistical multiplexing can offer the best use of re-
sources, however, this is done at the price of possible
congestion. Congestion in an ATM network can be han-
dled basically in two ways: reactive control and preven-
tive control. Reactive control mechanisms are commonly
used in the Internet, where control is triggered to allevi-
ate congestion after congestion has been detected. Typi-
cal examples of reactive control are 1) explicit conges-
tion notification (ECN); 2) node to node flow control and
3) selective cell discarding. In the more advanced pre-
Copyright © 2012 SciRes. ME
ventive control approach, congestion is avoided by allo-
cating the proper amount of resources and controlling the
rate of data transfers by properly scheduling cell depar-
tures. Some examples of preventive control mechanisms
are 1) admission and priority control; 2) usage parameter
control and 3) traffic shaping.
Reactive and preventive control can be used concur-
rently, but most reactive controls are unsuitable for high-
bandwidth real-time applications in an ATM network,
since reactive control simply is not fast enough to handle
congestion in time. Therefore, preventive control is more
appropriate for high speed networks.
3.4. Service Discipline
Traffic control occurs at various places in the network.
First, the traffic entering the network is controlled at the
input, second, the traffic is controlled at the switching
nodes. In either case, traffic is controlled by scheduling
the cell departures. There are various ways how to sched-
ule departure times, and these mechanisms are part of
service disciplines. The service discipline must transfer
traffic at a given bandwidth by scheduling the cells and
make sure that it does not exceed the buffer space re-
served (or the delay bound assigned) for each channel.
These functions are usually build into the hardware of the
ATM switch and into the switch controller. When im-
plementing a service discipline in an ATM network, it is
important to choose it simple enough that it can be easily
integrated into an ATM switch. However, the discipline
must support the provision of quality of service guaran-
tees. This also means that the service discipline is re-
sponsible for protecting “well-behaved” traffic from the
“ill-behaved” traffic and must be able to provide certain
levels of QoS guarantees. The service discipline also
needs to be flexible enough to satisfy the diverse re-
quirements of a variety of traffic types, and to be effi-
cient, that is, to permit a high utilization of the network.
Various service disciplines have been proposed, and
many of them have been investigated thoroughly and
compared. An important class is that of disciplines used
in rate-allocating servers.
3.5. Bandwidth-Buffer Tradeoff
A simple example on the representation of QoS parame-
ters is the bandwidth-buffer tradeoff. Bandwidth can be
traded for buffer space and vice versa to provide the
same QoS. If a bandwidth is scarce, then a resource pair
that uses less bandwidth and more buffer space should be
used (Gottinger 23). Resource pricing is targeted to
exploit this tradeoff to achieve efficient utilization of the
available resources. The pricing concept for a scarce re-
source is well-known in economics, but in the context of
exploiting the bandwidth-buffer tradeoff, Low and Va-
raiya 24 use non-linear optimization theory to deter-
mine centralized optimal shadow prices in large networks.
With respect to large scale application, however, the
complex optimization process limits the frequency of
pricing updates, which causes inaccurate information
about available resources. In order to make pricing in the
context of a buffer-bandwidth tradeoff more adjustable
and flexible it should be based on decentralized pricing
procedures according to competitive bidding in large
markets where prices will be optimal prices if the mar-
kets are efficient. This would also allow flexible pricing
which results in accurate representation of available re-
sources in that prices are updated as the instance connect
request arrives. The subsequent procedure is based on
distributed pricing as a more feasible alternative to opti-
mal pricing.
4. The Rationale of Economic Models in
There are intrinsic interfaces between human information
processing and networking that show the usefulness of
economic modeling.
Decentralization: in an economy, decentralization is
provided by the fact that economic models consist of
agents which selfishly attempt to achieve their goals.
There are two types of economic agents: suppliers and
consumers. A consumer attempts to optimize its individ-
ual performance criteria by obtaining the resources it
requires, and is not concerned with system-wide perfor-
mance. A supplier allocates its individual resources to
consumers. A supplier’s sole goal is to optimize its indi-
vidual resources to consumers. A supplier’s sole goal is
to optimize its individual satisfaction (profit) derived
from its choice of resource allocation to consumers.
Models of economic agents are summarized in the Ap-
Limiting Complexity: economic models provide sev-
eral interesting contributions to resource sharing algo-
rithms. The first is a set of tools for limiting the com-
plexity by decentralizing the control of resources. The
second is a set of mathematical models that can yield
several new insights into resource sharing problems.
Pricing and Performance: most economic models in-
troduce money and pricing as the technique for coordi-
nating the selfish behavior of agents. Each consumer is
endowed with money that it uses to purchase required
resources. Each supplier owns a set of resources, and
charges consumers for the use of its resources. The sup-
plier prices its resources based on the demand by the
agents, and the available supply. Consumers buy re-
sources or services such that the benefit they receive is
maximized. Consumer-agents buy resources based on
maximizing performance criteria. As a whole the system
Copyright © 2012 SciRes. ME
performance is determined by some combination of the
individual performance criteria.
Usage Accounting, Billing and Dimensioning: by us-
ing economic models for service provisoning in distrib-
uted systems, accounting for QoS becomes an important
task for suppliers, as they have to keep track of the re-
source usage in order to price the resources, and thereby
charge or bill the users for QoS. In addition, pricing can
be used to understand the user demands and thereby di-
mension systems appropriately.
