Table Of ContentOverlay Routing for Fast Video Transfers in CDN
Paolo Medagliani∗, Stefano Paris∗, Jérémie Leguay∗, Lorenzo Maggi∗, Xue Chuangsong†, Haojun Zhou†
∗Mathematical and Algorithmic Sciences Lab, France Research Center, Huawei Technologies Co. Ltd.
20 Quai du Point du Jour, 92100 Boulogne-Billancourt, France
†Carrier Software Unit, Huawei Technologies Co. Ltd., Nanjing, China
Abstract—Content Delivery Networks (CDN) are witnessing cache. However, to follow the evolution of usage towards
the outburst of video streaming (e.g., personal live streaming or more dynamic and real-time services, CDN are evolving to
Video-on-Demand)wherethevideocontent,producedoraccessed
support a large variety of content types which cannot always
by mobile phones, must be quickly transferred from a point to
7 another of the network. Whenever a user requests a video not becached,suchaswebapplications,teleconferencingandlive
1 directly available at the edge server, the CDN network must video streaming.
0 1) identify the best location in the network where the content DeliveringcontentatscaleovertheInternetwithlatencyand
2 is stored, 2) set up a connection and 3) deliver the video as reliability constraints is a real challenge. Indeed, the Internet
quickly as possible. For this reason, existing CDNs are adopting
n is best-effort with routing policies that do not address fined-
an overlay structure to reduce latency, leveraging the flexibility
a grained needs of applications and that are often guided by
J introducedbytheSoftwareDefinedNetworking(SDN)paradigm.
InordertoguaranteeasatisfactoryQualityofExperience(QoE) business relationships on large traffic volumes. The Triangle
1
to users, the connection must respect several Quality of Service Inequality Violation (TIV) [3] is a well known consequence
3
(QoS)constraints.Inthispaper,wefocusonthesub-problem2), of such policies. The minimum delay path is almost never
by presenting an approach to efficiently compute and maintain
] the one established by the underlying routing system. In
I paths in the overlay network. Our approach allows to speed
addition, outages are happening all the time in the Internet
N up the transfer of video segments by finding minimum delay
. overlay paths under constraints on hop count, jitter, packet loss due to cable cuts, misconfigurated routers, DDoS attacks,
s and relay processing capacity. The proposed algorithm provides power outages, or natural disasters [4]. Even if the Internet
c
a near-optimal solution, while drastically reducing the execution becomes flatter [5] with content service providers buying
[
time.WeshowontracescollectedinarealCDNthatoursolution direct connectivity closer to their end users, CDN operators
1 allows to maximize the number of fast video transfers.
are still fighting against TIV and best effort routing policies.
v
In reaction, overlay networks, such as RON [6], have been
1 I. INTRODUCTION
1 introduced to provide low latency and reliable connectivity
0 Globally,IPvideotrafficisexpectedtorepresent82percent overtheInternet.Similarly,CDNoperatorsdeployathree-tier
9 of all IP traffic (business and consumer) by 2020 [1]. Internet architecturecomposedoforiginserversthatcreatethecontent,
0
video traffic is expected to grow fourfold from 2015 to 2020. edge servers, which clients access to consume the content,
.
1 While a large variety of Video on Demand (VoD) and video- and an overlay network that is responsible for transporting
0 streaming services has emerged in the past years, the field the content from the origins to the edges. Clients request the
7
continuestoevolverapidly.Thewaysthatpeoplearewatching content from the closest edge server, and the edge server in
1
videoisconstantlyevolvingandisdrivenbymobileusage.For turn retrieves the requested content from the origin via the
:
v instance, live streaming embedded in social media platforms overlay network over the Internet.
