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Dimensioning Virtualized Wireless Access Networks
from a Common Pool of Resources
Mohammad J. Abdel-Rahman1, Kleber V. Cardoso2, Allen B. MacKenzie1, and Luiz A. DaSilva3
1Dept. of Electrical & Computer
Engineering
Wireless @ Virginia Tech
2Instituto de Inform´
atica
Universidade Federal de Goi´
as
Goiˆ
ania, GO, Brasil
3CONNECT Centre for Future
Networks & Communications
Trinity College Dublin
Abstract—Resource sharing in mobile wireless networks has
been employed to reduce costs, extend coverage, and ease the
entry of new players in the market. The introduction of pro-
grammability and virtualization is expected to amplify these
benefits of resource sharing. In this paper, we study a new
virtualization-based paradigm for resource sharing in mobile
wireless networks. Specifically, we consider the problem of re-
source allocation, particularly when user demands are uncertain.
We formulate several two-stage sequential stochastic allocation
schemes that provide tradeoffs between cost and user satisfaction.
These allocation schemes are studied under different resource
provider pricing models. Our simulations demonstrate that:
First, while reducing cost significantly, virtualization considerably
improves user satisfaction, and virtualization gains increase
with the number of operators that share resources. Second,
the improvements in cost, user satisfaction, and resource usage
increase substantially with the level of user clustering.
Keywords—Virtualized wireless networks, resource allocation,
capacitated set cover problem, multi-stage sequential optimization.
I. INT ROD UC TI ON
Infrastructure sharing has been a common practice between
mobile network operators (MNOs) as a solution to decrease op-
erational expenditures (OPEX) and extend network coverage.
However, the motivations and opportunities for resource shar-
ing have recently increased significantly due to the high cost
of technology innovations, the increasing demand for coverage
and capacity, and the introduction of programmability and vir-
tualization in mobile wireless networks. Resource sharing can
now contribute to savings on capital expenditures (CAPEX)
related to technology update and roll-out of infrastructure in
low subscriber density areas as well. Furthermore, resource
sharing can enable new specialized service providers (SPs),
such as over-the-top (OTT) SPs, offering video streaming or
online social networking, to ensure appropriate wireless cover-
age and capacity for their services without high infrastructure
investment. In fact, there are still unexplored opportunities
associated with resource sharing in mobile wireless networks,
but they depend on a paradigm shift to unleash the potential
of innovations such as virtualization.
Sharing was introduced in mobile wireless networks mainly
to fulfill two needs. First, MNOs needed to offer coverage
for users in areas where they did not have infrastructure,
This work has been partially supported by the grant 204486/2014-9 from the
Brazilian Research Agency (CNPq), the National Science Foundation (NSF)
under grant number 1443978, and the Science Foundation Ireland under grant
number 10/IN.1/I3007.
Fig. 1: Sharing architecture in virtualized wireless networks.
thus they established roaming agreements. Second, the cost
to maintain the sites of the mobile wireless infrastructure
became very high in some areas, and passive sharing in such
environments led to considerable cost savings [1]. The benefits
of these resource sharing scenarios motivated the development
of several resource sharing approaches that involve different
parts of the mobile wireless networks. Today, MNOs may share
antennas, base stations (BSs), radio access networks (RANs),
and core networks. Solutions such as multi-operator RAN
(MORAN) and multi-operator core network (MOCN) have
shown even higher cost savings on CAPEX and OPEX [2]. The
technologies developed for MNO sharing have also brought
other benefits, easing the introduction of new players in the
mobile value chain. This gave rise to mobile virtual network
operators (MVNOs), which provide mobile services without
owning an access network.
The benefits of resource sharing in mobile wireless net-
works and the increasing adoption of programmability and
virtualization in such networks motivate further investigation
and development on wireless network virtualization [3]–[6].
In [3], [4], the opportunities for cost saving and the additional
flexibility are the motivations behind introducing virtualization
schemes for LTE networks, focusing on resource sharing.
Doyle et al. [5] presented a new paradigm for resource
sharing that broadly explores the concepts of virtualization
and programmability. The authors proposed removing the
traditional constraints on spectrum and infrastructure sharing,
and presented a structure for mobile wireless networks that
is grounded in virtualization. In our work, we employ some
concepts of this new paradigm to investigate the potential of
resource sharing in virtualized wireless networks.
