PREPRINT VERSION

A Hybrid Neuro–Wavelet Predictor for
QoS Control and Stability

arXiv:1406.3156v1 [] 12 Jun 2014

C. Napoli, G. Pappalardo, and E. Tramontana
PUBLISHED ON: AI*IA 2013: Advances in
Artificial Intelligence
BIBITEX:
@incollection{
year={2013},
isbn={978-3-319-03523-9},
booktitle={AI*IA 2013: Advances in Artificial Intelligence},
volume={8249},
series={Lecture Notes in Computer Science},
editor={Baldoni, Matteo and Baroglio, Cristina and Boella, Guido and Micalizio, Roberto},
doi={10.1007/978-3-319-03524-6 45},
title={A Hybrid Neuro–Wavelet Predictor for QoS Control and Stability},
url={http://dx.doi.org/10.1007/978-3-319-03524-6 45},
publisher={Springer International Publishing},
keywords={Neural networks; wavelet analysis; QoS; adaptive systems},
author={Napoli, Christian and Pappalardo, Giuseppe and Tramontana, Emiliano},
pages={527-538}
}

Published version copyright c 2013 SPRINGER
UPLOADED UNDER SELF-ARCHIVING POLICIES
NO COPYRIGHT INFRINGEMENT INTENDED

A hybrid neuro–wavelet predictor for QoS
control and stability
Christian Napoli, Giuseppe Pappalardo, and Emiliano Tramontana
Dipartimento di Matematica e Informatica, University of Catania
Viale Andrea Doria 6, 95125 Catania, Italy
{napoli,pappalardo,tramontana}@dmi.unict.it

Abstract. For distributed systems to properly react to peaks of requests, their adaptation activities would benefit from the estimation of
the amount of requests. This paper proposes a solution to produce a
short-term forecast based on data characterising user behaviour of online
services. We use wavelet analysis, providing compression and denoising
on the observed time series of the amount of past user requests; and a
recurrent neural network trained with observed data and designed so as
to provide well-timed estimations of future requests. The said ensemble
has the ability to predict the amount of future user requests with a root
mean squared error below 0.06%. Thanks to prediction, advance resource
provision can be performed for the duration of a request peak and for
just the right amount of resources, hence avoiding over-provisioning and
associated costs. Moreover, reliable provision lets users enjoy a level of
availability of services unaffected by load variations.
Keywords: Neural networks, wavelet analysis, QoS, adaptive systems

1

Introduction

General public internet usage has become an essential everyday matter, e.g.
widespread use of social–networks and mass communication media, public administration, home banking, etc. Moreover, the request for stable and continuous
internet services has reached a pressing priority. Generally, the solutions employed by service providers to adapt server-side resources on-the-fly have been
based on content adaptation and differentiated service strategies [1,9,3,12,13].
However, such strategies could over-deteriorate the service during load peaks.
Moreover, for ensuring a minimum level of quality (QoS), even when sudden
variations on the number of requests arise, a large number of (over-provisioned)
resources is often used, hence incurring into relevant costs and wasted resources
for a considerable time interval. Some approaches guarantee a minimum QoS
level once the connection has been established (i.e. non-adaptive multimedia
services) [11,24], or by using bandwidth adaption algorithms (i.e. adaptive wireless services) [18]. However, such solutions are still liable to an effective loss
of QoS for end users, when we consider content quality or availability, and, in
the worst case, even denial of services (DoS). As an alternative to deterministic scheduling [17] or genetic algorithms [28], neural networks have been used