i
X isarelativelynewphenomenon,butthistechnologyisfinding CDN solutions are composed of building blocks such as
more and more support with services such as Facebook Live a caching system to store the most popular contents at the
r
a or Periscope. network edge, a load balancing system, integrated within a
With the explosion of streaming services that deliver In- DomainNameSystem(DNS)server,toredirectclientrequests
ternet video to the TV and other device endpoints, Content to the closest edge server and an overlay routing system
Delivery Networks (CDN) have prevailed as a dominant to transport content at low latency and high reliability. The
methodtodeliversuchcontent.Globally,72percentofInternet overlay routing system is invoked to find good paths at a
videotrafficwillcrossCDNby2019.Thelargestover-the-top number of occasions. This is for instance required to connect
playerAkamaicurrentlyhasover170,000edgeserverslocated a live streaming content producer to its consumers, or to
in over 1300 networks in 102 countries [2]. At a smaller retrieve segments of a non real-time video stream which
scale, Internet service providers are also deploying their own are cached at a given edge sever. Following the ongoing
infrastructure, referred to as Telco CDN, as an evolution of transformationofnetworkarchitectureswithSoftwareDefined
IPTV and VoD systems. CDN have been traditionally used to Networks (SDN) [7], CDN are adopting flow-oriented and
helpcontentprovidersdistributingstaticcontentatscale.They centralized controllers [8] to manage video traffic especially.
are typically composed of edge servers which are deployed The (logically) centralized control aims at improving the
as close as possible to end users and act as a proximity Quality of Experience (QoE) perceived by end users. The
challenge for such an overlay network controller is to quickly
find paths in the overlay when new demands arrive and to
maintain a good routing configuration over time so that the
transfer time of video segments is minimized.
Thispaperpresentsanefficientalgorithmtomaintainmini-
mum delay overlay paths with multiple QoS constraints on
capacity, jitter and packet loss. These optimization criteria
have been carefully selected to speed-up the transfer of video
segments, knowing that TCP or QUIC [9] is used under HLS
or MPEG-DASH [10] for live and regular streaming. While
the optimization problem it solves is NP-Hard, we use tools
from combinatorial optimization such as Lagrangian relax-
ation and column generation to quickly find a near-optimal
approximation. Our algorithm is based on the decomposition
of the original problem into two simpler problems, namely
findingaminimumdelaypaththatsatisfiesallQoSconstraints Figure 1: System model of a CDN overlay framework.
for a single demand (QoS path computation), and computing
the best set of paths for all demands (constrained multi-
Our work differs from state of art by focusing on delay
commodity flow). We present an evaluation of this algorithm
minimization subject to constraints on jitter and packet loss.
over measurements collected in a real Telco CDN. We extend
In addition, it considers that edge servers act at the same time
theevaluationoverasyntheticnetworktofurtherhighlightthe
as source, relay and end points in the overlay network. In this
performance of the algorithm.
context, we provide an algorithmic framework for the online
The rest of the paper is structured as follows. Sec. II and global control of fast video transfers in CDN.
provides an overview of the related work. Sec. III introduces
the system model considered and formulates the problem as III. PROBLEMFORMULATION
an MILP. Sec. IV describes the algorithms that we propose to
This section introduces the system model and the path
solvetheadmissionandroutingmaintenanceproblems.Sec.V
computation problem.
illustratesthenumericalevaluationoftheproposedalgorithms.
Finally, concluding remarks are provided in Sec. VI.
A. System model
II. RELATEDWORKS AtypicalCDNframeworkisdepictedinFig.1.Weconsider
the presence of several content sources that stream videos,
Overlay routing has received a lot of attention, especially bothliveandondemand,toconnectedremoteendusersusing
in the domains of peer-to-peer, conferencing and CDNs. the existing overlay network. Instead of connecting directly
QoS routing for multi-layer description video streams has the end users to the source, end users connect to an edge
beenproposedtocomputedisjointoverlaypathsforeachsub- server. In fact, since the edge server is able to replicate the
stream to increase reliability [11]. Thi et al. [12] allocate all same stream towards different end users, this results in a load
sub-streams at once by minimizing an estimate of the end- reduction at sources and a better bandwidth utilization in the
to-end video quality distortion. They minimize the end-to-end overlay. The choice of the best edge server which an end
probability of video stall based on packet loss and latency. user must be connected to is typically handled by a DNS
Distributed path computation algorithms have been pro- or HTTP proxy system. By leveraging different information
posed for peer-to-peer conferencing applications to build and such as geographical locations, content availability and edge
maintainapplicationlayermulticasttrees[13].Theygradually server load, it redirects end user connection requests towards
maintainatreeforeachmulticastsessionbydefiningjoinand the most suitable edge server. Once the best server has been
leaveprocedures.Conversely,ourworksuitsfortheCDNcase identified, two cases arise: (i) the edge server has already
with a centralized controller platform [8]. the content available and it can serve the end user, (ii) the
Andreev el al. [14] introduce an overlay network for live content is not available at the edge server. In the latter case,
streamingwithedgeservers,reflectorsandsourcenodes.They the edge server needs to retrieve the requested video from
propose a linear relaxation and rounding based algorithm to eithertheoriginserveroranotheredgeserverthatalreadyhas
select reflectors. As reflectors can split multimedia streams to the content available. To this end, it is necessary to compute
serve multiple receivers, the algorithm build an overlay forest the best overlay path to transfer the content to the edge server
to connect sources to receivers. To increase reliability, they querying for it. Fig. 1 shows a schematic description of the
also ensure that each source is served by two reflectors. Their interactions among the different overlay components.
