Multicast virtual network mapping for supporting multiple description coding-based video applications

Computer Networks 57 (2013) 990–1002

Contents lists available at SciVerse ScienceDirect

Computer Networks

journal homepage: www.elsevier .com/locate /comnet

Multicast virtual network mapping for supporting multipledescription coding-based video applications

Yuting Miao a, Qiang Yang b,⇑, Chunming Wu a, Ming Jiang c, Jinzhou Chen a

a College of Computer Science and Technology, Zhejiang University, Hangzhou, Chinab College of Electrical Engineering, Zhejiang University, Hangzhou, Chinac College of Computer Science, Hangzhou Dianzi University, Hangzhou, China

a r t i c l e i n f o

Article history:Received 21 May 2011Received in revised form 23 November 2012Accepted 23 November 2012Available online 1 December 2012

Keywords:Multiple description codingMulticast treeVirtual network mappingPath convergence

1389-1286/$ - see front matter � 2012 Elsevier B.Vhttp://dx.doi.org/10.1016/j.comnet.2012.11.013

⇑ Corresponding author. Tel.: +86 15167138974.E-mail address: [email protected] (Q. Yang

a b s t r a c t

Video applications have gradually become one of the mainstreams of Internet traffic alongwith the technological advances in recent years. In parallel, network virtualization tech-nique allows Internet Service Providers (ISPs) to be decoupled from the physical networkinfrastructure operators to provide various video services to customers through tailoredVirtual Networks (VNs). In a video multicast VN, the ISP could appropriately determineand configure the virtual nodes and links to deliver customized video service to the affili-ated end users. However, available multicast tree mapping algorithms are based on thestrong assumption that the locations of source and a collection of destination nodes areknown a priori. Also, they have not taken any intermediate nodes between source and des-tinations into the VN mapping request. These assumptions greatly limit the adoption ofadvanced video coding techniques. In this paper, the multicast networks mapping forenabling Multiple Description Coding (MDC) based video applications is explored. A novelmulticast mapping algorithm, MMPC, is proposed based on path convergence to flexiblyidentify and configure nodes (with automatic intermediate nodes identification) in multi-cast trees to meet certain criteria. The suggested approach is described in details and itskey characteristics are analyzed through a set of analytical proves. Extensive simulationexperiments are carried out to assess its performance (e.g. acceptance ratio, mapping costand mapping time) against a range of multicast VN request scenarios. The simulationresults demonstrate the superiority of MMPC algorithm in terms of multicast mapping effi-ciency and cost by using the conventional two-phase VN mapping algorithm as a compar-ison benchmark.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, video applications in conjunction withdiverse coding techniques have been rapidly developedand gradually became one of the most dominating trafficin the Internet [1]. Recent advances in network virtualiza-tion enable multicast virtual networks to be establishedfor delivering video services to users with expected ServiceLevel Agreements (SLAs) underpinned by numerous net-

. All rights reserved.

).

work mechanisms. In network virtualization, the multicastvirtual network mapping is with particular challenge, as itneeds to appropriately allocate physical network resourcesto ensure the required Quality of Experience (QoE) whilstminimizing the network operation costs. It is worth notingthat the existing work assumes that the multicast tree fordelivering video service is with a fixed source node withoutthe adoption of any advanced coding techniques, to enhancevideo delivery and quality. The Multiple Description Coding(MDC) [2] is considered an efficient video coding techniqueallowing a single media stream to be fragmented into multi-ple sub-streams (i.e. descriptions) and the packets of each

http://dx.doi.org/10.1016/j.comnet.2012.11.013

mailto:[email protected]

http://dx.doi.org/10.1016/j.comnet.2012.11.013

http://www.sciencedirect.com/science/journal/13891286

http://www.elsevier.com/locate/comnet

Fig. 1. A MDC based video multicast network.

Fig. 2. MDC based video multicast virtual network mapping.

