J. Service Science & Management, 2010, 3, 345-351
doi:10.4236/jssm.2010.33040 Published Online September 2010 (http://www.SciRP.org/journal/jssm)
345
Pricing Services in a Grid of Computers Using
Priority Segmentation
Emmanuel Fragnière1, Francesco Moresino2
1School of Management of the University of Bath; 2Haute École de Gestion de Genève.
Received May 27th, 2010; revised July 1st, 2010; accepted August 6th, 2010.
ABSTRACT
In the past decade many grids of computers have been built among non-profit institutions. These grids are built on a
voluntary participation and the resources are not charged to the users. When a resource is given free of charge its al-
location is in general not optimal. In this paper, we propose an original mechanism that allows an optimal resource
allocation without cash exchanges. We develop a pricing scheme where the service is segmented according to the prior-
ity level. The optimal prices of the different services are obtained by solving a Markov Decision Process (MDP). Each
participant receives a credit that is proportional to its contribution that enables him to have access to services offered
by the grid.
Keywords: Service Pricing, Grid Economy
1. Introduction
Grid computing has become increasingly important in
recent years with ever increasing demand of computing
and storage resources [1].
Sharing, selection and collection of geographically
distributed resources such as super computers, storage
systems, data resources and specialized devices are made
possible by grid network for solving large-scale re-
source-intensive problems in science, engineering and
commerce. Organizations that are looking for extremely
high computing power for short periods of time, but
which do not necessarily want to invest further in their
own computing resources are finding grid computing as
an attractive alternative. Several large firms such as IBM,
Unilever, Ericsson and Hitachi are investing large sums
of money in developing grid computing initiatives [2].
The idea of creating a grid to share resources which
seems to be very intuitive now was originally borrowed
from electrical power grid. In the mid-1990 scientists
began to explore the design and development of an infra-
structure which was analogous to electric grid due to its
pervasiveness, ease of use and reliability [3]. The moti-
vation for computational grids was initially driven by
large scale, resource-intensive (computational and data)
scientific applications that require more power than a
single computer (PC, workstation, supercomputer, or clu-
ster) [1].
In most grid projects, the connected PCs are generally
made available at no cost. Indeed it serves the needs of
research projects requiring huge computing power.
However, economic theory tells us that if prices are set in
a fair manner between the provider and the user of the
service, this should lead to an optimal allocation of re-
sources. For users, the value of a grid is higher than its
accounting value. Indeed, the grid offers more than soft-
ware and hardware: it offers a service. In practice, the
pricing of services is mainly based on the cost structure,
which does not take into account the real value provided
to the client.
In this paper, we propose an original mechanism that
provides an optimal resource allocation without involv-
ing cash exchanges. We propose a pricing scheme where
the service is segmented according to the notion of prior-
ity level. The optimal prices of the different services are
obtained by solving a Markov Decision Process (MDP).
Each participant receives a credit that is proportional to
its contribution that enables her/him to have access to
services proposed by the grid.
This paper is organized as follows. In Section 2, we
present the particular nature of grid pricing services. In
Section 3, we explain notions of market based resources
in the context of shared grid computing. In Section 4, we
present the pricing model using priority segmentation. In