primary objective is to optimize the cost of the infrastructure. While existing overlays are composed of edge servers be-
Similarly, Zhou et al. [15] proposed an algorithm to find longingtothesameprovider,weconsideralsothecasewhere
capacity and delay bounded minimum cost overlay forests. they can be extended with nodes placed at Internet eXchange
Symbol Description
Points (IXP) thanks the emerging technology of Software-
N Nodes (network devices).
DefinedExchange(SDX).Fressancourtetal.[16]haveshown
E Edges (network links).
thatIXPcanbeusedasthird-partyroutinginflectionpointsto
K Set of demands (i.e., commodities).
enhanceanexistingoverlaynetwork.Thisway,CDNoverlays rk Transmission rate for demand k∈K.
with even a few internal nodes can reach a high level of path d Delay of edge (i,j)∈E.
ij
diversity using external relays. b Capacity of edge (i,j)∈E.
i,j
Thesystemmodelpresentedaboveappliestotwousecases: fi,j Prob. of successful transmission for edge (i,j).
(i) video on demand (VoD) and (ii) personal live streaming Fk Minimum prob. of successful transmission for k.
z Jitter of edge (i,j)∈E.
(PLS). In the former scenario, end users request a video from i,j
Zk Maximum jitter for demand k∈K.
a content provider. The goal of the system is to guarantee
N Maximum processing rate for node i∈N.
i
that the user is served as quickly as possible. If the content is
already available at the edge server the problem is trivial and Table I: Notations for input parameters.
it only concerns the connection between end user and edge
server. Instead, if the content is not directly available at the of nodes and E denotes the set of edges. Each directed edge
edge server, then the problem is equivalent to computing a (i,j)∈E ischaracterizedbyitscapacityb ,delayd ,jitter
i,j i,j
path which minimizes the latency between two edge servers z and successful packet transmission probability f . Each
i,j i,j
in the network and which respects some QoS constraints. The node i∈N has a maximum processing rate N .
i
video content is either retrieved from the source or from the WeconsiderasetKofvideo-streamingconnectiondemands
cache of another edge server. whichneedtoberoutedinthenetwork.Demandkisidentified
In the PLS scenario, instead, content is generated and by a source node sk ∈ N, destination node tk ∈ N and
streamed by users, as it may happen for instance with Face- transmission rate rk. Table I summarizes the notation used
book Live. Other end users willing to watch the content
throughout the paper. Our primary objective is to accept the
connect to the overlay network in order to retrieve it. At this
maximum number of demands into the system; our secondary
point, a similar situation to VoD arises. The overlay network
goal is to minimize the total delay, while each demand must
firstidentifiesthebestedgeserverwhichtheusermustconnect
fulfill all hard constraints on link and node capacity, jitter and
to; if the edge server does not have the content available, then
packetlossprobability.Moreover,atmostonereflectorcanbe
itrequestsitfromeithertheoriginserverorfromanotheredge
usedforeachdemand.ThistranslatesintoaMulti-Commodity
server [4]. Once this choice has been made, the system will
Flow (MCF) problem, that can be expressed either via a link-
compute and maintain the fastest path between the content
orpath-basedformulation,accordingtotheneeds.Westartoff
sourceandthedemandingedgeserver.Throughoutthispaper,
withthelink-basedformulation,thatsetsthedecisionvariable
we consider that an external element has already chosen the xk = 1 if and only if the directed edge (i,j) is used for
i,j
best edge and origin servers from which the content must be routing demand k, i.e.,
retrieved. Hence, we will only focus on the path computation
problem.