A hybrid neuro–wavelet predictor for QoS control and stability

3

within the area of a multi-objective optimisation problems. In [2] authors provide dynamic admission control while preserving QoS by using hardware-based
Hopefield neural networks [33].
When autoregressive moving average models (ARMA), and related generalisations, are used, the underlying assumption, even for the study forecasting
host load [10], makes them inappropriate for predictions in non-linear systems
exhibiting high levels of variations. Artificial neural networks have been used in
several ways to provide an accurate model of the QoS evolution over time. Linear
regression models have been applied with the support of neural networks in [16],
however without some proper mechanisms, such as time delays or feedback, it is
still not possible to dynamically follow the evolution of the extended time series.
Machine learning approaches have also been used [25], however such approaches
were not designed for on-the-fly adaptation, and are unable to give advantages
with respect to user perceived responsiveness [27]. For the above approaches in
which the amount of connection requests is unknown, to avoid overloading the
server-side, only load balancing and admission control policies have been used.
Still when the amount of requests overcomes the available resources, service usability worsening or denial of service cannot be avoided. On the other hand,
when more resources can be dynamically allocated, since the amount of the required resources is unknown in advance, it often results in over-provisioning,
with negative effects on management and related cost.
This paper investigates the use of Second Generation Wavelet Analysis and
Recurrent Neural Network (RNN) to predict over time the amount of connection requests for a service, by using a hybrid wavelet recurrent neural network
(WRNN). Recurrent neural networks have been proven powerful enough to gain
advantages from the statistical properties of time series. In our experiments,
the proposed WRNN has been used to analyse data for the Page view statistics
Wikimedia(TM) project, produced by Domas Mituzas and released under Creative Common License1 . Wavelet analysis has been used in order to reduce data
redundancies so as to obtain a representation that can express their intrinsic
structure, while the neural networks have been used to have the complexity of
non-linear data correlational perform data prediction. Thereby, a relatively accurate forecast of the connection request time series can be achieved even when
load peaks arise. The estimated result is fundamental for a management service
that performs resource preallocation on demand. The precision of our estimates
allows just the right amount of resources to be used.
The rest of this paper is structured as follows. In section 2 the background
on wavelet theory is given. Section 3 describes second generation wavelets and
how their properties are useful for the proposed forecast. Section 4 provides
the proposed neural network configuration. Section 5 reports on the performed
experiments and results. Finally, Section 6 draws our conclusions.

1

See dumps.wikimedia.org/other/pagecounts-raw

4

2

Napoli C., Pappalardo G., Tramontana E.

The basis of Wavelet Theory

This work builds on wavelets and neural networks to model the main characteristics of user behaviour for an online service. Wavelet decomposition is a powerful
analysis tool for physical and dynamic phenomena that reduces the data redundancies and yields a compact representation expressing the intrinsic structure of
a phenomenon. In fact, the main advantage when using wavelet decomposition is
the ability to pack the energy signature of a signal or a time series, and then to
express relevant data as a few non-zero coefficients. This characteristic has been
proven very useful to optimise the performances of neural networks [14]. Like
sine and cosine for Fourier transforms, a wavelet decomposition uses functions,
i.e. wavelets, to express a function as a particular expansion of coefficients in
the wavelet domain. Once a mother wavelet has been chosen, it is possible, as
explained in the following, to create new wavelets by dilates and shifts of the
mother wavelet. Such novel generated wavelets, if chosen with certain criteria,
eventually form a Riesz basis of the Hilbert space L2 (R) of square integrable
functions. Such criteria are at the basis of wavelet theory and come from the
concept of multiresolution analysis of a signal, also called multiscale approximation. When a dynamic model can be expressed as a time-dependent signal, i.e.
described by a function in L2 (R), then it is possible to obtain a multiresolution
analysis of such a signal. For the space L2 (R) such an approximation consists
in an increasing sequence of closed subspaces which approximate, with a greater
amount of details, the space L2 (R), eventually reaching a complete representation of L2 (R) itself. A complete description of multiresolution analysis and the
relation with wavelet theory can be found in [20].
One-dimensional decomposition wavelets of order n for a signal s(t) give
a new representation of the signal itself in an n-dimensional multiresolution
domain of coefficients plus a certain residual coarse representation of the signal
in time. For any discrete time step τ then, the corresponding M order wavelet
decomposition Ws(τ ) of the signal s(τ ) will be given by the vector
Ws(τ ) = [d1 (τ ), d2 (τ ), . . . , dM (τ ), aM (τ )]