Administrative Domains: often large distributed sys-
tems and computer networks spread over several do-
mains, the control of resources is shared by multiple or-
ganizations that own distinct parts of the network. In
such an environment, each organization will have a set of
services that it supports. Economic principles of pricing
and competition provide several valuable insights into
decentralized control mechanisms between the multiple
organizations and efficient service provisioning.
Scalability: a key issue in designing architectures for
services in large computer networks and distributed sys-
tems is scalability. With the ever growing demand for
new services, flexible service architectures that can scale
to accommodate new services are needed. Economic
models of competition provide, in a natural fashion,
mechanisms for scaling services appropriately based on
service demand and resource availability.
5. Modelling Approaches
Most studies of resource allocation mechanisms have
used a performance model of the resource, where the
very concept of the resource is defined in terms of meas-
urable qualities of the service such as utilization, thruput,
response time (delay) and so on. Optimization of re-
source allocation is defined in terms of these measurable
qualities. One novelty introduced by the economic ap-
proach is to design a system which takes into account the
diverse QoS requirements of users, and therefore use
multiobjective (utilities)optimization techniques to char-
acterize and compute optimum allocations. Economic
modeling of computer and communication resource
sharing uses a uniform paradigm described by two level
modeling: QoS requirements as inputs into a perform-
ance model that is subject to economic optimization.
In the first step, one transforms QoS requirements of
users to a performance (example: queueing service
model).This model establishes quantifiable parameteriza-
tion of resource allocation. For example, average delay
QoS requirement, when based on a FIFO queueing model,
is a function of resources, bandwidth and buffer, and user
traffic demands. These parameters are then used to estab-
lish an economic optimization model. The question of
whether the resource is a piece of hardware, a network
link, a software resource such as a database or a server,
or a virtual network entity such as a TCP connection is
not of primary importance. The first modeling transfor-
mation eliminates the details and captures the relevant
behaviors and the optimization parameters.
Our approach evolves in the following sequence.
Many users present QoS demands, which are translated
into demands on resources based on a performance
model. The suppliers compute the optimal allocations
based on principles of economic optimization and market
mechanisms. Once the optimization is done, the results
provide inputs to mechanisms for QoS provisioning, such
as scheduling of resources and admission of users in
networks and load balancing in distributed systems. We
present briefly an overview of the problems and contri-
5.1. Optimal Allocation and QoS
We motivate and solve a problem of allocating resources
and providing services (QoS) to several classes of users
at a single link. The resources at the link are buffer space
and bandwidth. The link (network provider) prices per
unit buffer and bandwidth resources. The consumers
(user traffic classes), via economic agents, buy resources
such that their QoS needs are satisfied. The network pro-
vider prices resources based on demand from the con-
sumers. The ingredients are as follows:
Economic models: we use competitive economic
models to determine the resource partitions between
user traffic classes, which compete to obtain buffer
and bandwidth resources from the switch suppliers.
Optimal allocations using economic principles: we
look for Pareto optimal allocations that satisfy QoS
needs of agents. Agents represent QoS via utility
functions which capture the multiple performance
Pricing based on QoS: we compute equilibrium prices
based on the QoS demands of consumers. Prices are
set such that the market demand and supply are met.
Prices help in determining the cost of providing a ser-
Priorities: using the economic framework, we show a
simple way to support priority service among the
user-classes (or agents).
Decentralization: we show a natural separation be-
tween the interactions of the user-classes (represented
by agents) and the network switch suppliers. The in-
teraction is purely competitive and market based. This
decentralization promotes scalable network system
5.2. Scheduling and Pricing Mechanisms
We consider a dynamic system where sessions arrive and
Copyright © 2012 SciRes. ME
leave a traffic class, and demand fluctuates over time. In
such a setting, we investigate practical mechanisms, such
as packet level scheduling to provide bandwidth and
buffer guarantees, admission control mechanisms to pro-
vide class QoS guarantees, practical pricing to capture
the changing demand, and charging mechanisms for user
sessions within a class.
Scheduling algorithms for class based QoS provi-
sioning: we provide novel scheduling mechanisms,
which allocates bandwidth and buffer for meeting the
demand from traffic classes. The scheduling mecha-
nism allocates bandwidth, which is computed from
the economic optimization.
Admission Region and Control: we compute the ad-
mission control region of the agents on the economic
model. Due to the natural separation between who
controls the admission of sessions into the traffic
class, the admission region can be determined.
We propose simple pricing models which capture the
changing demand, and are easy to implement. We
also propose novel QoS based charging mechanisms
for sessions in a class with applications to charging in
ATM Networks and Integrated Services Internet.
We first consider a network economy, of many parallel
routes or links, where several agents (representing user
classes) compete for resources from several suppliers,
where each supplier represents a route (or a path) be-
tween a source and destination. Agents buy resources
from suppliers based on the QoS requirements of the
class they represent. Suppliers price resources, inde-
pendently, based on demand from the agents. The sup-
pliers connect consumers to information providers, who
are at the destination; the flow of information is from
information providers to the consumers. We formulate
and solve problems of resource allocation and pricing in
such an environment.