Figure 1 shows an architecture derived from the Network
without Borders (NwoB) paradigm, presented in [5]. A service
provider (SP) can be a traditional MVNO that provides data,
voice, and messaging services or a specialized MVNO that pro-
vides data services for specific applications (e.g., IoT devices)
or any of the current over-the-top services. The virtual network
builder (VNB) composes and aggregates virtual resources from
resource providers (RPs) to build virtual networks for SPs.
An RP is the owner of a set of physical resources that are
offered as virtual resources in a set of resource pools, according
to contracts established with VNBs. Traditional MNOs1and
cloud computing providers are two potential examples of RPs.
In this paper, we consider the problem of resource al-
location in virtualized wireless networks. First, we develop
resource allocation optimization problems that are solved at
the VNB to determine the optimal set of resources to be leased
from one or multiple RPs and sliced and allocated to various
SPs. We consider two optimality criteria: maximizing the SP
user satisfaction and minimizing the cost of the BSs required
to meet all SP demands. Using a multi-stage sequential opti-
mization, we explore a tradeoff between these two optimization
goals. Next, we extend the proposed allocation schemes to the
case when (i) the SP user demands are random variables with
known distributions and (ii) the goal of the VNB is to meet
the SP demands only with a certain probability (<1).
The rest of the paper is organized as follows. The system
model is presented in Section II. We formulate our deter-
ministic resource allocation schemes in Section III, followed
by the stochastic resource allocation schemes in Section IV.
All proposed schemes are numerically evaluated in Section V.
Finally, in Section VI we conclude the paper.
II. SY ST EM MO DE L
We consider a geographical area that consists of a set L
of locations and is covered by NRPs. Each RP has a set of
BSs, and the union of these sets is denoted by S. The capacity
of BS s∈ S is denoted by rs. Let uls ∈[0,1], l ∈ L, s ∈ S,
represent the normalized capacity (with respect to rs) of BS s
at location l, i.e., the normalized maximum rate that a user can
receive at location l.uls = 0 when lis outside the coverage
area of BS sand uls = 1 when lis within a small distance
of BS s. The cost of BS s∈ S is denoted by cs. We assume
that there is a set Mdef
={1,2, . . . , M }of SPs.
We consider two resource allocation models: deterministic
and stochastic. In the deterministic model, each SP requests
a fixed rate in each location, and the objective is to meet the
SP demands deterministically (i.e., with probability one). We
denote the rate requested by SP mat location lby dml. In the
stochastic model, the rate requested by SP mat location lis a
discrete random variable ˜
dml, which has a known distribution.
The goal in the stochastic resource allocation model is to meet
the demand of SP mat location lwith probability βml ∈(0,1).
In our resource allocation models, a BS s∈ S can be sliced
between multiple SP users that are collocated at position l∈ L,
and δmls ∈[0, rs]represents the rate of BS sthat is allocated
to SP mat location l.
Next, we develop several deterministic and stochastic
resource allocation optimization formulations for virtualized
wireless networks.
1A traditional MNO may play roles as both an SP and an RP in our
framework.
III. RES OU RC E ALL OC ATIO N WI TH DE TE RM IN IS TI C QOS
GUAR AN TE ES
In this section, we formulate the deterministic resource
allocation schemes, and in Section IV we discuss the stochastic
allocation schemes. We first consider the problem of minimiz-
ing the cost of meeting the demands of MSPs, assuming that
the VNB has enough resources to meet all demands. Then,
we consider the case when the available resources might not
be enough for all demands. In this case, we consider the
problem of maximizing the level of SP user satisfaction, with
minimizing the cost as a secondary objective.
A. Optimizing the Cost
We formulate two cost-efficient resource allocation
schemes that are executed at the VNB to determine the optimal
set of resources to be leased from one or multiple RPs and
sliced and allocated to various SPs. The two allocation schemes
differ in the adopted RP pricing approach. In the first scheme,
the price of a BS does not depend on the fraction of the BS
that is allocated, whereas in the second scheme, the price is a
function of the allocated portion of the BS2. Both problems are
formulated as modified versions of the capacitated set cover
(CSC) problem. The CSC problem can be described as follows.