Pricing Services in a Grid of Computers Using Priority Segmentation 346
Section 5, we illustrate our model with a simple instance
and present numerical results. Finally, in Section 6, we
indicate further research directions.
2. Service Proposal and Pricing for Grid
Users
What could be done for pricing grid services? Most of
the pricing techniques applied to the service sector are
devoted to service commodities like airplane seats or
hotel rooms. Service activities are traditionally described
with the help of the IHIP paradigm (intangibility, het-
erogeneity, instantaneity and perishability). Intangibility
and heterogeneity make the pricing scheme not easy to
model services. The pricing of a service relies upon three
pillars: internal organizational costs, the competitors’ pri-
ces and the perceived value by the customers. In this re-
search, we focus our attention on the latter, i.e. the value
perceived by the customers in the service experience.
As a matter of fact the question of pricing is essential
to analyzing the system of service production. Pricing
directly impacts how the service is positioned, and influ-
ences equally how clients and coproducers will interact.
The paradigm of the price/quantity economic model can
not be fully realized in the service world, however. Quan-
tity is replaced by the idea of value perception, which
naturally impacts the conventional production model.
Grid services fall in the category of knowledge based
services. Consequently, a service plan based on know-
how and expertise depends on the following: a thorough
and clear understanding of the needs and expectations of
clients, the ability to elaborate a diagnosis of client needs
from limited information, the outline of a specific service
proposal, the efficient use of delivery processes and of
existing products (or product modules), and finally a
custom-made solution that incorporates perceived value-
added (often referred to as problem resolution).
Very often, delivering more value in the knowledge-
based services means delivering more tangibility and
more customization. Customization has been defined as
the ability of the service delivery system and its employ-
ees to attend flexibly to customer needs [4]. Customiza-
tion may also induce more risky operations as services
would become inherently variable in how they are con-
ducted, and according to [5], it is to be expected that
problems will occur. Therefore, how to make attractive
and price service operations that increase tangibility and
customization for the customer while reducing (or main-
taining) the complexity of managing real heterogeneity?
In recent research, we are exploring the potential pric-
ing schemes that could be established and the relevant
criteria that should be used to determine a fair price in
the context of grid services taking into account the point
of views of providers and consumers of knowledge-based
services. To answer to this question, we must develop a
grid service model based on the main attributes (also
called salient attributes of the service in the share of
choice model terminology [6]) as perceived by the user.
In our case, we could retained several attributes such as
the capacity made available to the user (three formats -
small, medium and large), the proper priority manage-
ment of jobs executed (the objective that is to be retained
in the model presented hereafter), or reporting relevant
information to the users. In this paper we will assume
that priority management is a salient attribute of grid
services, which is perceived as important in terms of
value. However it is clear that in a subsequent research,
we need to investigate through survey techniques what
represent the most important salient attributes for grid
users.
In this project, we intend to develop a pricing scheme
based on the perceived value by the user of an actual grid
application. This contribution is based on interdiscipli-
nary research. Indeed, our pricing model essentially bor-
rows academic findings arising from Marketing and Ser-
vice Science. The solution relies on a number of different
fields: Operations Research, Game Theory and Negotia-
tion Theory. We can consider three cases that are rele-
vant for different situations: 1. the grid is managed by a
central agency, 2. the actors in the grid are competing
without cooperation, 3. the actors in the grid are compet-
ing but cooperation is possible.
In this paper, we will solely tackle the case where the
grid is managed by a central agency. For instance, we
have already explored the shadow prices approach through
an optimization problem called the share of choice model
[6]. This latter model attempted to optimize the design of
a service by selecting its attributes according to the per-
ceived value of a sample of clients. Perceived values
were expressed as utility functions obtained from con-
joint analysis. Conjoint analysis techniques permit the
construction of path-worth or utility functions for each
respondent regarding the different attributes of the ser-
vice.
Regarding what has been presented, our goal is to
compute a price for the utilization of the resources such
as CPU, RAM, bandwidth, libraries, etc. However, the
price will be differentiated as a function of the quality of
the service (in particular, privileged users that can have
priority for their jobs) and also as a function of the level
of demand (different prices for rush hours and off-peak
hours).
3. Market Based Resource Management
There has been extensive research on how to manage the
resources in an efficient way, optimize its usage, balance
the load and reach maximum user satisfaction. Sharing