Y. Miao et al. / Computer Networks 57 (2013) 990–1002 991

description can be routed over multiple and (partially) dis-joint paths to provide improved error resilience. Fig. 1depicts an example of MDC based video multicast service.The conventional video multicast tree (left) can only deliverone type of service, e.g. the 400 K video application, whilethe 800 K service cannot be provided as additional codingneeds to be carried out at intermediate service node. A via-ble solution to this issue (right) is to adopt MDC technique,and incorporate an intermediate service node for 800 Kvideo provisioning service (intermediate node can also beused for 400 K to enhance service quality). Fig. 2 illustratesthat with the identified source node, the multicast networkneeds to place certain intermediate nodes along the end toend path if required to carry out the encoding of videostreams to meet diverse user requirements, e.g. 800 KHigh-Definition (HD) node and 400 K Standard-Definition(SD) node. This paper in particular exploits the muticastVN mapping algorithm in the multicast tree with automaticidentified intermediate nodes to support MDC based videoservices. We present a novel MDC video multicast VN

mapping algorithm, MMPC, which maps multicast treesonto the substrate network through the path convergenceapproach to meet diverse VN request requirements whilstimproving global physical resources utilization efficiency.

The remainder of this paper is organized as follows:Section 2 overviews the related work, followed by thedescription of problem model and formulation in Section3. Section 4 presents the proposed MMPC algorithm in de-tails and Section 5 gives a set of key numerical resultobtained from the simulation experiments. Some conclu-sive remarks and future work are given in Section 6.

2. Related work

In literature, the VN mapping problem subject to multi-ple constraints can have NP-Complete (NPC) complexity,which has been widely exploited and well addressed by aset of heuristics-based proposals [3–12]. The pioneer algo-rithmic solutions presented in [3,4] merely consider thelink capacity constraint and assume that all the virtual

Fig. 3. A MDC video multicast VN mapping (dashed lines show the virtual link mapping).

992 Y. Miao et al. / Computer Networks 57 (2013) 990–1002

nodes are pre-determined in the substrate network. In [5],the authors provide a typical two-phase mapping approach,i.e. mapping virtual nodes onto physical nodes followed bythe mapping between virtual links and physical links,which can be considered as a generic mapping procedureto solve most of the mapping problems. The algorithm sug-gested in [6] further improves the two-phase mappingmethod. It maps a single virtual link onto multiple physicallinks based on Multi-commodity Flow Problem (MFP) solu-tion, which greatly improves the VN mapping acceptanceratio and load balance. An enhanced coordination withmixed integer programming for resolving virtual networkmapping is carried out in [7], which is effectively a combi-nation of heuristics and linear programming approach, andpromotes the performance of the two-phase mapping ap-proach. In [8], the presented approach provides an altera-tive method to two-phase mapping by implementing thenode and link mapping simultaneously through subgraphisomorphism detection. However, all existing contributionsare restricted to the VN unicast based applications, the di-rectly adoption of these approaches for delivering multicastnetwork services is inappropriate, even not applicable. Theauthors in [9] proposed a distributed algorithm that solvesthe mapping problem without any centralized control, butat the price that the network nodes need to obtain the glo-bal information via broadcasting throughout the overallnetwork. A policy-based inter-domain VN embedding(PolyViNE) framework is presented in [10] to heuristicallyaddress the inter-domain VN mapping problem withoutoptimizing the mapping performance and computationcost. A hierarchical management framework for VN map-ping across multiple domains is discussed in [11], wheremanagement elements are responsible for the resourceallocation within the scope of their own domain. However,no algorithmic solution and results are presented in thiswork. The authors in [12] proposed a new scalable VNembedding strategy based on the Ant Colony metaheuristicto deal with the computational hardness, which objects tomap virtual networks in the substrate network with mini-mum physical resources while satisfying its required QoSin terms of bandwidth, power processing and memory.