We then consider a server economy in a distributed
system. Again, we use a similar model of interaction
between agents and suppliers (servers). The servers sell
computational resources such as processing rate and
memory to the agents for a price. The prices of resources
are set independently by each server based on QoS de-
mand from the agents. Agents represent user classes such
as transactions in database servers or sessions for Web
servers that have QoS requirements such as response
time. Using such economic models, our contributions are
as follows:
We propose a decentralized model of network and
server economies, where we show efficient QoS pro-
visioning and Pareto allocation of resources (network
and server resources) among agents and suppliers,
which are either network routes or servers (content
We show how prices for resources are set at the sup-
pliers based on the QoS demands from the agents.
We propose alternative dynamic routing algorithms
and admission control mechanisms based on QoS
preferences by the user classes for the network econ-
omy, and we propose a simple way to perform trans-
action routing. We also show static optimal routing
policies by the agents for the network and server
5.3. Network and Server Economies
Consider a large scale distributed information system
with many consumers and suppliers. Suppliers are con-
tent providers such as web servers, digital library servers,
multimedia database and transaction servers. Consumers
request for and access information objects from the vari-
ous suppliers and pay a certain fee or no fee at all for the
services rendered.
Consider that third party suppliers provide information
about suppliers to consumers in order to let consumers
find and choose the right set of suppliers.
Access and dissemination: consumers query third-
party providers for information about the suppliers, such
as services offered and the cost (price). Likewise, suppli-
ers advertise their services and the costs via the third
party providers in order to attract consumers. Consumers
prefer an easy and simple way to query for supplier in-
formation, and suppliers prefer to advertise information
securely and quickly across many regions or domains.
For example, consider a user who wishes to view a mul-
timedia object (such as a video movie). The user would
like to know about the suppliers of this object, and the
cost of retrieval of this object from each supplier.
Performance requirements: users wish to have good
response time for their search results once the queries are
submitted. However, there is a tradeoff. For more infor-
mation about services offered, advanced searching
mechanisms are needed, but at the cost of increased re-
sponse time. In other words, users could have prefer-
ences over quality of search information and response
time. For example, users might want to know the service
costs in order to view a specific information object. In
large networks, there could be many suppliers of this
object, and users may not want to wait forever to know
about all the suppliers and their prices. Instead, they
would prefer to get as much information as possible
within a certain period of time (response time).
From the above example, in order to let many con-
sumers find suppliers, a scalable decentralized architec-
ture is needed for information storage, access and up-
Naming of services and service attributes of suppliers
becomes a challenging issue when hundreds of suppliers
spread across the globe. A simple naming scheme to
Copyright © 2012 SciRes. ME
connect consumers, across the internet, with information
about suppliers is essential. The naming scheme must be
extensible for new suppliers who come into existence. A
name registration mechanism for new suppliers and a
de-registration mechanism (automatic) to remove non-
existent suppliers is required. In addition, naming must
be hierarchical, domain based (physical or spatial do-
mains) for scalability and uniqueness. Inter-operability
with respect to naming across domains is an additional
challenging issue not covered here.
The format of information storage must be simple
enough to handle many consumer requests quickly within
and across physical domains. For better functionality and
more information, a complex format of information stor-
age is necessary, but at the cost of reduced performance.
For example, a consumer, in addition to current service
cost, might want to know more information such as the
cost of the same service during peak and off-peak hours,
the history of a supplier, its services, and its reputation,
in order to make a decision. This information has to be
gathered when requested. In addition, the storage formats
must be inter-operable across domains.
Performance: a good response time is important to
make sure consumers get the information they demand
about suppliers within a reasonable time period, so that
decision-making by consumers is done in a timely fash-
ion. In addition, the design of the right architectures for
information storage and dissemination is necessary for a
large scale market economy to function efficiently. Using
the previous example, consumers and suppliers would
prefer an efficient architecture to query for and post in-
formation. Consumers would prefer good response time
in obtaining the information, and suppliers prefer a se-
cure and fast update mechanism to provide up-to-date
information about their services.
Security in transferring information and updating in-
formation at the bulletin boards (name servers) is crucial
for efficient market operation and smooth interaction
between consumers and suppliers. For this the third party
suppliers (naming services) have to provide authentica-
tion and authorization services to make sure honest sup-
pliers are the ones updating information about their ser-
5.4. Allocation and Pricing Models
In economic models, there are two main ways to allocate
resources among the competing agents. One of them is
the exchange based economy and the other is the price
based economy. In the exchange based economy, each
agent is initially endowed with some amounts of the
resources. They exchange resources until the marginal
rate of substitution of the resources is the same for all the
agents. The agents trade resources in the direction of
increasing utility (for maximal preference). That is, two
agents will agree on an exchange of resources (e.g. CPU
for memory) which results in an improved utility for both
agents. The Pareto optimal allocation is achieved when
no further, mutually beneficial, resource exchanges can
occur. Formally, an allocation of resources is Pareto
optimal when the utility derived by the competing econ-
omic-agents is maximum. Any deviation from this allo-
cation could cause one or more economic agents to have
a lower utility (which means the agents will be dis-
In a price based system, the resources are priced based
on the demand, supply and the wealth in the economic
system. The allocations are done based on the following
mechanisms. Each agent is endowed with some wealth.