Pricing Services in a Grid of Computers Using Priority Segmentation347
resources fairly with economic efficiency, where effi-
ciency can be defined as ratio of the actual total benefit
for all users to optimal total benefit, at a low cost still
remains a challenge [7]. The fact that consumers have dif-
ferent goals, preferences and policy further adds to the
complexity of resources management [8]. Software agents
such as automatic scheduling programs and negotiation
agents can play an essential role in realizing this vision
of the grid. Numerous economic models for grid resource
management such as commodity market models, auction,
contract-net/tendering models, bargaining models, posted
price models, bid-based proportional resource sharing
models, cooperative bartering models, and monopoly and
oligopoly had been proposed in the literature [9]. While
some of the more commonly referenced work focused on
commodity markets, auctions and fixed budget based
marketing mechanism for the resource management [10],
auctioning has long been an important aspect of many
economies. Indeed, it provides a fair trading environment
as a decentralized structure, are easier to implement than
other economic models and respect the autonomy of re-
source owners [11]. In Another variant of auctioning
fixed budget mechanism efficiency and fairness of the
allocation of resources at equilibrium is evaluated through
the measures of “utility uniformity” and “envy-freshness”.
The grid resource allocation model is based on Continu-
ous Double Auctions (CDA). Different scheduling strate-
gies have been analyzed which can be applied by the user
to execute workflows in such an environment, and try to
identify the general behavioral patterns that can lead to a
fast and cheap workflow execution [12].
In history based pricing model consumers and produc-
ers determine their bid and Ask prices using a sophisti-
cated history-based dynamic pricing strategy and the
auctioneer follows a discriminatory pricing policy which
sets the transaction price individually for each matched
buyer-seller pair. The pricing strategy presented gener-
ally simulates human intelligence in order to define a
logical price by local analysis of the previous trade cases.
Here the authors employ a continuous double auction
protocol as an economic-based approach to allocate idle
processing resources among the demanding nodes [13].
In the economic model the center point is the interac-
tion between grid users and providers. While most mar-
ket models have been based on auctions, commodity
market models have also been interesting research topic.
Markets are considered to be based on commodity where
applications can treat computational and storage re-
sources as interchangeable and not as specific machines
and disk systems. Obviously, prices are a key element of
this model [14-16].
An alternative approach to market based and economy
based models is finance based model. Various grid re-
sources such as memory, storage, software, and compute
cycles are seen as individual commodities and pricing of
the resources is done in isolation and in combination of
various resources. A quality of service (QoS)-profit equi-
librium model has been proposed for pricing grid re-
sources that is based on finance concepts [17].
Two shortcomings in a grid economic environment
have been identified in [18]. The first shortcoming is that
there are no standards for pricing schemes, caused by a
large difference in the units that are traded (e.g. CPU
cycles or virtual clusters) in grid computing. The second
shortcoming is the lack of models for managing the pric-
ing of intangible elements (e.g. software applications)
and computational elements (e.g. virtual machines, which
comprise resources such as CPU, memory, disk space,
network bandwidth).
3.1. A Pricing Scheme Adapted to the Particular
Nature of Grid Services
This paper further presents a pricing service for grid com-
puting services, which resolves these shortcomings by
introducing a general pricing scheme for informational
and computational elements. We describe the functional
requirements, architecture, and the interfaces of the pric-
ing service. The pricing service allows expressing the
proposed general pricing scheme as an XML document,
which can be linked to the Service Level Agreements
(SLA). Contrary to other proposals on pricing, the pric-
ing service is separated from the functionality of meter-
ing, accounting, and payment.
Various kinds of solutions to grid resource discovery
have been suggested, including centralized and hierar-
chical information server approaches. However, both of
these approaches have serious limitations in regard to
scalability, fault tolerance, and network congestion. To
overcome these limitations, indexing resource informa-
tion using a decentralized, for instance peer to peer, net-
work model has been actively proposed in the past few
years [19].
A new infrastructure called Grid Bank provides ser-
vices for accounting of the grid resources thus filling the
gap of these needed services. The support of computa-
tional economy and accounting services can lead to a
self-regulated accountability in grid computing. This
paper presents requirements of grid accounting and dif-
ferent economic models within which it can operate and
proposes a Grid Accounting Services Architecture to
meet them [20].
Practically, we intend to focus on a particular salient
attribute of typical grid services which represents in our
case an intangible element of perceived value by the user.
This makes our approach original compared to previous
papers on grid pricing. The salient attribute developed in

Pricing Services in a Grid of Computers Using Priority Segmentation 348
our model corresponds to the idea that priorities of jobs
executed on the grid are most of the time satisfied. In-
deed services provide users with benefits that are per-
ceived with more or less value. Consequently, we assume
that the management of priorities in the execution of jobs
is perceived as an important element of value. In logistic
terms, the quality of this management corresponds in the
model to our service level. To be able to obtain a pricing
strategy leading to the best priority management of jobs
executed, we have developed a mathematical program-
ming model. It aims at minimizing inconveniences due to
mismanagement of priorities while taking into account
grid capacity constraints. As probabilities of a given job
being put “on hold” exist, we treat capacity constraints of
the grid as a Markov Decision Process (MDP). In the
following section, we present the detailed model that we
have developed for illustrative purposes.
4. The Model
4.1. Description of the Model
The grid is shared by U different users described by the
variable u = 1, ..., U. The jobs are classified in J different
categories according to the level of urgency. Categories
are described by the variable j = 1, ..., J. Category j = 1
includes very urgent jobs and category j = J includes job
that are not urgent at all. The grid can process jobs with P
different priority levels. The highest priority is p = 1
whereas the lowest priority is p = P.
For each user, jobs arrive randomly following an ex-
ponential distribution. Let
j
u