The issue of finding multicast trees in Service OverlayNetwork (SON) is proved to be with NP complexity anddiscussed in [13,14], which is relevant to our work. In[13], a SON multicast tree algorithm is proposed to meetnetwork constraints and balance network loads, so as tominimize the network congestion and fluctuation. The

work in [14] addresses three particular issues, namelyoverlay proxy location, overlay link selection, and band-width constraints. Once the allocation of the proxy isdetermined, two criterias are applied to identify the con-nections among them with the objective of minimizingend-to-end latency and network operation costs. Someother algorithms aiming to find multicast trees subject todelay and delay variation constraints are also available,e.g. DVBMA [15], DPDVB [16] and CHAINS [17]. Again, allthese multicast algorithmic solutions cannot be appliedto deliver the MDC based video services as no intermediatevirtual nodes are used in the VN multicast tree to deployadditional coding function. To the authors best knowledge,no ready solutions are available.

In summary, current VN mapping solutions, either forunicast or multicast applications, mainly follow the ap-proach of ‘‘node-mapping -> link-mapping’’ or simulta-neously mapping. The MDC multicast virtual networkscan be characterized as a set of pre-determined destinationnodes and the tree structure with a source node, with somepotential intermediate nodes to support the end-userswith their required video services. A novel algorithm inconjunction with a path convergence method is proposedin this paper, which carries link mapping before mappingphysical nodes for source node and a set of automaticidentified intermediate nodes in the VN request.

3. Problem model and formulation

This section models and formulates the MDC video mul-ticast virtual network mapping problem and presents a setof preliminary terminologies. For the sake of clarity, weadopt the concept presented in [8] in this paper, whichprovides the definition of physical network, virtual net-work, virtual network mapping and the residual network,together with the problem formulation of virtual networkmapping cost.

The physical network can be modeled as an undirectedgraph, denoted as Gp ¼ ðNp; Lp;Cp

N;CpLÞ, where Np and Lp are

the set of substrate nodes and substrate links, respectively.We consider the CPU capacity, Cp

N , as the key node attributefor an arbitrary node n 2 Np, and the bandwidth, Cp

L , as thekey link attribute for an arbitrary link l 2 Lp.

The MDC video multicast VN request is expressed withthe structure as Tv ¼ ðS;D; Lv ;Cv

N;CvL Þ, where S ¼ fsg and

D ¼ fd1; d2; . . . ; dtg are the source node and a set ofdestination nodes (t is the number of destination nodes)

Fig. 5. The MMPC flow diagram for finding a multicast VN mapping.

Fig. 4. The residual network of Gp after mapping Tv .


of the multicast tree, respectively. Lv denotes the set ofvirtual links between virtual network nodes, i.e. betweenthe source and the destination nodes. It is considered thatCPU consumption, Cv

N , is the primary node attribute for anyvirtual node n 2 S [ D, and the required bandwidth, Cv

L , isthe primary link attribute for any virtual link l 2 Lv . Forexample, S ¼ fsg and D ¼ fa; b; cg in the multicast VNrequest Tv shown in Fig. 3.

Thus, the MDC video multicast VN mapping problemupon a multicast VN request, Tv ¼ ðS;D; Lv ;Cv

N;CvL Þ, onto a

substrate network, Gp ¼ ðNp; Lp;CpN;C

pLÞ, can be formulated

as follows: finding a subgraph which is also a tree form,GT ¼ ðNT ; PTÞ, of Gp such that all virtual nodes are mappedonto different physical nodes and virtual links are mappedonto loop free paths concatenated by substrate links:

M : MðTvÞ ¼ ðNT ; PTÞ ð1Þ

where NT and PT denote the subset of substrate nodes andloop free paths in Gp, respectively. M can be resolved intonode and link mapping as follows:

MN : MNðS [ DÞ ¼ NT ð2ÞML : MLðLvÞ ¼ PT ð3Þ

M is considered a valid mapping only if M : MðTv Þ meetsthe constraints expressed in the following equations:

CvN 6 Cp

N;8n 2 S [ D;MNðnÞ 2 NT ð4ÞCv

L 6 CpL ;8l 2 Lv ;MLðlÞ 2 PT ð5Þ

For example, in Fig. 3, the multicast VN Tv is mappedonto the PN Gp with NT ¼ fE;A;B; Cg; PT ¼ fEA; EB; ECg, vir-tual node mapping MNðaÞ ¼ A;MNðbÞ ¼ B;MNðcÞ ¼ C andMNðsÞ ¼ E, and virtual link mapping MLðasÞ ¼ AE;MLðbsÞ ¼BE and MLðcsÞ ¼ CE. In this work, we adopt a cost functionto evaluate the performance of MDC video multicast VNmapping. The mapping cost is defined as the amount ofphysical resources (e.g. CPU, bandwidth) allocated to themulticast subgraph, GT ¼ ðNT ; PTÞ. In this work we definethe cost as the following weighted combination:

costðGTÞ ¼Xn

i¼1

ðai �X

ciÞ ð6Þ

which subjects to:

0 < ai < 1 andXn

i¼1

ai ¼ 1 ð7Þ

where ai are weight factors andP

ci is the cost generatedin the VN mapping process (e.g. allocating CPU or bufferspace on physical nodes, and bandwidth on physicalpaths).

Take the VN mapping illustrated in Fig. 3 as an example,assuming that only the CPU capacity and bandwidth areconsidered. If they are equally weighted, i.e. a1 ¼ a2 ¼0:5, the mapping cost can be calculated as: costðGTÞ ¼ 0:5�ð7þ 2þ 2þ 1Þ þ 0:5 � ð2:1þ 2:1þ 1:1Þ ¼ 8:5.

The residual network, Gres, can be obtained after mappinga certain VN request, Tv , onto the physical network, Gp, bysubtracting the CPU capacity of physical nodes, n 2 NT ,which allocated to the virtual nodes, n 2 S [ D, and thebandwidth of physical paths, p 2 PT (comprised of a set ofphysical links l 2 Lp), assigned to virtual links, l 2 Lv . Theresidual network of Gp after mapping Tv is shown in Fig. 4.

Fig. 6. The MMPC algorithm execution procedure.


4. Algorithmic design with path convergence

This section presents the idea behind the proposedalgorithm MMPC. The destination nodes (end-users) whichreceive video services are often known in the physical net-work (PN), and hence can be directly identified in the PN. Awell deployed source node with appropriate location in PN,which is capable of carrying out video stream coding/decoding, can meet end-users’ service requirement. How-ever, the service requests imposed by end-users may beoverwhelmed and diverse when the user population islarge, which degrades the source node delivered Qualityof Service (QoS). Thus, a set of intermediate nodes with vi-deo coding/decoding capability must be deployed in the PNto alleviate the load on the source to improve the users QoSperception. The source node and the intermediate nodesare identified automatically by the proposed path-conver-gence function (see Algorithm 5), assuming that theyhave the same CPU constraints imposed by the VN request.Also, the end-to-end paths consisting of the intermediatenodes should meet the bandwidth constraints in the VNrequest.

Specifically, suppose that there are k different types ofvideo services expected to be received by the destinationnodes, we use the destinations-allocation function (see Algo-rithm 1 to allocate all the destination nodes into k differentsets, i.e. R1;R2,. . ., Rk. For an arbitrary set Ri, the destination

nodes in Ri receive the ith video service. After allocating thedestination nodes, the MMPC algorithm (see Algorithm 2) iscarried out. We use the set-division function (see Algorithm

3 to divide the set Ri into several subsets, i.e. R1i ;R

2i ; . . . ; Rj

i .The topologically adjacent destination nodes are allocatedinto the same subset, which will improve the efficiency ofpath-convergence algorithm and alleviate the load of inter-mediate nodes. Upon the set-division completion, the desti-

nation nodes in subsets R1i ;R

2i ; . . . ; Rj

i will conduct thepath-convergence function to find j intermediate node

in1i ; in

2i ; . . . ; inj

i , which provides their end-users withdemanded coding/decoding capability. All identifiedintermediate nodes, j, can conduct the path-convergencefunction recursively after set-division until an intermediatenode ini is found. For k different video services, in the man-ner as follows: when the destination nodes in each set areconverged into an intermediate node, respectively, i.e.in1; in2; . . . ; ink, the path-convergence function will executebased on these k intermediate node to find the source node.The overall mapping process of a multicast VN request isillustrated in Fig. 5.