Each agent computes the demand from the utility func-
tion and the budget constraint. The aggregate demand
from all the agents is sent to the suppliers who then
compute the new resource prices. If the demand for a
resource is greater than its supply, the supplier raises the
price of the resource. If there is surplus supply, the price
is decreased. The agents again compute their demands
given the current prices and present the demand to the
suppliers. This process continues iteratively until the
equilibrium price is achieved where demand equals the
Bidding and auctioning resources is another form of
resource allocation based on prices. There are several
auctioning mechanisms such as the Sealed Bid Auction,
Dutch Auction, and English Auction. The basic philoso-
phy behind auctions and bidding is that the highest bid-
der always gets the resources, and the current price for a
resource is determined by the bid prices.
5.5. What Are the Economic Hard Problems?
Some of the interesting problems encountered when de-
signing an economic based computer system are dis-
cussed and stated.
How do agents demand resources? This is a funda-
mental question regarding the agents preferences on
the resources they consume. Are there smooth utility
functions that can capture the agents preferences of
the resources? Are there utility functions that can
capture the diversity of the agents preferences?
How are the prices adjusted to clear the economy or
to clear the markets? In an economic model, efficient
allocation of resources occurs when the demand
equals the supply at a certain equilibrium price vec-
What rational pricing mechanisms do the suppliers
adopt? This question raises issues on pricing mecha-
nisms that will attract agents (consumers).
How do suppliers provide price guarantees to agents?
Copyright © 2012 SciRes. ME
This is a fundamental question in advertising and pro-
viding price guarantees to agents. Delays in informa-
tion about prices, and surges in demand can cause
prices to vary. Therefore agents can make bad deci-
What are the protocols by which the consumers and
suppliers communicate to reserve resources?
What are the general allocation principles? Can eco-
nomic models give insight into the allocation mecha-
nisms that can cause the computer system to reach
equilibrium? Can these principles be used practically
to evolve the computer system in a way that price
equilibrium can be achieved?
6. Network Economy
The economic model consists of the following players:
Agents and Network Suppliers. Consumers or user
classes: Consumers (or user classes) request for QoS.
Each user class has several sessions (or user sessions).
Users within a class have common preferences. User
classes have QoS preferences such as preferences over
packet-loss probability, max/average delay and thruput.
Users within a class share resources.
Two variations of the model are referred to the Ap-
Agents and Network Suppliers: Each user class is rep-
resented by an agent. Each agent negotiates and buys
services (resource units) from one or more suppliers.
Agents demand for resources in order to meet the QoS
needs of the user classes. Network providers have tech-
nology to partition and allocate resources (bandwidth and
buffer) to the competing agents. In this competitive set-
ting network providers (suppliers) compete for profit
Multiple Agent-Network Supplier Interaction: Agents
present demands to the network suppliers. The demands
are based on their wealth and QoS preferences of their
class. The demand by each agent is computed via utility
functions which represent QoS needs of the user classes.
Agents negotiate with suppliers to determine the prices.
The negotiation process is iterative, where prices are ad-
justed to clear the market; supply equals the demand.
Price negotiation could be done periodically or depend-
ing on changes in demand.
Each agent in the network is allocated a certain
amount of buffer space and link capacity. The buffer is
used by the agent for queueing packets sent by the users
of the class. A simple FIFO queueing model is used for
each class. The users within a class share buffer and link
Agent and supplier optimality: Agents compete for
resources by presenting demand to the supplier. The
agents, given the current market price, compute the af-
fordable allocations of resources (assume agents have
limited wealth or budget). The demand from each agent
is presented to the supplier. The supplier adjusts the
market prices to ensure demand equals supply.
The main issues form the economic model are:
Characterization of class QoS preferences and traffic
parameters via utility functions, and computation of
demand sets given the agent wealth and the utility
Existence and computation of Pareto optimal alloca-
tions for QoS provisioning, given the agent utility
Computation of equilibrium price by the supplier
based on agent demands, and conditions under which
price equilibrium exists. Price negotiation mecha-
nisms operate between the agents and suppliers.
6.1. Problem Formulation
Network model: the network is composed of nodes
(packet switches) and links. Each node has several output
links. Each output link is associated with an output buffer.
The link controller, at the output link, schedules packets
from the buffers and transmits them to other nodes in the
network. The switch has a buffer controller that can par-
tition the buffer among the traffic classes at each output
link. We assume that a processor on the switch aids in
control of resources.
We have confined ourselves to problems for a single
link (output link) at a node, but they can be applied to the
network as well. Let B denote the output buffer of a link
and C be the corresponding link capacity. Let {ck, bk}be
the link capacity and buffer allocation to class k on a link,
where k [1, K]. Let p = {pc, pb} be the price per unit
link capacity and unit buffer at a link, and wk be the
wealth (budget) of traffic class k. The utility function for
TCk is Uk = f(ck, bk, Trk). The traffic of a class is repre-
sented by a vector of traffic parameters (Trk) and a vector
of QoS requirements (such as packet loss probabilities,
average packet delay and so on.).