be the parameter of the
distribution for the job’s category j and for user u. The
job’s size is random and follows also an exponential dis-
tribution. Let
j
u

be the parameter of the distribution
for the job’s category j and for user u.
Each user is rewarded at each period with a certain
amount of monetary units that permits him to pay the
services provided by the grid. Let u

be the amount
received at each period by user u. This repartition should
reflect the contribution of user u to the grid (i.e. number
of computers, IT specialist, etc. offered by user u to the
grid’s community).
The services provided by the grid are charged accord-
ing to the CPU time used and priority level p requested.
Let
p

be the price per CPU time for jobs with priority
p.
The objective of the grid manager is to provide the
best service to the users with the actual capacity of the
grid. The service quality is measured by a penalty func-
tion, the lowest the function the highest the quality. This
function increases each time a job is not completed on
time. This function can, for example, measure the per-
centage of jobs done with a delay. The grid manager has
to find the optimal prices
p

in order to have the lowest
penalty function.
The objective of the user is to minimize its own pen-
alty function choosing the right priority for each job.
They are two possible actions for a user. Firstly, when a
new job arrives he has to decide which level of priority
will be chosen. Secondly, when a job is in the queue, he
can decide to change the level of priority of the job. Of
course each decision is taken knowing the load of work
of the grid. The set of all possible actions is denoted with
A.
4.2. The Model’s Equations
This model is described by a MDP where budget con-
straints are added. The only possibility to solve this en-
riched MDP is to use the linear programming approach.
Value iteration or policy iteration algorithms are not
adequate for this enriched MDP.
At this point, we must say that the description of the
selfish behavior of each user should be done using Nash
equilibrium rather than a MDP. However, this would
conduct to a stochastic variational inequality that is very
difficult to solve. In order to mimic the selfish behavior,
additional constraints are included in the MDP model.
For each user u, let


,,
x
ujp be the number of jobs
of category j with priority p that is currently in the sys-
tem. Denote with




,,Sxujp
,,ujp
 the possible states
of the system.
Let


,,qssa
 be the generator of the MDP. For the
cases
s
s

,


,,sa

qs is computed from the corre-
sponding
j
u

and
j
u

. For the other cases, we have




,,qssa,,ss aqs

. It is important to realize that
the main difficulty in modeling a MDP is to compute its
generator. For example, the capacity constraints of the
grid are included in the generator. Modeling capacity
constraint in a MDP model is less intuitive than modeling
capacity constraints in a linear programming model.

Let


,
s
u be the price charged to user u for his
jobs that are currently treated by the grid. It depends of
course on the prices
p

.
The linear program associated with this enriched MDP
is

 
,
min ,,
sa
Csa Ysa

subject to




,
,,,0
sa
qssa YsasS






,
,1
sa
Ysa





,
,, 1,...,
u
sa
s
aYsau U   


Pricing Services in a Grid of Computers Using Priority Segmentation349

,0 , Ysas SaA 
The first equations represent the flow constraints and
the second equation is the normalization of the probabili-
ties. The last inequalities represent the budget constraints
for each user. From this model, the steady state proba-
bilities are computed as follows
 
,Ps Ysa
a
and the optimal policy is given by
 

,
,Ysa Dsa Ps 

,Dsa1
0
if policy a is implemented when the state
is s (otherwise ). Note that random policies
could be possible. In this case we have

,Dsa


0,Dsa1
and .

