Lazaros Gkatzikis PhD defense 23/7/2013 Electrical and Computer
Engineering, University of Thessaly Optimization and game theory
techniques for energy- constrained networked systems and the smart
grid Lazaros Gkatzikis Dissertation Committee: Leandros Tassiulas
(UTH,GR) Iordanis Koutsopoulos (AUEB, GR) Slawomir Stanczak (TUB,
GER) 1 Slide 2 Lazaros Gkatzikis PhD defense 23/7/2013 Outline 1)
Introduction 2) Energy efficiency of the power grid Residential
demand response Hierarchical demand response markets 3) Mobile task
offloading in the cloud 4) Energy-efficient wireless communications
Energy-constrained MAC Interference-aware relay selection and power
control 5) Conclusion 2 Slide 3 Lazaros Gkatzikis PhD defense
23/7/2013 Thesis Summary 3 Slide 4 Lazaros Gkatzikis PhD defense
23/7/2013 Outline 1) Introduction 2) Residential demand response 3)
Hierarchical demand response markets 4) Mobile task offloading in
the cloud 5) Energy-constrained MAC 6) Interference-aware relay
selection and power control 7) Conclusion 4 Slide 5 Lazaros
Gkatzikis PhD defense 23/7/2013 Energy consumption Annual worldwide
demand for electricity increased ten-fold within the last 50 years
almost doubled in the last decade 5 Cost of non-renewable sources
constantly increasing Electricity prices follow Slide 6 Lazaros
Gkatzikis PhD defense 23/7/2013 Pursue energy efficiency optimizing
the efficiency and reliability of the power grid improving
efficiency of individual devices or systems 6 Smart Grid Demand
response Time-varying prices to reduce demand in peak periods
Users: lower electricity bill Utility: lower generation cost
Networked systems ICT = 5% of worldwide electricity consumption
Major consumers Datacenters (cloud) Wireless access (WiFi, 4G)
Energy-constrained mobiles Battery- powered Contention for
resources Slide 7 Lazaros Gkatzikis PhD defense 23/7/2013 Outline
1) Introduction 2) Residential demand response 3) Hierarchical
demand response markets 4) Mobile task offloading in the cloud 5)
Energy-constrained MAC 6) Interference-aware relay selection and
power control 7) Conclusion 7 Slide 8 Lazaros Gkatzikis PhD defense
23/7/2013 Flat pricing Same price throughout the day Users schedule
demands for most convenient time Result: unbalanced demand Balanced
demand guarantees stability of electricity network reduced
generation cost (convex function of demand) reduced electricity
bill (user side) Solution: Dynamic pricing (day-ahead DR market)
enabled by smart meters motivates demand shifting Balancing demand
through dynamic pricing Slide 9 Lazaros Gkatzikis PhD defense
23/7/2013 Negotiation phase (repeated until convergence) operator
updates prices individuals respond (automated) Wholesale auction
auction to meet demand: generators make energy/price bids all
accepted offers paid at market clearing price Real time spot market
whenever actual demand exceeds prediction usually at a higher cost
Day-Ahead Market 9 Slide 10 Lazaros Gkatzikis PhD defense 23/7/2013
Convenient model of splittable demands Operator: maximize social
welfare price=marginal cost End-users: for given prices p maximize
utility Control : x the daily electricity consumption vector
However, most appliances have a specific consumption pattern Our
contribution Devise a realistic DR market model Quantify DR
benefits for each entity through realistic traces Related Work and
Contribution PaymentComfort 10 Slide 11 Lazaros Gkatzikis PhD
defense 23/7/2013 User objective: for given day ahead prices find
the optimal shift Control : time shift vector (separable per
appliance) A realistic model for residential DR Payment Comfort For
each demand arrival/end time (a,e) consumption requirement (w )
deadline(d ) elasticity parameter Feasible shifts Slide 12 Lazaros
Gkatzikis PhD defense 23/7/2013 Operator objective: minimize
electricity generation cost cost is a convex function of the total
demand t within a timeslot constraint guarantees that average price
is at most equal to flat price (attract users to enroll) Result:
Even when operator has direct control over demands, optimal
scheduling is NP-Hard Additional challenge: elasticity is users
private information Negotiation-based iterative approach use total
demand as the gradient increase price at peak consumption periods
reduce price at low demand periods Price setting strategy 12 Slide
13 Lazaros Gkatzikis PhD defense 23/7/2013 Numerical Results
Significantly better than the proportional scheme Similar to lower
bound Proposed pricing Demand-proportional pricing scheme [19] A
lower bound of the generation cost 13 Slide 14 Lazaros Gkatzikis
PhD defense 23/7/2013 Numerical Results and Conclusion 14
Significantly reduced cost even for low elasticity Highly inelastic
users experience increased prices and hence reduced utility
Conclusion: Existing models overestimate cost benefits of
residential DR Future Work: Devise regression based methods that