Agent (TC: traffic class) buys resources from the net-
work at the given prices using its wealth. The wealth
constraint of agent TCk is: pb bk + pc ck wk. A budget
set is the set of allocations that are feasible under the
wealth constraint (budget constraint). The budget set is
defined as follows:
:, k
BxxXxw pp (1)
Computation of demands sets: The demand set for
each agent is given by the following:
 
:,,xx BUxxB
 pp p
The goal of TCk is to compute the allocations that pro-
vide maximal preference under wk and p. Each TCk per-
Copyright © 2012 SciRes. ME
forms the following to obtain the demand set (defined
 
Find :,
such that:max
Constraints :
0, ,0,
, ,
ck k
6.2. Utility Parameters
In the previous section, we show a general utility func-
tion which is a function of the switch resources; buffer (b)
and bandwidth (c). The utility function could be a func-
tion of the following:
Packet loss probability Ut = g(c, b, Tr);
Average packet delay Ud = h(c, b, Tr);
Packet tail utility Ut = v(c, b, Tr);
Max packet delay Ub = f(b, bT);
Thruput Uc = g(c, ct).
The variables b and c in the utility functions refer to
buffer space allocation and link bandwidth allocation. In
the utility functions Ub and Uc; the parameters bT and cT
are constants. For example, the utility function Ub = f(b,
bT) for max packet delay is simply a constant as b in-
creases, but drops to 0 when b = bT and remains zero for
any further increase in b.
We look at utility functions which capture packet loss
probability of QoS requirements by traffic classes, and
we consider loss, max-delay and thruput requirements.
After this we proceed to utility functions that capture
average delay requirements, followed by utility functions
that capture packet tail utility requirements. We also
could give examples of utility functions for agents with
many objectives; agents have preferences over several
QoS parameters as shown below.
U fUU (4)
6.3. Packet Loss
The phenomenon of packet loss is due to two reasons:
the first, packets arrive at a switch and find that the
buffer is full (no space left), therefore, are dropped. The
second is that packets arrive at a switch and are buffered,
but they do not get transmitted (or scheduled) in time,
then they are dropped. A formal way of saying this: for
real-time applications, packets, if delayed considerably in
the network, do not have value once they reach the des-
We consider K agents, representing traffic classes of
M/M/1/B type, competing for resources from the network
provider. The utility function is packet loss utility (U1)
for the user classes. We choose the M/M/1/B model or
traffic and queueing for the following reasons:
The model is tractable, where steady state packet loss
utility is in closed-form, and differentiable. This helps
in demonstrating the economic models and the con-
There is a renewed interest in M/M/1/B or M/D/1/B
models for multiplexed traffic (such as video), where
simple histogram based traffic models capture the
performance of queueing in networks (Kleinrock ;
Wolff 7).
For more complex traffic and queueing models (ex-
ample of video traffic) we can use tail utility functions to
represent QoS of the user class instead of loss utility.
In the competitive economic model, each agent prefers
less packet loss, as the more packet loss, the worse the
quality of the video at the receiving end. Let each agent
TCk have wealth wk, which it uses to purchase resources
from network provider.
Let each TC transmit packets at a rate
(Poisson arri-
vals), and let the processing time of the packets be expo-
nentially distributed with unit mean. Let c, b be alloca-
tions to a TC. The utility function U for each TC is given
as follows:
,, 1
for,, resp.
Ufcb b
The above function is continuous and differentiable for
all c [0, C], and for all b [0, B]. We assume that b
R for continuity purposes of the utility function.
7. Equilibrium Price and Convergence
Pareto efficient allocations are such that no traffic class
can improve upon these allocations without reducing the
utility of one or more traffic classes. The more formal
definition of Pareto efficiency is given in Varian 25.
The set of Pareto allocations that satisfy the equilibrium
conditions forms the Pareto surface.
Each agent computes the demand set, which is a set of
allocations, that maximizes the preference under the
wealth constraint. The demand set is obtained by mini-
mizing the utility function under the budget constraint.
The Lagrangian is given below with L as the Lagrange
min,, 0, 0
fcbLp cpwcb
 
Copyright © 2012 SciRes. ME
The function f(c, b,
) is smooth, strictly convex and
compact, thus the demand set is just one element [1,2].
Using the Kuhn-Tucker optimality conditions, the opti-
mal resource allocation vector is obtained, where L is the
Lagrange multiplier
Lp (7)
From this the equilibrium condition is obtained. This
condition states that the marginal rate of substitution is
equal among the competing traffic classes. The economic
problems are to establish competitive equilibrium, com-
pute the equilibrium prices cb
and Pareto optimal
allocations. The equilibrium condition is shown as fol-
Ub p
 (8)
Using the utility function given by Equation (5), the
price ratio is given below. From the equation, it is evi-
dent that the price ratio is a function of the resource allo-
cations and the traffic parameter
cc c
 
This equation can be rewritten in the following way,
where function N has a nice interpretation. It is the ratio
of the effective queue utilization (
(1 U)) to the effec-
tive queue emptiness (1 –
(1 U)), where
log 1
This can also be interpreted as the effective number in
an equivalent M/M/1 queueing system, where the system
utilization is
(1 U). For an M/M/1 system, the
average number in the system is .
The following gives the equilibrium condition for K
agents competing for resources from a single network
provider. From this condition, and the resource con-
straints, the Pareto allocations and the corresponding
equilibrium price ratios can be computed.