Given a set Xof nelements, each with a certain demand (d(e)
for element e), and a collection Sof msubsets of X, each
with a certain supply and cost; the goal is to find a minimum-
cost collection of subsets in Ssuch that for each element e,
the total supply of the subsets that cover eis at least d(e). The
difference between our formulations and the CSC problem is
that in our formulations the supply (capacity) of each set (BS)
can be sliced/divided among its elements (users). We denote
the CSC problem with slicing by CSCS. The two proposed
cost-efficient resource allocation problems above are denoted
by CSCS-1 and CSCS-2, respectively.
1) CSCS-1 Allocation Scheme: Our goal is to find the
cheapest subset of BSs to be leased from the RPs, such that,
when sliced and allocated to SPs, these BSs can determin-
istically meet all SP demands at every location l∈ L. Let
xs, s ∈ S, be a binary decision variable indicating whether
to lease BS sor not. Then, the CSCS-1 problem can be
formulated as follows:
Problem 1 (CSCS-1):
minimize
(δmls,xs
m∈M
l∈L,s∈S)(X
s∈S
csxs)(1)
subject to:
X
s∈S
uls δmls ≥dml,∀m∈ M,∀l∈ L (2)
X
m∈M X
l∈L
δmls ≤rsxs,∀s∈ S (3)
where uls,δmls ,dml, and rsare defined in Section II. The
objective function (1) represents the cost of the leased BSs.
2We note that a real RP might choose a pricing approach that is a
combination of these two approaches.
Constraint (2) ensures satisfying the demand of each SP at
every location. Constraint (3) prevents the total assigned rate
of a BS from exceeding its capacity.
2) CSCS-2 Allocation Scheme: In CSCS-2, the price of a
BS depends on the assigned/used portion of this BS.
Problem 2 (CSCS-2):
minimize
(δmls
m∈M
l∈L,s∈S)(X
m∈M X
l∈L X
s∈S
cs
δmls
rs)(4)
subject to:
X
s∈S
uls δmls ≥dml,∀m∈ M,∀l∈ L (5)
X
m∈M X
l∈L
δmls ≤rs,∀s∈ S.(6)
B. Optimizing the User Satisfaction
In many cases, the available resources might not be enough
to meet all SP demands. In such scenarios, Problems 1 and 2
will be infeasible. In this section, we propose two optimization
problems (one corresponds to CSCS-1 and the other to CSCS-
2) to obtain the percentage of fully-satisfied SP users and the
level of satisfaction of users that are not completely satisfied.
In the proposed formulations, the goal is to maximize the level
of SP user satisfaction by providing them with the closest rate
to their demand. In addition, we consider minimizing cost as a
secondary objective. Our problems are formulated as two-stage
sequential optimization problems, as follows.
1) CSCS-1 Allocation Scheme: The two-stage CSCS-1
problem can be formulated as follows:
Problem 3 (Two-stage CSCS-1):
STAGE 1: maximize
(δmls
m∈M
l∈L,s∈S)(X
m∈M X
l∈L X
s∈S
uls δmls)(7)
subject to:
X
s∈S
uls δmls ≤dml,∀m∈ M,∀l∈ L (8)
X
m∈M X
l∈L
δmls ≤rs,∀s∈ S (9)
STAGE 2: minimize
(δmls,xs
m∈M
l∈L,s∈S)(X
s∈S
csxs)(10)
subject to:
X
m∈M X
l∈L X
s∈S
uls δmls ≥
(1 −ǫ)X
m∈M X
l∈L X
s∈S
uls δ∗
mls (11)
X
m∈M X
l∈L
δmls ≤rsxs,∀s∈ S (12)
where ǫ∈[0,1] and δ∗
mls, m ∈ M, l ∈ L, s ∈ S, is the optimal
solution of the first-stage problem. In the first-stage problem,
the goal is to maximize the total rate that can be supported
by the leased resources, while ensuring that the supported
rate does not exceed the SP demands. If ǫ= 0 (see (11)),
the purpose of the second-stage problem is to select from the
first-stage optimal solutions (if there are multiple) the one that
minimizes the cost of the BSs. If ǫ > 0, the second-stage
problem tries to reduce the cost of the cheapest optimal first-
stage solution, by allowing the level of user satisfaction to be
degraded within an ǫfrom the optimal satisfaction level (see
constraint (11)). The larger the value of ǫ, the more impact the
BSs cost has on the allocation decisions.