Inbothcases,videosarestreamedusingHTTPLiveStream- min (cid:88) (cid:88) xki,jdi,j+M (cid:88) (cid:88) xki,j (1)
x
ing or MPEG-DASH over TCP or QUIC. Minimizing trans- k∈K(i,j)∈E k∈K(i,j)∈E
fer durations then translates into maximizing the throughput s.t. (cid:88) xk − (cid:88) xk =γk, ∀i∈N,k∈K (2)
i,j j,i i
of each transport session. For TCP, the throughput can be j:(i,j)∈E∪E j:(j,i)∈E∪E
approximated by the following formula RMTSTS.√.Cp [17] which (cid:88)xki,jrk ≤bi,j, ∀(i,j)∈E∪E (3)
takes in to account the Maximum Segment Size (MSS), the
k∈K
Round-Trip Time (RTT) and the packet loss probability p. As (cid:88) xk z ≤Zk, ∀k∈K (4)
i,j i,j
a consequence, our path finding and maintenance algorithm
(i,j)∈E∪E
aimsatboundingpacketlossandjitterwhileminimizingRTT. (cid:88) (cid:88) xk rk ≤N , ∀i∈N (5)
Theparametersarecontinuouslymonitoredbyanactivemon- i,j i
k∈Kj:(i,j)∈E∪E
itoring system. In addition, as the relaying of flows induces a
burdenonoverlaynodes,wealsoconsideramaximumamount (cid:88) (cid:88) xkj,irk ≤Ni, ∀i∈N (6)
of traffic that each one can process. k∈Kj:(j,i)∈E∪E
We point out that the demands accepted by our algorithm (cid:88) xk logf ≥logFk, ∀k∈K (7)
i,j i,j
will be routed in the CDN overlay, following the computed (i,j)∈E∪E
paths.Fortherefuseddemands,instead,theywillbeaccepted (cid:88) xk ≤2, ∀k∈K (8)
i,j
anywaybytheCDNoverlaybutusingthedirectpathbetween
(i,j)∈E∪E
origin and edge server in a best-effort way.
xk ∈{0,1}, ∀i,j,k. (9)
i,j
B. Mathematical formulation
We remark that, via the formulation in (1-9), we implicitly
In this paper we model the CDN overlay network as a augmented the original graph G into a clique, where all
weighted directed graph G = (N,E), where N is the set the new (artificial) edges E have a large delay M. More
specifically,M shouldbesetaslargerthan2|K|maxi,jdi,j in IV. PATHFINDINGALGORITHMFORFASTTRANSFERS
ordertoprioritizethemaximizationofthenumberofaccepted
As illustrated in the previous section the overlay rout-
demands over the delay minimization goal. Eq. (2) describes
ing problem is NP-Hard. Therefore, the computational time
the standard flow conservation constraints, where γk = 1 if
i steeply increases with the network size and the number of
i = sk, γk = −1 if i = tk and γk = 0 otherwise. Eqs. (3)
i i demands. To solve the overlay routing problem even in large
and (4) account for the capacity and jitter hard constraints,
scalescenarios,weproposetodecomposetheoriginalproblem
respectively. Zk is the maximum jitter value for demand k.
into simpler subproblems that can be solved more efficiently.
Expressions(5),(6)ensurethateachnodeiprocessestrafficat
More specifically, we first relax the integrality constraints
a rate not exceeding N . Eq. (7) claims that the probability of
i for the variable y , enabling the use of multiple paths for
successful transmission for demand k is at least Fk. Finally, p
the routing of each demand, and then we design a column
Eq. (8) translates the requirement that at most one reflector
generation algorithm [19] to solve the underlying MCF prob-
is used for each demand, i.e., the maximum number of hops
lem. In order to deal with the QoS constraints, we use a
equals 2.