Before discussing the MMPC algorithm, we firstly intro-duce the destinations-allocation function as shown inAlgorithm 1. Taken an example illustrated in Fig. 3, it issupposed that the destination nodes a and b require400 K video service while c requires 200 K video service,i.e. two types of video service are in Tv (k ¼ 2). Thus,R1 ¼ fa; bg;R2 ¼ fcg, and

P¼ fR1;R2g ¼ ffa; bg; fcgg.

Algorithm 1. destinations� allocationðTv ; kÞ

Require:a MDC video multicast VN, Tv ; and the types ofreceived video services k

1: R ¼ /2: for i = 1 to k do3: Ri ¼ /4:end for5: for each destination node d in D do6: if d receives the ith video service then7: add d into Ri //allocate the end-users to different

end-user sets8: end if9: end for

10: R ¼Sk

i¼1Ri

11: return R //return a set consisting of k end-user sets


4.1. MMPC Algorithm

The proposed MMPC algorithm for multicast VN map-ping consists of a key function (i.e. path-convergence) anda set of auxiliary functions (i.e. set-division and hierarchy-traverse), as shown in Algorithm 2.

Algorithm 2. MMPCðTv ;Gp;MðTvÞ;PÞ

Require:a MDC video multicast VN, Tv ; a PN, Gp; a VNmapping, MðTv Þ; and a group set,

P, of all

destination nodes1: if jR1j ¼ jR2j ¼ . . . ¼ jRkj ¼ 1 then

2: R ¼Sk

i¼1Ri

3: s ¼ path� convergenceðTv ;Gp;R;MðTv ÞÞ //find asource node

4: add s into MðTv Þ5: return MðTvÞ //return a valid VN mapping6: end if7: for each group set Ri in

Pdo

8: D ¼ set � divisionðRi; dÞ //divide Ri based on d9: Ri ¼ /

10: for each sub sets Rji of Ri in D do

11: inji ¼ path� convergenceðTv ;Gp;Rj

i;MðTv ÞÞ //find

an inte. node

12: Ri ¼ RiSfinj

ig //update Ri

13: end for14: end for15: MMPCðTv ;Gp;MðTvÞ;

PÞ //recursive

The MMPC algorithm execution procedure is shown inFig. 6. The MDC video multicast VN request indicates 14 in-volved destination nodes (end-users) and three types of vi-deo services (i.e. 200 K, 400 K, and 800 K video streamservice). The destination nodes are grouped into three sets,R1;R2 and R3, by destinations-allocation function based ontheir required service type before the execution of theMMPC algorithm. The set-division function (line 8) dividesthe set Ri (i ¼ 1;2;3) into several subsets with the rule thatmaximum d topologically adjacent nodes are grouped intothe same subset (i.e. d ¼ 3 in this case). After the executionof line 14, we find 5 intermediate nodes after the 1st itera-tion and the three sets R1;R2 and R3 are updated. In line 15,the MMPC continues to execute recursively to find more

Fig. 7. The path-convergence fun

intermediate nodes in the upper level or the source nodebased on the three updated node sets. After the 2nd itera-tion, the nodes in the three sets R1;R2 and R3 are all con-verged to a node, respectively (i.e. R1 ¼ fin1g;R2 ¼ fin2gand R3 ¼ fin3}). The statement from line 1–5 will executeto find the source node and return the VN mapping MðTv Þ.

4.2. The set-division () function

The set-division function is used to divide a node set intoseveral subsets based on the network topology in PN, i.e.the topologically adjacent nodes will be grouped into thesame subset. The division factor d is an integer with the va-

lue in the interval 2; aðCpL Þ

aðCvL Þ

h i, where aðCp

LÞ, represents the

average link bandwidth in PN and aðCvL Þ represents the

average link constraint in VN request. The lower boundtwo indicates that there should be at least two nodes in a

subset, and the upper bound aðCpL Þ

aðCvL Þ

imposes a threshold

attempting to avoid the potential physical link overflow.