∀ τ ∈ {τ1 , τ2 , . . . , τN }

(1)

where d1 is the most detailed multiresolution approximation of the series, and
dM the least detailed, and aM is the residual signal. Such coefficients express
some intrinsic time-energy feature of a signal, i.e. features of a time series, while
removing redundancies, and offering a well suited representation, which, as described in Section 3, we give as inputs for a neural network.
It is now possible to give a more rigorous definition of a wavelet. Let us take
into account a multiresolution decomposition of L2 (R)
∅ ⊂ V0 ⊂ . . . ⊂ Vj ⊂ Vj+1 ⊂ . . . ⊂ L2 (R)
If we call Wj the orthogonal complement Vj , then it is possible to define a
wavelet as a function ψ(x) if the set of {ψ(x − l)|l ∈ Z} is a Riesz basis of W0
and also meets the following two constraints:
Z +∞
ψ(x)dx = 0
(2)
−∞

A hybrid neuro–wavelet predictor for QoS control and stability

and
||ψ(x)||2 =

Z

5

+∞

ψ(x)ψ ∗ (x)dx = 1

−∞

If the wavelet is also an element of V0 then it exists a sequence {gk } such that
X
ψ(x) = 2
gk ψ(2x − l)
k∈Z

then the set of functions {ψj,l |j, l ∈ Z} is now a Riesz basis of L2 (R). It follows
that a wavelet function can be used to define an Hilbert basis, that is a complete
system, for the Hilbert space L2 (R). In this case, the Hilbert basis is constructed
as the family of functions {ψj,l |j, l ∈ Z} by means
√ of dilation and translation
of a mother wavelet function ψ so that ψj,l = 2j ψ(2j x − l). Hence, given a
function f ∈ L2 (R) it is possible to obtain the following decomposition
X
X
f (x) =
hf |ψj,l i =
dj,l ψj,l (x)
(3)
j,l∈Z

j,l∈Z

where dj,l are called wavelet coefficients of the given function f in the wavelet
basis given by the inner product of ψj,l . Likewise, a projection on the space Vj
is given by
X
Pj f (x) =
hf |ϕi,j iϕi,j (x)
i

where ϕi,j are called dual scaling functions. When the basis wavelet functions
coincide with their duals the basis is orthogonal. Choosing a wavelet basis for
the multiresolution analysis corresponds to selecting the dilation and shift coefficients. In this way, by performing the decomposition we obtain the {di |aM }
coefficients sets of (1). From now on we will refer to the described schema as
first generation wavelets, whilst Section 3 describes second generation wavelets.
For the present work, we adopted Biorthogonal wavelet decomposition (this
wavelet family is described in [20]), for which symmetrical decomposition and
exact reconstruction are possible with finite impulse response (FIR) filters [26].

3

Second generation Wavelets with RNNs

A multiresolution analysis like the one described in Section 2 can be realised
by conjugate wavelet filter banks that decompose the signal, and act similarly
to a low/high pass filter couple [29]. An advanced solution has been devised
to obtain the same decomposition using a lifting and updating procedure. This
procedure, named second generation wavelet, takes advantage of the properties of
multiresolution wavelet analysis starting from a very simple set-up and gradually
building up a more complex multiresolution decomposition to have some specific
properties. The lifting procedure is made of a space-domain superposition of
biorthogonal wavelets developed in [30].
The construction is performed by an iterative procedure called lifting and
prediction. Lifting consists of splitting the whole time series x[τ ] into two disjoint

6

Napoli C., Pappalardo G., Tramontana E.