pseudo-polynomial algorithm to generate only shortest paths
that satisfy constraints (4), (7), and (8). Finally, we design a
Proposition 1. The overlay routing problem formalized in
randomized method to assign a single path to those demands
Eqs.(1)-(9) is NP-Hard.
whoseLPsolutionconsistsinsplittingthetrafficovermultiple
Proof. We prove that overlay routing problem is NP-hard by paths.
considering a simplified instance of the problem where QoS A general description of the steps of the proposed over-
constraints (4)-(8) are neglected. In other words, we do not lay routing method, referred to as Column Generation-
limit the set of feasible paths to those that satisfy the QoS Generalized LARAC (CG-GLC), is illustrated in Alg. 1. In
constraints. In this case, the overlay routing problem becomes the next subsections we provide more details.
aMulti-CommodityIntegralFlowproblem,whichisknownto
be NP-hard [18]. Thus, the overlay routing problem contains Algorithm 1: CG-GLC
an NP-hard problem as special case, which makes the overlay Input: d , b ,G(N,E,w(·))
e e
routing problem itself NP-hard. Output: y
/* Routing */
1 Find an initial feasible solution yp for the reduced master
We now present the path-based formulation for our opti- problem (10)-(12);
mization problem, that is equivalent to the link-based one in 2 Compute the dual point µ=[λ,σ] corresponding to y;
3 while µ is not feasible do
Eqs.(1)-(9).Asexplainedinthenextsection,thisformulation
for k∈K do
enables the decomposition of the original overlay routing Generate a graph G(N,E,w(·)) with links weights
problem into simpler and smaller sub-problems that can be equal to we =de+rkλe;
solvedmoreefficiently.WedefinePk asthesetofpathsfrom Compute the constrained shortest path p over G;
(cid:80)
if σ ≤ w then
sourcesk todestinationtk fulfillingtheconstraintsonnumber k e
e∈p
of hops (≤ 2), jitter (≤ Zk) and probability of successful /* This var. improves (10) */
transmission (≥ Fk). We call Pk ⊆ Pk the set of paths Add yp to the reduced master problem (10)-(12)
i
visiting node i ∈ N. Similarly, Pk ⊆ Pk is the set of paths (primal problem);
e
crossing edge e ∈ E. Moreover, let dp be the total delay of Solve the new reduced master problem and get the new
pathp,byaccountingthatedgesnotinE havedelayM.Then, solution y;
the path-based formulation for MCF writes as follows: Compute the dual point µ corresponding to y;
/* Rounding */
(cid:88) (cid:88) 4 while solution y has changed do
myin ypdp (10) for k∈K, ∃p∈Pk :0<yp <1 do
k∈Kp∈Pk Select path p with probability yp;
s.t. (cid:88) (cid:88) y rk ≤b , ∀e∈E (11) if any of the capacity constraints (11) is violated then
p e Restore the value of y ∀p∈P ;
p k
k(cid:88)∈Kp(cid:88)∈Pekyprk ≤Ni, ∀i∈N (12) elseSet yp =1;
k∈Kp∈Pik Set yq =0 ∀q(cid:54)=p;
(cid:88) Reduce the capacity of link in the path p by r ;
y =1, ∀k∈K (13) k
p
p∈Pk return y;
y ∈{0,1} (14)
p
where y =1 whenever path p∈Pk is used for k ∈K.
p
A. Solving the Constrained MCF problem
We observe that the two set of constraints (11)-(12) repre-
sent the transmission and processing capacity limits of links The column generation technique enables us to consider
and nodes, respectively. onlyasubsetofdecisionvariablesintheprimalformulationat
eachiteration,anditusesthedualformulationtoincludeonly rejected by column generation, can be allocated.