Algorithm 3. set � divisionðRi; dÞ

Require:a node set, Ri; and a division factor, d

1: D ¼ /

2: j ¼ jRi jd

l m//Ri should be divided into j subsets

3: for k = 1 to j-1 do4: add d topologically adjacent nodes of Ri into

subset Rki

5: add Rki into D

6: end for7: add the rest topologically adjacent nodes of Ri into

subset Rji

8: add Rji into D

9: return D //return a node set consists of j subsets

As shown in Fig. 6, the node set R1 is divided intoR11 ¼ fn1;n2;n3g;R12 ¼ fn5;n8;n9g and R13 ¼ fn10; n12g,given d ¼ 3 and their topological locations in the PN.Similarly, node set R2 is divided into R21 ¼ fn4;n6;n7g andR22 ¼ fn13g. R3 is not be divided since jR3j ¼ 2 < d.

ction execution procedure.

Fig. 8. An instance of multicast VN mapping updating.


4.3. The hierarchy-traverse () function

This heuristic query function invoked in the key func-tion is motivated by the Breath First Search (BFS) algorithmand is described in Algorithm 4. Consider the PN shown inFig. 3, the virtual node, a, can be mapped onto the physicalnode, A. The parent node of a, denoted by paa, is node s inTv (i.e. paa ¼ s). Assuming that there are a node set, de-noted by qa ¼ fAg and a boolean array, denoted byva½A� ¼ true, the hierarchy-traverse () function can be con-ducted based on node A. Since the bandwidth of virtual link½a; s� ¼ 2 which is less than that of physical links ½A;D� ¼ 5and ½A; E� ¼ 5, therefore the node set, qa, can be replaced byfA;D; Eg.

Algorithm 4. hierarchy� traverseðdi; qi;v iÞ

Require:a virtual node, di; a node set, qi; and a Boolean array,v i

1: for each node u in qi do2: for each node w adjoin to u do3: ifv i½w� ¼ false and the bandwidth of virtual link½pai; di� is less than the bandwidth of physical link½u;w�

4: v i½w� ¼ true //note that node w has been visited,which meets the condition above

5: add w to qi //qi is updated by adding w6: end if7: end for8: end for

4.4. The path-convergence () function

The main contribution of this paper relies on thispath-convergence function, which is inspired by thehierarchical structure of multicast trees, and theadoption of path convergence to obtain the potentialintermediate nodes and the source. The details of theVN mapping procedure based on path convergence ispresented in Algorithm 5 and illustrated in Fig. 7through an example scenario. All destination nodes needto be identified (i.e. mapped onto their correspondingphysical nodes) in the PN, before conducting thepath-convergence function.

Algorithm 5. path� convergenceðTv ;Gp;R;MðTvÞÞ

Require:a MDC video multicast VN, Tv ; a PN, Gp; a node set,R; and a VN mapping, MðTvÞ

1: if jRj ¼ 12: return di 2 R3: end if4: for each node di in R do5: initialize an empty set qi

6: initialize a Boolean array v i for MNðdiÞ with allfalse

7: v i½MNðdiÞ� ¼ true8: add MNðdiÞ into qi

9: end for10: while C ¼¼ / do11: for i = 1 to jRj do12: hierarchy� traverseðdi; qi;v iÞ13: C ¼

TjRji¼1qi //C is a set consisting of the

convergence nodes14: if np 2 C satisfies the CPU capacity constraint

of the parent node pai of di and np R MNðRÞ then15: select a node np 2 C with the largest CPU

capacity16: Cp

np ¼ Cpnp � Cv

pai//update the CPU capacity of

np

17: update MðTvÞ by adding physical node np

18: for i = 1 to jRj do19: Cp

½np;MNðdiÞ�¼ Cp

½np ;MNðdiÞ�� Cv

½di ;pai � //update the

link bandwidth20: update MðTvÞ by adding physical link/

path ½np;MNðdiÞ�21: end for22: update Gp to Gres //update Gp

23: return np //return an intermediate node or asource node

24: end if25: end for26: end while

Fig. 7 illustrates the MDC video VN request mapping pro-cess in the PN scenario. Before conducting the path-conver-gence function, the destination nodes have been classifiedinto a node set denoted as R ¼ fa; b; cg. The statements from