subsets xe [τ ] and xo [τ ], for the even and odd positions, respectively; whereas
prediction consists of generating a set of coefficients d[τ ] representing the error
of extrapolation of time series xo [τ ] from series xe [τ ]. Then, an update operation
combines the subsets xe [τ ] and d[τ ] in a subset a[τ ] so that


d[τ ] = xo [τ ] − Pxe [τ ]
a[τ ] = xe [τ ] + Ud[τ ]

(4)

where P is the prediction operator, and U is the update operator. Eventually,
one cycle for the above procedure creates a complete set of discrete wavelet
transforms (DWT) and the relative coefficients d[τ ] and a[τ ]. It follows that


xe [τ ] = a[τ ] − Ud[τ ]
xo [τ ] = d[τ ] + Pxe [τ ]

(5)

The said construction yields discrete wavelet filters that preserve only a certain number N of low order polynomials in the time series. Having such low-order
polynomials, in turn, makes it possible to apply non-linear predictors without
affecting the a[τ ] coefficients, which provide a coarse approximation of the time
series itself.
A neural network can be build to perform such a construction, i.e. a neural
network would act as an inverse second generation wavelet transform. In [6],
a neural network with a rich representation of past outputs like a fully connected recurrent neural network (RNN), known as the Williams-Zipser network
or Nonlinear Autoregressive network with eXogenous inputs (NARX) [31], has
been proven able to generalise and reproduce the behaviour of P and U operators, and to structure itself to behave as an optimal discrete wavelet filter.
Moreover, for such a kind of RNNs, when applied to the prediction and modelling of stochastic phenomena, like the considered behaviour of users, which
lead to a variable number of access requests in time, real time recurrent learning
(RTRL) has been proven to be very effective. A complete description of RTRL
algorithm, NARX and RNNs can be found in [32,15].
RTRL has been used to train the RNN and such a trained RNN achieves the
ability to perform lifting stages, hence the matching of the time series dynamics
at the corresponding wavelet scale. This construction brings the possibility to
match non-polynomial and nonlinear signal structures in an optimised straightforward N-dimension means square problem [21]. NARX networks have been
proven able to use the intrinsic features of time series in order to predict the
following values of the series [23]. One of a class of transfer functions for the
RNN has to be chosen to approximate the input-output behaviour in the most
appropriate manner. For phenomena having a deterministic dynamic behaviour,
the relative time series at a given time point can be modelled as a functional of
a certain amount of previous time steps. In such cases, the used model should
have some internal memory to store and update context information [19]. This
is achieved by feeding the RNN with a delayed version of past data, commonly
referred as time delayed inputs [8].

A hybrid neuro–wavelet predictor for QoS control and stability

4

7

Proposed setup for WRNN predictor

As stated in Section 3, it would be desired to have a neural network able to
perform the wavelet transform as in a recursive lifting procedure. For this, we
could use a mother wavelet as transfer function, however mother wavelets lack
of some elementary properties needed by a proper transfer function, such as
e.g. the absence of local minima and a sufficient graded and scaled response [14].
This leads us to look for a close enough substitute to approximate the properties
of a mother wavelet without affecting the functionalities of the network itself.
The function classes that more closely approximate a mother waveform have to
be found among the Radial Basis Functions (RBFs) that are good enough as
transfer functions and partially approximate half of a mother waveform. It is
indeed possible to properly scale and shift a couple of RBFs to obtain a mother
wavelet. If we define an RBF function as an f : [−1, 1] → R then we could dilate
and scale it to obtain a new function

+f (2x + 1) x ∈ [−1, 0)
f˜(x + 2l) =
∀l∈Z
(6)
−f (2x − 1) x ∈ (0, +1]
With such a definition, starting from the properties of the RBF, it is then possible
to verify the following
Z 2k+1
f˜(x)dx = 0 ∀ (h, k) ∈ Z2 : h < k
(7)
2h+1