  
112 2
112 2
log log
bN bN
pc clog
  (11)
Using the buffer constraint b1 + b2 + b3+ ··· + bk = B,
the equilibrium price ratio and optimal buffer allocation
for each agent i can be represented by the following
bN c
The issue of determining the equilibrium prices, so
that supply equal demand for different types of utility
functions can use convex optimization tools (Chen, Ye
and Zhang, 2007)
Competitive Pricing Algorithm
1) Set initial prices: cc
, .
2) Compute demand set, i.e. find minimum of min [Ui
= fi(ci,bi,
[1,K] given
pcci + pbbi wi (wealth constraint).
. 3) Demand:
4) If (Dc C) < (>) 0, then, pc = pc – (+)Δc.
If (Db B) < (>) 0, then, pb = pb – (+)Δb.
Go back to step (2).
5) Else if Dc = C at pc, and Db = B at pb, then the equi-
librium is attained and prices are at equilibrium
The algorithm computes iteratively the equilibrium
prices in a competitive economy using the utility func-
tions. Given the wealth in the economy, the prices con-
verge to a point on the Pareto surface, which can be
computed using the first-order conditions. There is a
minimum price p
, that each traffic class has to pay, if the
equilibrium prices are lower than pi. Once the prices are
computed, the network service provider releases the re-
sources to the agents.
8. Example of Two Agents and One Supplier
We consider two agents, representing traffic classes of
the M/M/1/B model. The utility function is shown in
Equation (5). The agents have wealth w1 and w2 respec-
tively. The agents compete for resources, which then are
used to provide services to users.
Two Classes: We consider two competing traffic
classes. Using the equilibrium conditions, the equilib-
rium price ratio is given by,
112 2
log log
PNb Nb
 (14)
The above equation states that at equilibrium, the log
of the ratio of utilizations of the two traffic classes is
equal to the ratio of the time to evacuate the residual
buffer space of the traffic classes. Rewriting the above
Nb c
By using the resource constraints c1 + c2 = C and b1 +
b2 = B, the equilibrium conditions become a function of
just two variables. The Pareto surface is the set of alloca-
Copyright © 2012 SciRes. ME
tions that satisfy Equation (14). The function Ni and Ui
(for all i {1,2}) have several interesting properties for
different values of
i. We study the properties of these
functions for various regions of
1 and
2, where
1 and
2 are utilizations of TC1 and TC2 respectively.
1 < 1,
2 < 1: As the buffer is varied to infinity, the
utility function (loss utility) becomes 0, and the effec-
tive average number (N1, N2) become the average
number in an M/M/1 queue. The lim1
b N1 =
, lim U1 = 0. The quantity b1N1 0
for b1 [0,).
1 > 1,
2 > 1: The allocated capacity is less than the
mean rates of TC1 and TC2. We consider the case
where the buffer tends to infinity. lim1
b N
1 = ,
lim 1
b U1= 0. The quantity b1N1 < 0 for b1
1 1,
2 1: The quantity is N1 = b1, N2 = b2. The
equilibrium condition for offered loads equal to 1 is
 
2 2
Several other cases such as
1 > 1,
2 = 1 are omitted,
but are essential in determining the Pareto surface.
For the two competing traffic classes, the following
relation between the utility functions of the traffic classes
with respect to the Pareto optimal allocations is obtained:
11 2
log (17)
This relation has an interesting physical meaning: The
loss of the ratio of the utilities of the traffic classes is
equal to the ratio of the time to evacuate the residual
buffer in the queues. The residual buffer is simply: biNi,
where Ni is given by Equation (10).
9. Conclusions
We demonstrate the application of economic tools to
resource management in distributed systems and com-
puter networks. The concepts of analytical economics
were used to develop effective market based control me-
chanisms, and to show the allocation of resources are
Pareto optimal.
Methodologies of decentralized control of resources,
and pricing of resources are based on QoS demand of
users. We bring together economic models and perform-
ance models of computer systems into one framework to
solve problems of resource allocation and efficient QoS
provisioning. Such a scheme can be applied to pricing
services in ATM networks and Integrated Services In-
ternet of the future.
There are drawbacks to this form of modeling where
several agents have to use market mechanisms to decide
where to obtain service (which supplier?). If the demand
for a resource varies substantially over short periods of
time, then the actual prices of the resources will also vary
causing several side effects such as indefinite migration
of consumers between suppliers. This might potentially
result in degradation of system performance where the
resources are being underutilized due to the bad deci-
sions (caused by poor market mechanisms) made by the
users in choosing the suppliers.
Unlike economies, the resources in a computer system
are not easily substitutable. The future work is to design
robust market mechanisms and rationalized pricing
schemes which can handle surges in demand and vari-
ability, and can give price guarantees to consumers over
longer periods of time. Another drawback is that re-
sources in a computer system are indivisible resulting in
non-smooth utility functions, which may yield sub-op-
timal allocations, and potential computational overhead.
In summary, economic models are useful for designing
and understanding internet-type systems. The Internet
currently connects hundreds of millions of users and
thousands of sites. Several services exist on many of
these sites, notably the World Wide Web (WWW) which
provides access to various information sources distrib-
uted across the Internet. Many more services (multimedia
applications, commercial transactions) are to be sup-
ported in the Internet. To access this large number of
services, agents have to share limited network bandwidth
and server capacities (processing speeds). Such large-
scale networks require decentralized mechanisms to con-
trol access to services. Economic concepts such as pric-
ing and competition can provide some solutions to re-
duce the complexity of service provisioning and decen-
tralize the access mechanisms to the resources.