accurately estimate the utility function of a user through
historical data Slide 15 Lazaros Gkatzikis PhD defense 23/7/2013
Outline 1) Introduction 2) Residential demand response 3)
Hierarchical demand response markets 4) Mobile task offloading in
the cloud 5) Energy-constrained MAC 6) Interference-aware relay
selection and power control 7) Conclusion 15 Slide 16 Lazaros
Gkatzikis PhD defense 23/7/2013 Aggregators as DR enablers An
intermediate is required, due to: the large number of home users
(scalability) the utility operator lacks DR knowhow each home
controls tiny demand limited negotiation power Aggregator
installation of the smart meters at homes compensate users to shift
demands resell DR services to the operator Operator: Rewards
aggregators for their DR services Users: Adjust demand to dynamic
prices Objective: Investigate share of DR benefits among market
entities 16 Slide 17 Lazaros Gkatzikis PhD defense 23/7/2013
Related Work and Contribution The role of aggregators has received
limited research attention Single timeslot models where operator
sets the demand target Aggregator has no incentive to participate
Commercial programs Direct load control in emergency events Fixed
monthly compensation to contracted end-users (mainly industrial)
Main issue: Utilities reap DR benefits, users have to invest
Contribution Formulate objectives of utility operator, several
competing aggregators and home users Investigate impact of
operators reward strategy on DR gains Devise a day-ahead DR market
scheme that guarantees a fair fraction of DR benefits for each
entity 17 Slide 18 Lazaros Gkatzikis PhD defense 23/7/2013
Day-ahead market T timeslots Utility operator: minimize operating
cost electricity generation + reward J competing aggregators:
maximize net profit reward - compensation N home users: maximize
net utility compensation - discomfort discomfort function v i
inelasticity parameter of user i Each user is tied to an aggregator
Hierarchical DR market model 18 Slide 19 Lazaros Gkatzikis PhD
defense 23/7/2013 Operator: min operating cost controls reward
generation cost c t (): convex and increasing function of total
demand y t DR gain portion of DR gains provided as reward
Hierarchical DR market model Aggregator j: max reward -
compensation indirectly controls its users demand distribution d jt
through time-varying compensation p jt reward depends also on
demand / strategy of other aggregators 19 Slide 20 Lazaros
Gkatzikis PhD defense 23/7/2013 Hierarchical DR Market Model User:
max compensation discomfort controls demand distribution x i total
demand is fixed (only demand shifting) for given compensation p jt,
a convex optimization problem Three level DR market Slide 21
Lazaros Gkatzikis PhD defense 23/7/2013 Proposed market mechanism
Day-ahead DR market 1.Operator announces a reward per unit of cost
reduction. 2.Each aggregator bids the cost reduction it can provide
for the given reward. 3.The best offer is accepted. 4.An increased
reward is announced to achieve further DR gains. 5.Repeat until no
further DR benefits In order to calculate their bid, aggregators
estimate inelasticity of users 21 Slide 22 Lazaros Gkatzikis PhD
defense 23/7/2013 Numerical results Generation cost is decreasing
in reward Operating cost is not monotonic DR gain and rewards of
lower levels are increasing in 22 Slide 23 Lazaros Gkatzikis PhD
defense 23/7/2013 Numerical Results and Conclusions Elasticity of
demands is beneficial for DR Users utility is not monotonic
Non-profit utility operators maximize DR benefits Future work:
coalition formation of home users (virtual aggregators) 23 Slide 24
Lazaros Gkatzikis PhD defense 23/7/2013 Outline 1) Introduction 2)
Residential demand response 3) Hierarchical demand response markets
4) Mobile task offloading in the cloud 5) Energy-constrained MAC 6)
Interference-aware relay selection and power control 7) Conclusion
24 Slide 25 Lazaros Gkatzikis PhD defense 23/7/2013 Virtualization:
multiple VMs on a single physical machine Multitenancy cost due to
access to the same physical resources (CPU, caches, memory, disks,
I/O) generally increasing in the number of co-located VMs
task-dependent Objective: minimize execution time Control:
Allocation and migrations of VMs Migration cost = data transfer
time required for initialization of a new VM Mobiles of limited
energy offload tasks to the cloud Novel MCC architecture servers in
wireless access hubs avoid communication delay of the Internet 25
Mobile Cloud Computing Slide 26 Lazaros Gkatzikis PhD defense
23/7/2013 Related Work and Contribution Modeling multitenancy cost
profiling of each type of task (BUT significantly diverse tasks
exist in the cloud) estimate probability of contention for each
resource (BUT requires a priori knowledge of the resource access
pattern of each task) Commercial cloud services (Amazon EC2,
Windows Azure) only availability SLAs (99,9%) no QoS guarantees