Starting from (6) and (7) it is possible to verify the equations (2) to (3)
for the chosen f˜ which we can now call a mother wavelet. The chosen mother
wavelet is a composition of two RBF transfer functions that are realised by the
proposed neural network to obtain the properties of a wavelet transform. The
proposed WRNN has two hidden layers with RBF transfer function.
For this work, the initial dataset was a time series representing access requests
coming from users. We call this series x(τ ), where τ is the discrete time step of the
data, sampled with intervals of one hour. A biorthogonal wavelet decomposition
of the time series has been computed to obtain the correct input set for the
WRNN as required by the devised architecture. This decomposition has been
achieved by applying the wavelet transform as a recursive couple of conjugate
filters (Figure 1) in such a way that the i-esime recursion Ŵi produces, for any
time step of the series, a set of coefficients di and residuals ai , and so that
Ŵi [ai−1 (τ )] = [di (τ ), ai (τ )]

∀ i ∈ [1, M ] ∩ N

(8)

where we intend a0 (τ ) = x(τ ). The input set can then be represented as an N ×
(M +1) matrix of N time steps of a M level wavelet decomposition (see Figure 2),
where the τ -esime row represents the τ -esime time step as the decomposition
u(τ ) = [d1 (τ ), d2 (τ ), . . . , dM (τ ), aM (τ )]

(9)

Each row of this dataset is given as input value to the M input neurons of the
proposed WRNN. The properties of this network make it possible, starting from

8

Napoli C., Pappalardo G., Tramontana E.

x( )
a5 ( )

7

4
2
0
3
2
1

x 10

7

x 10

d5 ( )
d4 ( )

1
0
−1

d3 ( )

2
0
−2

d2 ( )

5
0
−5

d1 ( )

6

5
0
−5

5
0
−5

x 10

7

x 10

6

x 10

6

x 10

6

x 10

0

Fig. 1. Filter logic

100

200

300

400

500

600

Discrete time samples [ ]

700

800

900

1000

Fig. 2. 5-level biorthogonal 3.7 wavelet decomposition

an input at a time step τn , to predict the effective number of access requests at
a time step τn+r . In this way the WRNN acts like a functional
N̂ [u(τn )] = x(τn+r )

(10)

where r is the number of time steps of forecast in the future.

5

Experimental setup

For this work, a 4-level wavelet decomposition has been selected that properly
characterises data under analysis. Therefore, the devised WRNN (Figure 3) uses
a 5 neuron input layer (one for each level detail coefficient di and one for the
residual a5 ). This WRNN architecture presents two hidden layers with sixteen
neurons each and realises a radial basis function as explained in Section 4.
Inputs are given to the WRNN in the following form:
– The wavelet decomposition of the time series u(τn ) for time step τn
– The previous delayed decompositions u(τn−1 ) and u(τn−2 )
– The last four delayed outputs x(τn+r ) predicted by the WRNN
Delays and feedback are obtained by using the relative delay lines and operators (D). These feedback lines provide the WRNN with internal memory, hence
the modelling abilities for dynamic phenomena.

A hybrid neuro–wavelet predictor for QoS control and stability

9

Fig. 3. Devised neural netwok

An accurate study has shown that the biorthogonal wavelet decomposition
optimally approximates and denoises the time series under analysis. Such a
wavelet family is in good agreement with previous optimal results, obtained by
the authors, for the decomposition of other physical phenomena. In fact, such
a decomposition splits a phenomenon in a superposition of mutual and concurrent predominant processes with a characteristic time-energy signature. For
stochastically-driven processes, such as stellar oscillations [7], renewable energy
and systems load [5,4], and for a large category of complex systems [22], wavelet
decomposition gives a unique and compact representation of the leading features
for a time-variant phenomenon.
For the case study proposed in this paper we have used the raw data of
connection requests over time to predict the behaviour of the users of a widely
used an internet service, i.e. the one provided by Wikimedia(TM). Raw data
were taken from the page-view statistics Wikimedia(TM) project and released
by Domas Mituzas under Creative Common License2 . Original data report the
amount of accesses and bytes for the replies that were sampled in time-steps of
one hour for each web page accessible in the project. Data were collected for the
whole services offered by Wikimedia projects including Wikipedia(r), Wikidictionary(r), Wikibooks(r) and others. Data were gathered and composed by an
automatic procedure, obtaining the total requests made to the wikimedia servers
for each hour. Therefore, a 2-years long dataset of hourly sampled access requests
has been reconstructed. Then, this dataset was decomposed by using a wavelet
biorthogonal decomposition identified by the couple of numbers 3.7, which means
that are implemented by using FIR filters with 7th order polynomials degree for
the decomposition (see also Figure 4 and 5) and 3rd order for the reconstruction.
2