thosevariablesthatcanimprovetheobjectivefunction.Indeed,
B. Rounding procedure
from the duality theory we know that every feasible point to
the dual problem µ∗ gives a lower bound on the optimum To address the splitting of demands over multiple paths,
value of the primal y∗, and every feasible point to the primal which can be caused by the resolution of the LP relaxation of
problem y∗ gives an upper bound on the optimal value of the the problem (10)-(12), we introduce a randomized rounding
dual µ∗. Therefore, a feasible primal solution y∗ is optimal phase at the end of the column generation algorithm, in
if the corresponding dual point µ∗ is feasible. Our algorithm order to convert the fractional solution into a feasible integer
solution. Whenever multiplepaths are used toroute a demand
exploits this property in order to consider, for each demand,
from its origin to its destination, a single route is selected
only a small set of variables representing feasible paths and
with probability equal to the portion of the demand allocated
add new variables to the primal formulation as long as the
toeachspecificpath.Inparticular,foreachdemandk thathas
corresponding dual solutions are unfeasible. In our problem,
been split, we consider all possible paths where y > 0 and
the vector of dual variables µ = [λ,σ] is split into two p
we select a path p according to the overall flow allocated to
differentsetsofvariables,whereλcorrespondstothecapacity
it. If the whole demand k can be transmitted at its nominal
constraints (11)-(12) and σ corresponds to constraint (13),
whichindicatesthatasubsetofPk isusedtorouteademand. raterk overtheselectedpathpwithoutviolatinganycapacity
constraint, we keep only the path p by fixing the variable
We underline that, as long as the paths generated during
y = 1 and all other variables corresponding to alternative
the column generation procedure satisfy all QoS constraints, p
paths to 0. Finally, we reduce the capacity of the links that
the final solution computed by our algorithm is optimal for
belong to p by the demand’s rate r . The randomized routing
the LP relaxation of the overlay routing problem, in the sense k
procedure terminates either when a single path has been
that each demand is fully satisfied by one or multiple paths.
allocated to all demands or when the solution y does not
To this aim, we use the GEN-LARAC (GLC) algorithm as
change between two consecutive iterations. In this latter case,
a subroutine for solving the constrained shortest path prob-
alldemandsthatarestillsplitovermultiplepathsarerejected.
lem [20], since it computes in pseudo-polynomial time a path
thatsatisfiesallQoSconstraints(4),(7),and(8).Therefore,at C. Multicast Overlay routing
the end of the column generation algorithm we only have to Our CDN framework can be adapted to solve the mul-
choose a single path for each demand, without reconsidering ticast overlay routing problem, typical of scenarios where
all constraints of the original problem. overlay nodes can treat video streams at application layer by
If λ ≥ 0, the constraints of the dual problem can be decapsulating, processing, and re-encapsulating them before
formulated as follows: forwarding. In this case, the operator can save bandwidth in
(cid:88) the overlay network by building a multicast tree among the
σ∗− r λ∗ ≤d , ∀k ∈K,p∈P , (15)
k k e p k source and the nodes that are interested in the same content.
e∈p A demand k is therefore identified by a source node sk ∈N,
Eq. (15) states that in a feasible point of the dual problem multipledestinationnodesTk ⊂N andatransmissionraterk.
µ∗ = [λ∗,σ∗], there exists no path for any demand such Thegoalistoconnectasinglesourcesk toseveraldestinations
that σk∗ > (cid:80) rkλ∗e + dp, which can be rewritten as σk∗ > tk ∈ Tk using the multicast tree that satisfies all QoS con-
(cid:80) (r λ∗+ed∈p). In other words, there exists no path for any straints and has the minimum delay. To this end, we redefine
k e e Pk as the set of trees connecting source sk to its destinations
e∈p
demand that can further improve the objective function (10). tk ∈ Tk fulfilling all QoS constraints, while binary variable
In contrast, if such a path exists, i.e., ∃k ∈ K,p ∈ Pk: σk∗ > yp indicates whether the tree p ∈ Pk has been selected. The
rk (cid:80) (rkλ∗e +de), then the dual point µ∗ is unfeasible and main difference with respect to the previous overlay routing
e∈p problem dwells in the subroutine used to generate constrained
the objective function of the primal problem can be further
trees with minimum delay. In this case, this problem becomes
reduced by considering such a path (recall that the primal
anextensionoftheSteinertreeproblem,whichisknowntobe
solution is an upper bound of the dual solution).