2) CSCS-2 Allocation Scheme: Similar to the two-stage
CSCS-1 problem, the two-stage CSCS-2 problem can be
formulated as follows:
Problem 4 (Two-stage CSCS-2):
STAGE 1: First stage of Problem 3 ((7) −(9))
STAGE 2: minimize
(δmls
m∈M
l∈L,s∈S)(X
m∈M X
l∈L X
s∈S
cs
δmls
rs)(13)
subject to:
X
m∈M X
l∈L X
s∈S
uls δmls ≥
(1 −ǫ)X
m∈M X
l∈L X
s∈S
uls δ∗
mls (14)
X
m∈M X
l∈L
δmls ≤rs,∀s∈ S.(15)
IV. RES OU RC E ALL OC ATIO N WI TH ST OC HA ST IC QOS
GUAR AN TE ES
In this section, we formulate the stochastic resource al-
location problems. Specifically, we extend Problems 1–4 to
the case when the SP user demands are stochastic (modeled
as random variables with known distributions). The VNB
goal in this case is to meet the user demands with a certain
probability3.
Adding the uncertainty in the SP user demands to the
allocation problem causes the feasibility region of the problem
to be uncertain. Different stochastic optimization approaches
have been proposed in the literature to deal with the uncertainty
of the feasibility region of an optimization problem [7]. In
this section, we adopt a ‘chance constraint approach.’ As an
example, we present in this section the stochastic extension of
the CSCS-1 problem, which we refer to as chance-constrained
CSCS-1. The stochastic versions of Problems 2–4 can be
derived similarly. The chance-constrained CSCS-1 can be
described as follows:
3Note that by allowing the VNB to choose not to serve the most costly
demands in Problems 3 and 4, positive ǫcan also represent another form of
non-deterministic resource allocation.
Problem 5 (Chance-constrained CSCS-1):
minimize
(δmls,xs
m∈M
l∈L,s∈S)(X
s∈S
csxs)(16)
subject to:
Pr (X
s∈S
uls δmls ≥˜
dml)≥βm,
∀m∈ M,∀l∈ L (17)
X
m∈M X
l∈L
δmls ≤rsxs,∀s∈ S (18)
where βml is defined in Section II. In our simulations, we
assume that for each m∈ M,βml =βm,∀l∈ L. We solve
Problem 5 by deriving its deterministic equivalent program
(DEP). To do this, we reformulate the chance constraint in (17)
as: X
s∈S
uls δmls ≥Qβm(˜
dml)(19)
where Qβm(˜
dml)is the βm-quantile of ˜
dml.
Remark: In Problem 5, the goal is to satisfy the demand
of SP m, for instance, at every location with probability at
least βm. This causes the DEP of Problem 5 to be identical
to Problem 1. In future research, we plan to consider another
model, in which the goal is to satisfy the demand of SP min
at least βm×100% of the locations in L, when the demand
is time-varying.
V. P ER FO RM AN CE EVAL UATION
In this section, we evaluate our proposed stochastic re-
source allocation schemes4. Because all plotted figures are
for the stochastic schemes, we removed the term ‘chance-
constrained’ from the figure captions. Thus, what is referred
to as two-stage CSCS-1 in the figures, for instance, is actually
the two-stage chance-constrained CSCS-1 scheme.
A. Evaluation Setup
We consider NRPs. Each independently deploys a set
of BSs, following a Poisson point process (PPP) [8], in
a common geographical area. We consider two stochastic
processes for distributing the SP demands: the Poisson point
process (PPP) and the Poisson cluster process (PCP) [9]. In
PPP, the SP demands are randomly distributed within the
considered geographical area, whereas in PCP process the
SP demands are distributed around the BSs according to
a Gaussian distribution. In both processes, the number of
demand points follows a Poisson distribution. All BSs have
the same capacity, but different costs. The SP demand in each
location is a discrete uniform random variable over the set
{x−2, x −1, x, x + 1, x + 2}with a location-dependent mean
x∈ {3,4,5,6}. Unless stated otherwise, we use the default
parameter values shown in Table I. We used MATLAB to
generate the stochastic network deployments and CPLEX to
solve the optimization problems. Our results are averaged over
4The deterministic schemes represent a special case of the stochastic ones.