See dumps.wikimedia.org/other/pagecounts-raw

10

Napoli C., Pappalardo G., Tramontana E.
1

(t)
(t)

1

g [x]
h [x]

0.8
0.6

0.5

0.4
0

0.2
0

−0.5

−0.2
−0.4

−1
−1

−0.5

0

0.5

1

−0.6
−8

−6

−4

−2

0

2

4

6

8

Fig. 4. Biorthogonal wavelet 3.7 decompo- Fig. 5. Biorthogonal wavelet 3.7 high-pass
sition (ψ) and scaling (φ) functions
(h) and low-pass (g) filers

Decomposed data, as shown in Figure 2, were then given as inputs for the neural
network as described in Section 4. The network was trained by using a gradient
descent back-propagation algorithm with momentum led adaptive learning rate
as presented in [15].
For a prediction 6 hours in advance of the time series of the amount of
requests, the root mean squared error of prediction for the access requests over
time was of 1.3156 · 1004 requests, which means a relative error of less than 0.6
per thousands (less than six requests over ten thousands). Figure 6 shows the
shape of the mean square error while training is being performed. Figure 7 shows
the actual time series of the incoming requests in black, and the predicted values
for the incoming requests in red for a time period of 500 hours. The actual values
for the shown time period had not been given as input to the neural network
for training, however have then been used to compare with the predicted values
and to compute the error (see the bottom part of Figure 7). A smaller period
of time has been shown in Figure 8 to highlight the differences of actual and
predicted values. As can be seen, the neural network manages to closely predict
even relatively small variations of the trends. The output of the neural network
was then given to a resource management service to perform allocation requests
in terms of needed bandwidth and virtual machines [12].

6

Conclusions

This paper has provided an ad-hoc architecture for a neural network that is able
to predict the amount of incoming requests performed by users when accessing
a website. Firstly, the past time series of accesses has been analysed by means
of wavelets, which appropriately retain only the fundamental properties of the
series. Then, the neural network embeds both the ability to perform wavelet
analysis and prediction of future amount of requests. The performed experiments have proven that the provided ensemble is very effective for the desired
prediction, since the computed error can be considered negligible.

A hybrid neuro–wavelet predictor for QoS control and stability

11

7

x 10

15

Measured
Predicted

Number of requests

3.5

14

10

13

10

3
2.5
2
1.5
6

x 10

12

10

Error ( )

Mean Squared Error (mse)

10

11

10

0

200

400

Epochs

600

800

1000

2
0
−2
0

100

200

Time [h]

300

400

500

Fig. 6. Error while training the network Fig. 7. Actual time series and predicted
values

Estimates can be fundamental for a resource management component, on a
server side of an internet based system, since they make it possible to acquire
just the right amount of resource (e.g. from a cloud). Then, in turn it is possible
to avoid an unnecessary cost and waste of resources, whilst keeping the level of
QoS as desired and unaffected by variations of requests.

7

Acknowledgments

This work has been supported by project PRISMA PON04a2 A/F funded by
the Italian Ministry of University within PON 2007-2013 framework.