Main issue: Dynamic + unpredictable environment Solution: Exploit
VM migrations to reconfigure the cloud Our Contribution Propose
three online VM migration mechanisms that capture multitenancy and
migration costs Demonstrate how VM migrations can be used for
energy efficiency purposes. 26 Slide 27 Lazaros Gkatzikis PhD
defense 23/7/2013 A task of increasing data footprint No-migration:
worst performance Join the least loaded server attempts to exploit
available processing capacity, does not consider the increasing
cost of each migration and the additional cost of downloading the
final data from a distant server Mobility-aware: minimizes total
lifetime (considers both DL time and migration cost)=> minimizes
both execution and DL time 27 Motivating example Slide 28 Lazaros
Gkatzikis PhD defense 23/7/2013 demand varies unpredictably with
time and location new tasks arise continually at various locations
others complete service same holds for the resource supply due to
multitenancy The available processing capacity changes due to the
unpredictable interaction of co-located VMs tasks carry/generate
data whose volume varies with time Video compression: decreasing
data footprint Scientific experiments: increasing data access links
are also time varying 28 Challenges Slide 29 Lazaros Gkatzikis PhD
defense 23/7/2013 tasks arrive continually with unknown
distribution at time t each task i is characterized by d i (t):
data footprint evolution b i (t): remaining processing requirement
at server j hosting n VMs actual service capacity stochastic due to
multitenancy cost 29 System model Slide 30 Lazaros Gkatzikis PhD
defense 23/7/2013 Online task migration mechanisms triggered
periodically (every seconds) or by load-imbalance signal or by
SLA-violation key idea: migrate only if beneficial for the total
processing time, including both migration cost and download time
online estimation of multitenancy online measurements as tasks are
being executed 30 Balancing the cloud through migrations Slide 31
Lazaros Gkatzikis PhD defense 23/7/2013 cloud facility operated by
a single provider A migration affects the tasks running at the
current and the destination server consider only migrations
beneficial for the system as a whole Strategy : For each task
hosted in each server, calculate the gain of migrating to any other
server prefer migrating tasks of increasing data footprint, of
significant remaining processing burden, introducing significant
multitenancy cost (noisy neighbours) 31 Cloud-wide migration Slide
32 Lazaros Gkatzikis PhD defense 23/7/2013 Strategy : each server
individually selects its migration strategy select the task of
maximum anticipated gain, in terms of completion time (does not
consider the impact of the migration on the tasks located at the
destination host) executed whenever a server detects that it is
overloaded compared to the average of the system Application
scenario: Intercloud several providers form coalitions, enabling
access to each others infrastructure Reduce the deployment costs
Efficient utilization of resources 32 Server initiated task
migration Slide 33 Lazaros Gkatzikis PhD defense 23/7/2013 Each
user decides independently his migration strategy towards
minimizing his own completion time. Challenge: the users of a cloud
facility do not have a detailed view of the system Only aware of
advertised processing capacities Strategy: myopically select a
migration to the best destination server Application scenario: each
task/user may select out of a set of available cloud-providers/
servers. 33 Task initiated migration Slide 34 Lazaros Gkatzikis PhD
defense 23/7/2013 Numerical results 34 significant benefits
compared to one-shot placement performance degrades as we move from
the centralized approach (systemwide information) to decentralized
ones (local information) migrations crucial for overcommitted
clouds or light tasks Slide 35 Lazaros Gkatzikis PhD defense
23/7/2013 Energy Concerns and Conclusions Mobile: when is
offloading beneficial? Energy cost of transmitting required data is
less than that of local execution 35 Cloud provider: How could
electricity cost be reduced through migrations? Consolidation into
minimum number of servers Exploitation of spatiotemporal variation
of prices Conclusions Minimizing energy consumption and execution
time are contradictory objectives Multitenancy-aware VM migration
schemes necessary for overcommitted clouds Future work:
energy-driven VM migration schemes with QoS Slide 36 Lazaros
Gkatzikis PhD defense 23/7/2013 Outline 1) Introduction 2)
Residential demand response 3) Hierarchical demand response markets
4) Mobile task offloading in the cloud 5) Energy-constrained MAC 6)
Interference-aware relay selection and power control 7) Conclusion
36 Slide 37 Lazaros Gkatzikis PhD defense 23/7/2013 Energy
efficiency wireless mobile devices are battery powered (i.e. tight
energy budget) energy is consumed at electronic compartments (e.g.