TABLE I: Numerical values of relevant parameters.
Parameter Value
Number or RPs (N) 4
BS capacity (rs,∀s∈ S) 100
Set of BS costs (cs){1, 2, 4, 8}
Average number of BSs per RP 25
Average number of locations per SP 150
βm,∀m∈ M, in (17) 0.9
ǫin (11) 0
30 simulation runs, each corresponding to one realization of
the stochastic network deployment and the SP demands. The
95% confidence intervals are shown in all simulation figures.
To compute uls (defined in Section II), we used the COST
231-Walfish-Ikegami propagation model [10], with the BS and
the mobile terminal heights set to 10 m and 1.5m, respectively.
Therefore, a user located within 8.5m from the BS has a
perfect signal reception. Because the COST 231 model is
recommended for distances >20 m, we use the free-space
path loss model when the distance is between 8.5m and 20
m. uls = 0 when the distance is >300 m. We set the carrier
frequency to 1800 MHz, the BS transmission power to 31.62
Watts (45 dBm), and the bandwidth to 25 MHz.
In our simulations, we only evaluate the 2-stage CSCS-1
and 2-stage CSCS-2 schemes, in which the primary objective
is to maximize the user satisfaction. By increasing ǫin (11),
we also evaluate the performance of our resource allocation
schemes when the cost has a significant impact in our opti-
mizations.
B. BSs Cost and User Satisfaction
In this section, we evaluate the gains achieved by having
a common pool of resources from which virtual networks are
built (we express this in short as ‘virtualization’). Specifically,
we evaluate the BS cost reduction and the improvement in
the user satisfaction. First, we gradually increase the number
of RPs and plot in Figure 2 the cost and average probability
of user satisfaction in the cases of virtualization and no-
virtualization, when SP demands are distributed according to
the PPP as well as the PCP stochastic processes. We consider
two clustering levels for the PCP process, 50% and 100%. The
requested probability of demand satisfaction (β) is set to 0.9.
As shown in Figure 2, even with incurring significantly
higher cost, the level of user satisfaction is much lower without
virtualization. In contrast to no-virtualization, the level of
demand satisfaction considerably increases with the number of
RPs in the virtualization case. Figure 2 also shows that when
the level of user clustering increases, the ability to meet their
demands improves. The benefits of virtualization become less
significant when the level of clustering increases; however, in
practice, the level of clustering is time-varying and it is difficult
to ensure high user clustering around the BSs (although the
BSs are fixed, user/demand locations are dynamic).
Furthermore, we show in Figure 3 the pmf of the probabil-
ity of demand satisfaction. As shown in the figure, clustering
considerably improves user satisfaction, especially in the no-
virtualization case. However, the percentage of users with no
satisfaction at all is relatively high.
0
100
200
300
400
500
600
2 3 4 5 6
Cost
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
100
200
300
400
500
600
2 3 4 5 6
Cost
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
100
200
300
400
500
600
2 3 4 5 6
Cost
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
0.2
0.4
0.6
0.8
1
2 3 4 5 6
Achieved prob. of demand satisfaction
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
0.2
0.4
0.6
0.8
1
2 3 4 5 6
Achieved prob. of demand satisfaction
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
0.2
0.4
0.6
0.8
1
2 3 4 5 6
Achieved prob. of demand satisfaction
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
(a) PPP (b) PCP (50%) (c) PCP (100%)
Fig. 2: Cost and achieved probability of demand satisfaction as functions of the number of RPs (N).
0.01
0.05
0.1
0.5
1
0 0.1 0.3 0.5 0.7 0.9
pmf
Achieved probability of demand satisfaction
no-virtualization
virtualization
0.01
0.05
0.1
0.5
1
0 0.1 0.3 0.5 0.7 0.9
pmf
Achieved probability of demand satisfaction
no-virtualization
virtualization
0.01
0.05
0.1
0.5
1
0 0.1 0.3 0.5 0.7 0.9
pmf
Achieved probability of demand satisfaction
no-virtualization
virtualization
(a) PPP (b) PCP (50%) (c) PCP (100%)
Fig. 3: Pmf of the achieved probability of demand satisfaction.