References
1. T. F. Abdelzaher, K. G. Shin, and N. Bhatti. Performance guarantees for web
server end-systems: A control-theoretical approach. IEEE Transactions on Parallel
and Distributed Systems, 13:80–96, 2002.
2. C. W. Ahn and R. Ramakrishna. Qos provisioning dynamic connection-admission
control for multimedia wireless networks using a hopfield neural network. Transactions on Vehicular Technology, 53(1):106–117, 2004.
3. F. Bannò, D. Marletta, G. Pappalardo, and E. Tramontana. Tackling consistency issues for runtime updating distributed systems. In Proceedings of International Symposium on Parallel & Distributed Processing, Workshops and Phd
Forum (IPDPSW), pages 1–8. IEEE, 2010. DOI: 10.1109/IPDPSW.2010.5470863.
4. F. Bonanno, G. Capizzi, A. Gagliano, and C. Napoli. Optimal management of
various renewable energy sources by a new forecasting method. In Proceedings of
International Symposium on Power Electronics, Electrical Drives, Automation and
Motion (SPEEDAM), pages 934–940. IEEE, 2012.
5. G. Capizzi, F. Bonanno, and C. Napoli. A wavelet based prediction of wind and
solar energy for long-term simulation of integrated generation systems. In Proceedings of International Symposium on Power Electronics Electrical Drives Automation and Motion (SPEEDAM), pages 586–592. IEEE, 2010.

12

Napoli C., Pappalardo G., Tramontana E.
7

3.4

x 10

Measured
Predicted

3.2

Number of requests

3
2.8
2.6
2.4
2.2
2
1.8
1.6

10

20

30

40

50
60
Time [h]

70

80

90

Fig. 8. Top of the curves for actual time series and predicted values, for an arbitrary
chosen time-interval

6. G. Capizzi, C. Napoli, and F. Bonanno. Innovative second-generation wavelets
construction with recurrent neural networks for solar radiation forecasting. Transactions on Neural Networks and Learning Systems, 23(11):1805–1815, 2012.
7. G. Capizzi, C. Napoli, and L. Paternò. An innovative hybrid neuro-wavelet method
for reconstruction of missing data in astronomical photometric surveys. In Proceedings of Artificial Intelligence and Soft Computing, pages 21–29. Springer, 2012.
8. J. T. Connor, R. D. Martin, and L. Atlas. Recurrent neural networks and robust
time series prediction. Transactions on Neural Networks, 5(2):240–254, 1994.
9. A. Di Stefano, M. Fargetta, G. Pappalardo, and E. Tramontana. Supporting
resource reservation and allocation for unaware applications in grid systems.
Concurrency and Computation: Practice and Experience, 18(8):851–863, 2006.
DOI: 10.1002/cpe.980.
10. P. A. Dinda and D. R. O’Hallaron. Host load prediction using linear models.
Cluster Computing, 3(4):265–280, 2000.
11. B. Epstein and M. Schwartz. Reservation strategies for multi-media traffic in a
wireless environment. In Proceedings of Vehicular Technology Conference, volume 1, pages 165–169. IEEE, 1995.
12. R. Giunta, F. Messina, G. Pappalardo, and E. Tramontana. Providing qos strategies and cloud-integration to web servers by means of aspects. Concurrency and
Computation: Practice and Experience, 2013. DOI:10.1002/cpe.3031.
13. R. Giunta, F. Messina, G. Pappalardo, and E. Tramontana. Kaqudai: a dependable
web infrastructure made out of existing components. In Proceedings of Workshops
on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE).
IEEE, 2013. DOI:10.1109/WETICE.2013.47.
14. M. M. Gupta, L. Jin, and N. Homma. Static and dynamic neural networks: from
fundamentals to advanced theory. Wiley-IEEE Press, 2004.
15. S. Haykin. Neural networks and learning machines, volume 3. Prentice Hall New
York, 2009.
16. S. Islam, J. Keung, K. Lee, and A. Liu. Empirical prediction models for adaptive resource provisioning in the cloud. Future Generation Computer Systems,
28(1):155–162, 2012.