local oscillator), even when idle Bandwidth scarcity Limited
bandwidth for an ever-increasing number of wireless devices Result:
extreme competition for the medium Additional constraints
autonomous nature of mobile terminals limited knowledge available
at node level difficulty of synchronization Need for: Game
theoretic models for energy-constrained probabilistic medium access
Energy Constraints and Medium Access 37 Slide 38 Lazaros Gkatzikis
PhD defense 23/7/2013 Related work and Contribution Cut down
unnecessary energy costs Turn-off electronic parts if not used
Support low power (sleep) modes Switching time / consumption
tradeoff Mode transition not feasible at timeslot timescale Related
Work game theoretic formulation of probabilistic medium access
interplay of medium access contention and energy consumption
Contribution Derive throughput optimal and proportional fair
probabilistic strategies under energy constraints Quantify the
impact of energy constraints on probabilistic medium access 38
Slide 39 Lazaros Gkatzikis PhD defense 23/7/2013 Single channel
Aloha network (slotted) N throughput maximizing self-interested
users of energy budget Two power modes: ON/OFF We introduce a new
timescale (frame) for the mode switching Probabilistic ON/OFF with
q i being the ON probability Within a frame the ON nodes access the
medium probabilistically (p i ) System Model 39 Slide 40 Lazaros
Gkatzikis PhD defense 23/7/2013 The impact of energy constraints on
system throughput Derive throughput optimal p,q (coordinated) to
quantify the impact of energy constraints to serve as a benchmark
where and 40 Slide 41 Lazaros Gkatzikis PhD defense 23/7/2013
Coordinated approaches Throughput optimal probabilistic access
without energy constraints Any strategy that eliminates contention
Throughput optimal for our case Activate the j less constrained
terminals with The optimal strategy is of the form Proportional
fairness substitute the original objective by The optimal strategy
is of the form 41 Slide 42 Lazaros Gkatzikis PhD defense 23/7/2013
Game theoretic model Players: the N users Strategies: the ON-OFF
probability and the medium access probability User preferences: any
user prefers the strategy that maximizes his throughput Optimal
strategy Unique Nash Equilibrium Point (NEP) Bounded price of
anarchy In contrast to the classic Aloha games 42 Slide 43 Lazaros
Gkatzikis PhD defense 23/7/2013 A modified (sensing) strategy
Assumption: fixed medium access probability within a frame two or
more users are ON within a frame zero payoff Ideally: whenever a
collision is detected in the first timeslot, all but one should
backoff until the next frame Save energy Reduce contention Our
approach: If the transmission fails the user adjusts his strategy
by reducing his transmission probability to Derive analytic
expressions of throughput and energy Formulation of a
non-cooperative game: Multiple NEPs 43 Assumption: fixed medium
access probability within a frame Slide 44 Lazaros Gkatzikis PhD
defense 23/7/2013 Numerical Evaluation the additional power budget,
increases the performance degradation due to the additional
collisions caused Performance plateau (a single user has sufficient
energy to capture the medium on its own) 44 Slide 45 Lazaros
Gkatzikis PhD defense 23/7/2013 Numerical Evaluation and
Conclusions High transmission cost makes the users less aggressive,
leading thus to reduced collisions Conclusions Channel sensing
provides significant benefits Due to lack of coordination,
probabilistic access is sensitive to increased energy availability
Future work: Mechanism design for more efficient equilibria 45
Slide 46 Lazaros Gkatzikis PhD defense 23/7/2013 Outline 1)
Introduction 2) Residential demand response 3) Hierarchical demand
response markets 4) Mobile task offloading in the cloud 5)
Energy-constrained MAC 6) Interference-aware relay selection and
power control 7) Conclusion 46 Slide 47 Lazaros Gkatzikis PhD
defense 23/7/2013 Cooperative communications exploit the broadcast
nature of the wireless medium use intermediate nodes as relays
Multihop communications - require additional radio resources