APX-complete.Therefore,wecannotcomputeamulticasttree
All we need to do at each iteration of the column gen-
arbitrarily close to optimum in polynomial time, but we can
eration algorithm is checking whether the condition σ∗ >
r (cid:80) (r λ∗+d ) holds for all possible paths of allkde- only use schemes that compute a solution in polynomial time
k k e e withinanconstantapproximationfactorlike[21].Weobserve
e∈p
mands (i.e., ∀p ∈ P ). We observe that the computation that even if the algorithm will not converge to the optimal
k
of (cid:80) (r λ∗+d ) can be performed efficiently using an fractional solution of the multicast overlay routing problem, it
k e e
e∈p can still improve the starting solution computed by a heuristic
algorithmfortheconstrainedshortestpathcomputationonthe
approach like the one proposed in [15].
weightedgraphG(N,E,w(·)),wherethelinkweightfunction
w(·):E →R≥0 is computed as we =rkde+λe. V. PERFORMANCERESULTS
Wepointoutthat,inordertomaintainthefeasibilityofthis In this section, we analyze the performance our Column
routine, we also add some dummy paths on which demands, Generation(CG)approachbasedonGLC(CG-GLC).Inorder
N 11 Number of nodes
E 82 Number of links
b 50 Link capacity [Gbps]
i,j
N 150 Node processing capacity [Mbps]
i
K 82 Number of demands
r 50 Transmission rate [Mbps]
k
Fk 99% Minimum prob. of successful transmission
Zk 2 Maximum jitter for demand k [s]
Table II: Parameters for the Telco CDN scenario.
to show the distance of CG-GLC from the optimal solution,
also called “optimality gap”, we use the solution of the ILP
presented in Section III-B as a benchmark.
Results are evaluated in two different scenarios: (i) Telco (a)Distributionofpairwiseaveragedelaywithbinsof5ms.
CDN whereweusedtracescollectedonarealoverlaynetwork
ofaTelcoCDNand(ii)SyntheticCDN wherewegenerateda
larger random network. We present a performance evaluation
overtimeconsideringasindicatorsthepercentageofaccepted
demands,therunningtimeandtheaveragedelay.Wepointout
that in both scenarios, nodes can be either source/destination
of a demand or reflector if the demand is not originated in or
destined to the considered node. Without loss of generality,
for each demand, we considered Fk >99% and Zk <2 s.
All the tests have been executed on a machine with Intel
Core i7-5600U 2.6 GHz with 8 GB of RAM. The C++
librariesusedtobuildandupdatethenetworkgraphhavebeen
providedbyLemon.TheILPandtheresolutionofthereduced
master problem have been carried out using CPLEX. (b)Distributionofpairwiseaveragejitterwithbinsof5ms.
A. Real CDN Overlay Network
In this subsection, first we present the traces used for
simulations and then we compare the performance of CG-
GLC and ILP via numerical evaluations. In Table II, we list
the main parameters considered in the CDN overlay scenario.
Transmissionrateandnodeprocessingcapacityaresetto50
Mbps and 150 Mbps, respectively, which leads to a scenario
wherenodesarefairlystressed.ThelinkQoSmetricsusedfor
our experiments, as delay, jitter and packet loss, are described
in Subsection V-A1. (c)Distributionofpairwiseaveragepacketlosswithbinsof0.1%.
1) Dataset presentation: We used real traces from a Telco Figure 2: Overlay link statistics of the Telco CDN overlay.
CDN operator. Since the QoS of the considered overlay
network varies over time, a monitoring system carries out
2) Performance Evaluation: We now compare the perfor-
periodic probing between overlay nodes. In this subsection,
mance of CG-GLC and the solution of ILP in two scenarios.
we show the results of QoS metrics monitoring considering
The former is the one described before, where an overlay
an aggregation period of 5 minutes.
network is considered (overlay in the Figures). The latter
InFig.2a,weshowthepairwisedistributionoftheaverage
neglects the presence of the overlay, while only relying on
delay. We can see that the support of delay distribution is the direct path between source and destination (direct).
5-80 ms, while only few links present larger delay. The
We compare CG-GLC and ILP solutions in terms of per-
jitter distribution presented in Fig. 2b shows that the jitter
centageofaccepteddemandsandrun-timeinFig.3andFig.4,
is massively concentrated in the first bins. In fact, 90% of the
respectively. At each time instant we try to allocate all the 82
jitter samples are smaller than 330 ms. Finally, as shown in
demands. As the network capacity is not saturated, the node
Fig. 2c, most of the links have an average packet loss smaller
processing capacity is the real bottleneck of the system (i.e.,
than0.3%,although6%ofthelinkshaveapacketlossof3%.
constraints (5) and (6)).