10. Acknowledgements
This paper is an extended, updated and technically more
advanced version of Chap. 9 in  with permission by
the publisher Nova Science, New York which is highly
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1. The Network Economy
The network consists of V nodes (packet switches) and N
links. Each node has several output links with an output
buffer. The resources at output link are transmission ca-
pacity (or link capacity) and buffer space. The link con-
troller at the output link schedules packets from the
buffer. This is based on how the buffer is partitioned
among the traffic classes and the scheduling rule be-
tween the traffic classes. Sessions are grouped into traffic
classes based on similar traffic characteristics and com-
mon QoS requirements. Sessions that belong to a class
share buffer and link resources, and traffic classes com-
pete for resources at a packet switch. Each session ar-
rives to the network with a vector of traffic parameters
Tr, vector of QoS requirements and wealth. A session is
grouped or mapped to a corresponding traffic class. A
traffic class has common QoS requirements, and we con-
sider QoS requirements per traffic class rather than per
session. Once a session is admitted along a path (a route),
it will continue along that path until it completes.
Each agent k performs the following to obtain the de-
mand set on each link. The allocations are buffer (b) and
bandwidth (c) on each link for each agent. The wealth is
distributed across the links by each agent to buy re-
That is, the problem is to find pairs
that max Uk = f(ck, bk, Trk), constraints pb
, cb
, ,
k + pcck wk.
In the above formulation, each agent k buys resources
from each link. The allocation for agent k is
2 *
kkk k
, ,, c**
bbk k
. An
agent can invest wealth in either some or all the links.
We assume that at each link there is competition among
at least some of the agents for buying resources. As pre-
viously, Gottinger [1999], we show a general utility
function which is a function of the switch resources:
buffer (b) and bandwidth (c). A utility function of the
agent could be a function of:
b b
Packet loss probability Ut = g(c, b, Tr);
Average packet delay Ud = h(c, b, Tr);
Packet tail probability Ul = v(c, b, Tr);
Max packet delay Ub = f(b);
Thruput Uc = g (c).
We consider that an agent will place demands for re-
sources based on a general utility function, which is a
combination of the various QoS requirements:
,, lddb
UfcbTr xUxU xU
where Ul is the packet loss probability utility function,
Ud is the average delay utility function, Ut is the packet
tail probability, Ub is the utility function for max-delay
requirements, and Uc is for bandwidth (throughput) re-
quirements. x1, xd, xb, xc, xt are constants. Agents could
use such a utility function. As long as the convexity
property with respect to buffer b and bandwidth c holds.
Pareto optimal allocations and price equilibria exist.
However, if they are not convex, then depending on the
properties of the functions, local optimality and price
equilibrium could exist. To show the main ideas for
routing and admission control, we use packet loss prob-
ability as the main utility function (Ul), which means we
assume that x1 from the above equation are the only con-
stant and the rest are zeros. For doing this, we need first
some further specifications of the loss probability. We
later show results for Pareto optimality and price equilib-
rium, and then we propose routing and admission control
algorithms. In general, one can assume that agents, on
behalf of user classes, demand for resources from the
link suppliers based on the utility function shown above.
The agent uses the utility function to present the demand
for resources over the whole network of parallel links.
Loss Probability Specifications. At each output link j
the resources are buffer space Bj and link capacity Cj.
Let j
be the link capacity and buffer alloca-
tion to class k on link j where k [1,K]. Let
c and p
b be the price per unit link capacity and unit buffer
respectively at link j, and wk be the wealth (budget) of a
traffic class k. For a link j from the source to the destina-
tion, the packet loss probability (utility) for traffic class k
is given by the following
loss 1
lkj k
 
where k
p is the packet loss probability at link j of agent
The goal of the agent is to minimize the packet loss
probability under its wealth or budget constraints. If the
traffic classes have smooth convex preferences with re-
spect to link capacity and buffer allocation variables at
each link, then the utility function Ulk is convex with
respect to the variables.
2. The Server Economy
We now discuss the server economy where servers offer
processing resources and memory to agents representing
user classes. The agents compete for these resources and
buying as much as possible from suppliers. The agents
perform load balancing based on the OoS preferences of
the class it represents.
The economic model consists of the following players:
Agents and Server Suppliers, Consumers or user classes
and Business. User sessions within a class have common
preferences. User classes have QoS preferences over
average delay and throughput, and in some cases com-
pletion times of sessions (deadlines). Users within a class
share resources at the servers.
Copyright © 2012 SciRes. ME
Agents and Network Suppliers: Agents represent user
classes. An agent represents a single user class. Agents
negotiate with the supplier and buy resources from ser-
vice providers. Agents on behalf of user classes demand
for resources to meet the QoS needs. Suppliers compete
to maximize revenue. Suppliers partition and allocate
resources (processing rate and memory) to the competing
Multiple Agent Network Supplier Interaction: Agents
present demands to the suppliers. The demands by agents
are based upon their wealth and user class preferences.
The demand by each agent is computed via utility func-
tions which represent QoS needs of the class. Agents
negotiate with suppliers to determine the prices. The ne-
gotiation process is iterative where prices are adjusted to
clear the market. Price negotiation could be done peri-
odically or depending on changes in demand.