C. Percentage of the Idle BSs Capacity
In Figure 4, we plot the percentage of idle capacity in the
assigned BSs as a function of N. As shown in the figure, in
the virtualization case the resources are used more efficiently,
and the gains of virtualization increase with the number of
RPs. Furthermore, the two-stage CSCS-1 scheme tends to use
a smaller number of BSs, and have less idle capacity compared
to the two-stage CSCS-2 scheme. Finally, it can be observed
that clustering significantly reduces the idle BSs capacity in
the no-virtualization case.
D. Effect of βon BSs Cost, User Satisfaction, and Idle
Capacity
In Figure 5(a), we show the impact of βon the BSs
cost, when SP demands are distributed according to the PPP
process. In the case of no-virtualization, almost all BSs are
assigned under any requested value of β. This is common in
real networks that aim to guarantee coverage for all users that
are distributed across the network. In the virtualization case,
increasing βincreases the network load, and hence the cost.
In general, the cost in the case of virtualization is much lower
than that when there is no virtualization, but the difference
tends to decrease as the load increases, as expected.
In Figure 5(b), we show the impact of βon the average
probability of demand satisfaction. As shown in the figure,
the improvement in the demand satisfaction brought by virtu-
alization increases significantly with β, hence, improving the
ability to support new high-demand applications, e.g., video
streaming. Finally, Figure 5(c) depicts the idle capacity as
a function of β. As expected, the amount of idle resources
decreases as the demand becomes more stringent.
E. Tradeoff between User Satisfaction and Cost
We study the tradeoff between the user satisfaction and
cost by adjusting the value of ǫin (11). Setting ǫabove zero
may reduce the cost, but also reduces the user satisfaction. The
VNB may accept some planned user dissatisfaction in order to
alleviate the network load or make room for more users, for
example. In Figure 6, we illustrate the effects of ǫon the cost,
achieved probability of demand satisfaction, and idle capacity.
VI. CO NC LU SI ON S
In this paper, we considered the problem of stochastic
resource management in virtualized wireless networks. We
developed schemes for a virtual network builder to optimally
determine the set of resources to be leased from resource
0
20
40
60
80
100
2 3 4 5 6
Idle capacity (%)
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
20
40
60
80
100
2 3 4 5 6
Idle capacity (%)
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
20
40
60
80
100
2 3 4 5 6
Idle capacity (%)
Number of RPs (N)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
(a) PPP (b) PCP (50%) (c) PCP (100%)
Fig. 4: Percentage of the idle capacity as a function of the number of RPs (N).
0
50
100
150
200
250
300
350
400
450
0.1 0.3 0.5 0.7 0.9
Cost
Requested probability of demand satisfaction (β)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
0.2
0.4
0.6
0.8
1
0.1 0.3 0.5 0.7 0.9
Achieved prob. of demand satisfaction
Requested probability of demand satisfaction (β)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
20
40
60
80
100
0.1 0.3 0.5 0.7 0.9
Idle capacity (%)
Requested probability of demand satisfaction (β)
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
(a) (b) (c)
Fig. 5: Effect of βon (a) cost, (b) demand satisfaction, and (c) percentage of the idle capacity (SP demands are distributed according to a
PPP).
0
50
100
150
200
250
300
350
400
450
0 0.02 0.04 0.08 0.16
Cost
ε
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
0.2
0.4
0.6
0.8
1
0 0.02 0.04 0.08 0.16
Achieved prob. of demand satisfaction
ε
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
0
20
40
60
80
100
0 0.02 0.04 0.08 0.16
Idle capacity (%)
ε
2-stage CSCS-1, virtualization
2-stage CSCS-2, virtualization
2-stage CSCS-1, no-virtualization
(a) (b) (c)
Fig. 6: Effect of ǫon (a) cost, (b) demand satisfaction, and (c) percentage of the idle capacity (SP demands are distributed according to a
PPP).
providers and sliced and allocated to various service providers.
We evaluated the proposed allocation schemes under various
system parameters and studied the gains brought by virtualiza-
tion, mainly the cost reduction and the substantial improvement
in user satisfaction.
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