Thisisduetolocalperturbationsthatcausedconsistentpacket
losses. Wefirstremarkthatwhilethroughtheoverlay(overlay)we
Figure 3: Percentage of accepted demands over time for the
Figure4:RunningtimeoftheCG-GLCandILPovertimefor
Telco CDN scenario.
the Telco CDN scenario.
manage to accept in average 90% of the demands, without
the overlay (direct) we cannot accept more than 20 % of
the demands. Accepted demands are flows for which QoS
constraintsintermofjitterandpacketlossaremet.Thisresult
highlights the benefit of overlay networking compared to the
casewhenonereliesonlyontheunderlay.Indeed,itincreases
path diversity and the chances to find feasible paths.
Secondly, we observe that our CG-GLC solution strikes a
good performance/complexity trade-off. In fact, CG-GLC is
characterized by an average optimality gap of 3% in terms of
percentage of accepted demands. Moreover, CG-GLC has a
running time around 10 times smaller than ILP solution, that
was produced by standard commercial software CPLEX. This
Figure 5: Average delay over time for CG-GLC for the Telco
is due to the fact that CG-GLC, instead of solving the whole
CDN scenario.
problem, focuses only on a subset of the original problem
(faster to be solved), by adding to it only the solutions (i.e.,
N 50 Number of nodes
paths)whichimprovetheobjectivefunction.Wepointoutthat
E 450 Number of links
the CG-GLC can compute an entire network reconfiguration
b ∼Unif[300,500] Link capacity [Mbps]
i,j
in less than 200 ms. d ∼Unif[1,500] Link delay [ms]
i,j
AsthenumberofaccepteddemandsisnotthesameforCG- α ∼Unif[0,50] Link jitter [ms]
i,j
GLC and ILP, it is not possible to carry out a fair comparison fi,j ∼Unif[0,0.2] Link packet loss
between the two approaches in terms of average delay. As Ni 400 Node processing capacity
[Mbps]
shown in Fig. 5, the average delay without overlay (direct)
K [90, 110, ... , 210] Number of demands
is smaller than the one with the overlay (overlay). This is
r ∼exp(50) Transmission rate [Mbps]
k
because the number of accepted demands is smaller without Zk ∼Unif[25,200] Max jitter [ms]
the overlay and, according to the CG routine, CG-GLC tries Fk ∼Unif[0.1,0.8] Max packet loss
to use first paths with low delay but, as long as new demands
TableIII:NetworkparametersfortheSyntheticCDNscenario.
are accepted, they are routed on more “expensive” paths.
B. Synthetic Overlay Network experiment.Foreachdemand,sourceanddestinationnodesare
In this section, we further evaluate the performance of randomly chosen among the set of nodes. Transmission rate
the proposed CG-GLC algorithm, in terms of percentage of of demands are distributed as an exponential random variable
accepted demands and running time, on a synthetic CDN net- of parameter 50 Mbps.
workgeneratedwithaBarabasimodel.Inthisscenarioaswell, In Fig. 6, the percentage of accepted demands is presented
we compare the results with (overlay) and without (direct) as a function of the number of demands. Both with and
overlay network. We point out that the ILP results are only without overlay network, the two algorithms have the similar
provided for less than 150 demands, due to simulation time performance as they manage to allocate the same number of
constraints:theILPsolutionrunningtimequicklyexplodesfor demands, meaning that CG-GLC is very close (less than 2 %)
bigger instances. In Table III, we show the parameters of this to the optimum provided by the ILP. However, when the load
flow under several QoS constraints derived from the require-
ments of CDN overlays networks. The proposed solution
applies to the fast video delivery problem for both personal
livestreamingandVideo-on-Demandusecases.Ourapproach,
based on column generation and randomized rounding, has
been tested against the optimal solution computed by solving
the associated ILP formulation with commercial software. We
used real traces from a Telco CDN and a random network.
Results show that our approach is an excellent compromise in
terms of running time and optimality.
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