The agent and network supplier become service pro-
viders in the market. The role of the supplier is to pro-
vide technologies to sell resources (buffer and bandwidth
units) and to partitioning them flexibly based on the de-
mand by the agents. The agents transform the goods
(buffer and bandwidth) and provide QoS levels to the
user-classes. The agents strive to maximize profits (mini-
mize buying costs) by using the right utility functions
and the right performance models in order to provide
QoS to the user-class. More users within a user-class im-
plies more revenue for the agent. The agent is decoupled
from the traffic class and the supplier.
In this economy, user classes are transaction classes
that send transactions to database servers for processing.
The transaction processing time at each of the server is
based on the type of transaction. Consider K classes of
transactions and each class is represented by an agent
(economic agent). In the economy, the agents negotiate
with the servers for server capacity. We assume that
transactions of any class can run on any of the database
servers. Therefore, agents negotiate with all the servers
for server thruput (or processing speed). A model where
K agents compete for services in a transaction processing
system, each class could do the following based on its
preferences on average delay and thruput: 1) each agent i
can minimize its average response time under throughput
constraints; 2) each agent i can maximize throughput of
its transactions under an average delay constraint; 3)
each agent i can look at a combination of QoS require-
ments and have preferences over them.
Therefore, each class can choose either one of these
preferences and let the agent control the flow of transac-
tions through the system. The problem now becomes a
multi-objective optimization problem as every agent is
trying to maximize its benefit in the system based on the
class of QoS preferences. Consider that the classes wish
to choose various objectives, the the utility function as-
sumes U xdUd xlUl where Ud is the utility function for
average delay and Ul is the utility function for through-
put, and xd and xl are constants. Consider that there are
requirements for transaction completion time. Instead of
scheduling transactions to meet deadlines, we try to
minimize the number of transactions that have missed
the deadlines (in a stochastic sense). Consider that each
transaction class is assigned a service queue at each
server, then we try to minimize the probability of the
number of transactions of a class exceeding a certain
threshold in the buffer. This is the tail probability P(X
b) where X is the number of transactions of a class in a
queue at a server, and b is threshold is threshold for the
number in the queue, beyond which transactions miss
deadlines. If we include this QoS requirement, then the
above utility function will be U xdUd xlUl xtUt
where Ut is the tail probability utility function and xt is a
Pareto Optimality: We now have a simple formulation
for classes competing for server capacity (processing rate)
in order to minimize average delay (or average response
time). The utility function is simply U xdUd as the rests
of the constants are zero. Let pj be the price per unit
processing rate at server j. The maximum processing rate
at server j is Cj. The problem therefore for each agent is
the following: find {} such that min
ijiij ji
with constraints
In the above problem definition, each agent will try
and minimize the utility function under the wealth
conbstraint and under the throughput constraint. This
constraint is necessary to make sure that positive values
of throughput are obtained as a result of the optimization.
The transaction agents compete for processing rate at
each server, and transaction servers compete for profit.
The objectives of the transaction classes are conflicting
as they all want to minimize their average response time.
In the above formulation Wij
The average number of class i transactions in queue at
system j. The average delay in the system for each class i
is simply the average number in the system divided by
the overall throughput 1ij
The main goal of the agent representing the transac-
tion class is to minimize a utility function which is sim-
ply the average number in the overall system. This will
also minimize the average delay or average response
time of the transaction class.
Proposition 1. The utility function Ud is convex with
respect to the resource allocation variable cij where
[0, cij), and cij (0, Cj].
The proof follows from Gottinger 23.
The utility function Ud is discontinuous when
ij cij.
Demand Set. The demand set for an agent i, given the
Copyright © 2012 SciRes. ME
Copyright © 2012 SciRes. ME
prices (pj of server j) of the processing rates (or capaci-
ties) at the servers is {ci1, ci2, ···, ciN} over all the servers.
We use the standard techniques of optimization to find
the demand set, which is given as follows for all j [1,
Proposition 2. Consider K agents competing for proc-
essing resources from N servers. If the utility function of
these agents is Ud and the performance model at the
servers is an M/M/1 model, then price equilibrium and
Pareto optimality exist.
ijijiij jij
 
jij j
. The proof of this proposition is the same as described
in Gottinger 23. The utility function Ud is continuous
and decreasing convex with respect to the allocation
variables cij. The function is discontinuous when
ij cij.
Price Equilibrium: Once the demand set is obtained,
then using the wealth constraints, we can solve for the
equilibrium price. This is not easily tractable. However,
numerical results can be computed using the tatonnement
process whereby agents compute the demand set, given
the processing rate prices by each server.
Due to this, Pareto allocations or price equilibrium
may not exist. However, we solve this problem by stating
that the agents, when they present their demands, have to
make sure that the transaction throughput rate
ij at a
server has to be lower than the capacity allocation cij. If
this is not met, then the price iteration process or the ta-
tonnement process will not converge. We assume that the
servers know the transaction thruput or arrival rate from
each agent during the iteration process.
An iteration process between the agents and the servers
takes place. This will converge to an equilibrium price,
when demand equals the supply which is 1ij j
We now state formally the result for K agents com-
peting for processing resources from N servers.