A hybrid neuro–wavelet predictor for QoS control and stability

13

17. C. G. Kang, Y. J. Kim, and M. J. Hwang. Implicit scheduling algorithm for dynamic slot assignment in wireless atm networks. Electronics Letters, 34(24):2309–
2311, 1998.
18. T. Kwon, I. Park, Y. Choi, and S. Das. Bandwidth adaption algorithms with
multi-objectives for adaptive multimedia services in wireless/mobile networks. In
Proceedings of International Workshop on Wireless Mobile Multimedia, pages 51–
59. ACM, 1999.
19. A. Lapedes and R. Farber. A self-optimizing, nonsymmetrical neural net for content
addressable memory and pattern recognition. Physica D: Nonlinear Phenomena,
22(1):247–259, 1986.
20. S. Mallat. A wavelet tour of signal processing: the sparse way. Academic press,
2009.
21. D. P. Mandic and J. Chambers. Recurrent neural networks for prediction: Learning
algorithms, architectures and stability. John Wiley & Sons, Inc., 2001.
22. C. Napoli, F. Bonanno, and G. Capizzi. Exploiting solar wind time series correlation with magnetospheric response by using an hybrid neuro-wavelet approach. In
Advances in Plasma Astrophysics, number S274 in Proceedings of the International
Astronomical Union, pages 250–252. Cambridge University Press, 2010.
23. C. Napoli, F. Bonanno, and G. Capizzi. An hybrid neuro-wavelet approach for longterm prediction of solar wind. In Advances in Plasma Astrophysics, number S274 in
Proceedings of the International Astronomical Union, pages 247–249. Cambridge
University Press, 2010.
24. G. Novelli, G. Pappalardo, C. Santoro, and E. Tramontana. A grid-based infrastructure to support multimedia content distribution. In Proceedings of the workshop on Use of P2P, GRID and agents for the development of content networks
(UPGRADE-CN), pages 57–64. ACM, 2007. DOI: 10.1145/1272980.1272983.
25. R. Powers, M. Goldszmidt, and I. Cohen. Short term performance forecasting in
enterprise systems. In Proceedings of the eleventh ACM SIGKDD international
conference on Knowledge discovery in data mining, pages 801–807. ACM, 2005.
26. L. R. Rabiner and B. Gold. Theory and application of digital signal processing.
Englewood Cliffs, NJ, Prentice-Hall, Inc., 1975. 777 p., 1, 1975.
27. S. Schechter, M. Krishnan, and M. D. Smith. Using path profiles to predict http
requests. Computer Networks and ISDN Systems, 30(1):457–467, 1998.
28. M. R. Sherif, I. W. Habib, M. Nagshineh, and P. Kermani. Adaptive allocation
of resources and call admission control for wireless atm using genetic algorithms.
Journal on Selected Areas in Communications, 18(2):268–282, 2000.
29. W. Sweldens. Lifting scheme: a new philosophy in biorthogonal wavelet constructions. In Proceedings of Symposium on Optical Science, Engineering, and Instrumentation, pages 68–79. International Society for Optics and Photonics, 1995.
30. W. Sweldens. The lifting scheme: A construction of second generation wavelets.
Journal on Mathematical Analysis, 29(2):511–546, 1998.
31. R. J. Williams. A learning algorithm for continually running fully recurrent necurren neural networks. Neural Computation, 1:270–280, 1989.
32. R. J. Williams and D. Zipser. Experimental analysis of the real-time recurrent
learning algorithm. Connection Science, 1(1):87–111, 1989.
33. M. H. Zadeh and M. A. Seyyedi. Qos monitoring for web services by time series
forecasting. In Proceedings of International Conference on Computer Science and
Information Technology (ICCSIT), volume 5, pages 659–663. IEEE, 2010.