(frequency channels or time slots) + reduce the path loss, by
shortening the propagation path + create diverse paths that
mitigate the effects of fading Upcoming 4G cellular networks use
relays to extend coverage enhance throughput minimum deployment
cost 47 Relay-assisted networks SD R Slide 48 Lazaros Gkatzikis PhD
defense 23/7/2013 Most existing works assume that the transmissions
take place over orthogonal channels consider interference either
negligible or handle it as noise In practice Channel
scarcityfrequency reuse Maximizing the sum rate of a system N
source-destination unicast pairs single channel (interference)
contention for K relays Controls: Relay Selection+ Power Control
Our contribution Develop distributed lightweight resource
allocation algorithms Derive conditions for the optimality 48
Related Work and Contribution Slide 49 Lazaros Gkatzikis PhD
defense 23/7/2013 Relay selection Objective: maximizing the sum
rate of the system where Decode and Forward scenario (half-duplex)
Challenges due to interference relay selection and power control
strongly coupled ones transmission power affects all the others
first and second hop transmission rates are coupled 49 Problem
Formulation Slide 50 Lazaros Gkatzikis PhD defense 23/7/2013 The
optimality of a relay assignment depends on the selected
transmission powers and vice versa joint RS and PC extremely
difficult decouple by solving the two problems in an iterative way
initial transmission power allocation Logical assumption: Given the
others powers, the rate of a node is an increasing function of its
transmission power 50 Decoupling Relay selection & Power
control Slide 51 Lazaros Gkatzikis PhD defense 23/7/2013 Bipartite
Maximum Weighted Matching (MWM) approach map into the problem of
finding the maximum weighted matching in a properly constructed
complete bipartite graph introduce virtual nodes interference in
the receiver of each link needs to be known (true only for the 1 st
hop) conservative approach: assume that in the optimal assignment
all the relays are used overestimate interference 51 Relay
selection Slide 52 Lazaros Gkatzikis PhD defense 23/7/2013 Given a
relay assignment, we need to find the optimal transmission powers
for the sources and the relays Rate equalization (Req) approach
coupled power control in the 1 st and the 2 nd hop for each
communication pair we reduce the transmission power to match the
rate of the other hop (until convergence) Guarantees reduced
interference and energy consumption Joint source and relay power
control (JsrPC) approach we extend for the two hop scenario the
approach of [90] that is based on the high SINR approximation 52
Power control Slide 53 Lazaros Gkatzikis PhD defense 23/7/2013
Benchmark Direct Transmission one-shot greedy approach: Each source
greedily selects the best relay Impact of number of relays K Dense
network : interference overestimation degrades performance Sparse
network: performance beyond 15 relays is less affected Conclusion:
Significant benefits from interference management and relaying
(main features of 4G) for both energy and throughput. 53 Simulation
Results and Conclusion Slide 54 Lazaros Gkatzikis PhD defense
23/7/2013 Outline 1) Introduction 2) Residential demand response 3)
Hierarchical demand response markets 4) Mobile task offloading in
the cloud 5) Energy-constrained MAC 6) Interference-aware relay
selection and power control 7) Conclusion 54 Slide 55 Lazaros
Gkatzikis PhD defense 23/7/2013 Conclusion Explored the challenges
arising from limited availability of energy at device, system and
community level Energy constraints modify medium access (different
NEPs, reduced PoA) Relay selection and power control lead to better
utilization of available energy (interference management) VM
migrations enable better exploitation of cloud resources, reduce
energy consumption and operating cost DR leads to less costly and
more stable power grid and can be beneficial for all market
entities 55 Slide 56 Lazaros Gkatzikis PhD defense 23/7/2013
Related Publications Journal publications [J.01] L. Gkatzikis, I.