,1 s
s
As S has to be finite, we impose reflection conditions
on the boundaries. The interested readers can find a de-
tailed description of the modeling methods offered by the
MDP paradigm in [21] and [22].
Ds
a
If the prices
p

are taken as a variable, the model is
a quadratic program with a non positive definite matrix.
In this case, standard software cannot solve the model.
To avoid this problem, we consider the prices as pa-
rameters. In this case, the model is a linear program that
is easily solved if not too big. As the model is not convex
in
p

we use a uniform space covering method in order
to find the global optimum.
5. Numerical Illustration
The aim of this illustration is to present a numerical ap-
plication of the general model. Our goal is just to show
the efficiency and implementability of the method. We
have thus on purpose simplified it. In this small model,
we assume to have two categories of jobs: urgent and not
urgent ones. We have two kinds of priorities: high and
low priority.
This model attempts to describe users that need a huge
number of computers for running their jobs. In this ex-
ample we suppose that each job need the third of the grid
resources. This means that maximum three jobs can be
processed simultaneously without congestion. In case of
congestion, jobs with high priority are processed first. If
there are more than 3 jobs with high priority, the last
coming jobs are sending in the queue. Doing so, jobs are
always processed at full speed or send in the queue.
For this numerical illustration, we assume to have two
different kinds of users. The first kind of users expect a
lot of urgent jobs that are on average small whereas the
second users expect less urgent jobs that are on average
big.
In this numerical experiment the objective is to maxi-
mize the service level, which is the percentage of jobs
that are done without delay.
Table 1 indicates the main parameters employed in the
instance developed for the model presented in the previ-
ous section. The model was written in AMPL and solved
with the software MOSEK. Table 2 presents the optimal
solution for different prices. Prices are given in monetary
units per CPU time. We ran the model for more prices
but show only few representative results.
We see distinctly that the price policy has an effect on
the service level. Indeed, choosing the right prices per-
mits the community to avoid wasting the resources and
as a consequence to increase the service quality. In this
example, the maximal service level can be attained with
several price policies. More than the results, this small
model show the applicability of this method.
However, we must emphasize that MDPs are subject
to the “curse of dimensionality”. For bigger models, the
state’s set S can become too big. In this case it is neces-
sary to reduce the size of the model, applying, for ins-
tance, a decomposition and parallel processing method
[23].
6. Conclusions and Future Research
In this paper, we propose a new approach to share opti-
mally the resources of a grid of computers. This ap-
proach is based on a segmentation of the service where
different prices are computed using an enriched MDP
model. The method is versatile and can be adapted to
numerous problems. Here, the service is segmented accor-
Table 1. Data inputs for the model.
Parameter Value
α11 0.02
α21 0.05
α12 0.2
α22 0.1
β11 0.005
β21 0.005
Table 2. Service level for different prices.
Price for high
priority jobs
Price for low
priority jobs Jobs on time
1 0.2 97.8%
1 0.4 97.8%
1.2 0.2 91.8%
1.2 0.4 90.2%
1.4 0.6 81.9%
2 0.2 80%

Pricing Services in a Grid of Computers Using Priority Segmentation 350
ding to the priority level. The service level corresponds
to the percentage of jobs executed without delay, but it
could be any other kind of utility functions. As a matter
of fact, we have also implemented a more comprehensive
model where the service is segmented according to the
quality of the computers (speed and size of the memory).
Stochastic models described with MDPs can have a
huge size and therefore very difficult to solve. A solution
to this problem consists of applying a decomposition and
parallel processing method. The structure of the MDP
could be exploited to decompose the model into U (i.e.
the number of users) smaller single user models. These U
smaller models are then linked together with a coupling
linear program.
As we mentioned earlier, the selfish behavior of each
user is mimic including in the MDP model additional
constraints. Unfortunately, this way of doing is only an
approximation. To perfectly describe this behavior, we
should incorporate in the model game theory. The model
should be described by a Nash equilibrium rather than a
MDP. However, this would lead to a stochastic varia-
tional inequality that can be challenging to solve.
7. Acknowledgements
This work has been sponsored by the project Virtual
EZ-Grid from the Swiss national fund AAA/SWITCH. A
preliminary version of this paper has been presented in
the proceedings of IEEE/INFORMS International Con-
ference on Service Operations, Logistics and Informatics.
We thank Nabil Abdennadher and Aarti Agrawal for
their help.
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