Koutsopoulos and T. Salonidis, The Role of Aggregators in Smart
Grid Demand Response Markets, in IEEE JSAC- Special series on Smart
Grid Communications, vol.31, no.7, pp 1247 - 1257, July 2013.
[J.02] L. Gkatzikis and I. Koutsopoulos, Migrate or Not? Exploiting
Dynamic Task Migration in Mobile Cloud Computing Systems, in IEEE
Wireless Communications Magazine: Special Issue on Mobile cloud
computing vol.20, no.3, June 2013. [J.03] L. Gkatzikis, and I.
Koutsopoulos, Mobiles on Cloud Nine: Efficient Task Migration
Policies for Cloud Computing Systems, under review in Elsevier
Computer Networks, Special Issue on Communications and Networking
in the Cloud. [J.04] L. Gkatzikis, T. Salonidis, N. Hegde and L.
Massoulie, The Impact of Shiftable Demands on Residential Demand
Response, to be submitted in IEEE Transactions in Smart Grid.
Conference publications [C.01] L. Gkatzikis, G. Iosifidis, I.
Koutsopoulos and L. Tassiulas, Collaborative Placement and Use of
Storage Resources in the Smart Grid, under review in IEEE
International Conference on Smart Grid Communications
(SmartGridComm), 2013. [C.02] L. Gkatzikis, G.S. Paschos and I.
Koutsopoulos, Medium Access Games: The impact of energy
constraints, in proc. of International Conference on Network Games,
Control and Optimization (NETGCOOP), 2011. [C.03] L. Gkatzikis and
I. Koutsopoulos, Low Complexity Algorithms for Relay Selection and
Power Control in Interference-Limited Environments, in proc. of
Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and
Wireless Networks (WiOpt), 2010, Avignon, France 56 Slide 57
Lazaros Gkatzikis PhD defense 23/7/2013 Not Directly Related
Publications Journal publications [J.05] Vasilis Sourlas, Lazaros
Gkatzikis, Paris Flegkas and Leandros Tassiulas, Autonomic Cache
Management and Performance Limits in Information-Centric Networks,
to appear in IEEE Transaction on Network and Service Management
(TNSM), 2013. [J.06] I. Koutsopoulos, L. Tassiulas and L.
Gkatzikis, Client and Server Games and Nash Equilibria in
Peer-to-Peer Networks, under review in Elsevier Computer Networks.
Conference publications [C.04] P. Mannersalo, G.S. Paschos and L.
Gkatzikis, Geometrical Bounds on the Efficiency of Wireless Network
Coding, to appear in proc. of Intl. Symposium on Modeling and
Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt),
2013. [C.05] L. Gkatzikis, T. Tryfonopoulos and I. Koutsopoulos, An
Efficient Probing Mechanism for Next Generation Mobile Broadband
Systems, in proc. of IEEEWireless Communications and Networking
Conference (WCNC), Paris, France, 2012. [C.06] Vasilis Sourlas,
Paris Flegkas, Lazaros Gkatzikis and Leandros Tassiulas, Autonomic
Cache Management in Information-Centric Networks, in 13th IEEE/IFIP
Network Operations and Management Symposium (NOMS 2012), pp.
121-129, Hawaii, USA, April 2012. [C.07] L. Gkatzikis, T.
Salonidis, N. Hegde and L. Massoulie, Electricity Markets Meet the
Home through Demand Response, in proc. of IEEE Conference on
Decision and Control (CDC), Maui, Hawai 2012. [C.08] Vasilis
Sourlas, Lazaros Gkatzikis and Leandros Tassiulas, On-Line Storage
Management with Distributed Decision Making for Content-Centric
Networks, in 7th Conference on Next Generation Internet (NGI) 2011,
pp. 1-8, Kaiseslautern, Germany, June 2011. [C.09] I. Koutsopoulos,
L. Tassiulas and L. Gkatzikis, Client and Server Games in
Peer-to-Peer Networks, in proc. of IEEE International Workshop on
QoS (IWQoS), 2009, Charleston, SC, USA. 57 Slide 58 Lazaros
Gkatzikis PhD defense 23/7/2013 Thank you!!! 58