Fig. 9. Comparison between conventional VN mapping algorithm and MMPC on MDC VN request.


line 4–9 indicates we will get three sets: qa ¼ fAg; qb ¼ fBgand qc ¼ fEg (Fig. 7a). When the loop from line 11–25accomplished its execution, we get qa ¼ fA;C;Dg; qb ¼fB; Eg and qc ¼ fA;C; Eg, and hence C ¼ /, which means nointermediate or source node np is found (Fig. 7b). Thus, theprogramming process will go back to line 10 to run this loopagain until finding a proper node np. After the second accom-plishment of this loop, we get qa ¼ fA;C;D; Eg; qb ¼fB;C;D; Eg and qc ¼ fA;C;D; Eg, and hence C ¼ fC;D; Eg.Since C belongs to the set MNðRÞ (i.e. MNðcÞ ¼ C) and thecapacity of E is greater than that of D, the node E is selected(Fig. 7c). We will add corresponding physical links into theVN mapping MðTv Þ, update the PN Gp to the Gres (line 16–22) and return the node np (line 23). If there is only one nodein set R, return this node as the intermediate nodeimmediately (line 1–3).

4.5. Multicast VN mapping updating

In the multicast VN mapping procedure, the video ser-vice type k is pre-defined to allocate the resources in accor-dance to the users requirements, and finally a valid VNmapping MðTv Þ is found. However, the video service typek can be dynamic in reality, which means that the end-users can switch their video services to a new video servicewith higher or lower quality. Thus, the multicast VN map-ping MðTv Þ needs to be updated, which can be carried outthrough the following steps:

� Deleting the physical links in MðTv Þ which connect theend-users change in demand and the intermediatenodes or source node.� If some current intermediate nodes in MðTv Þ can meet

part of the new requirements imposed by users, findingseveral physical links/paths to connect these end-usersand their corresponding nearest unsaturated (i.e. thenumber of leaf nodes is less than d) intermediate nodes(i.e. using the Dijkstra algorithm between two nodes),respectively, and adding these physical links/paths intoMðTv Þ.

� Conducting the MMPC algorithm based on the rest end-users until returning a source node, finding a physicallink/path to connect the new source node and the for-mer one in MðTvÞ (i.e. using the Dijkstra algorithmbetween two nodes), and adding this physical link/pathinto MðTv Þ.

Through the updating function, it can minimize thescope of the re-mapping of MðTvÞ, as well as meet thenew requirements from the end-users for accessing ex-pected services.

We use an example to explain the updating process asshown in Fig. 8. A multicast VN (k ¼ 2 and d ¼ 3) delivers200 K and 400 K video service (see Fig. 8a). The 200 Kend-user n3 expects to receive 400 K video service, andthe 400 K end-users n5 and n6 expect to receive 800 k videoservice, which results in k ¼ 3 and leads to the updating ofmulticast VN mapping. Firstly, n3;n5 and n6 are discon-nected from in1 and in1

2 (step-1). Then, n3 is connected toits nearest unsaturated 400 K intermediate node in1

2 sincethe nodes deliver 400 K video service have already existed(step-2, see Fig. 8b). Finally, the MMPC algorithm is exe-cuted based on n5 and n6 to find a source to deliver the800 K video service. Once the source node is identified(i.e. in3), we connect this source to the former source nodes (step-3, see Fig. 8c). Finally, the multicast VN mappinghas been updated successfully.

4.6. Discussion and theoretical analysis

The MDC based video multicast applications could beaddressed potentially through revising the former VNmapping algorithms in SON, by preprocessing the fixed2-level MDC VN request into the multi-level multicast treestructure by adding some intermediate nodes based on dif-ferent description codings. The multi-level tree mappingproblem can be solved by the conventional solutions, suchas the conventional two-phase VN mapping algorithm(Fig. 9a). This approach is considered inappropriate as theefficiency of VN request mapping can be significantlyundermined due to the time consumption of the procedure


of the MDC VN request preprocessing and the VN mappingalgorithm execution. Therefore, this paper presents theMMPC algorithm through automatic intermediate nodesidentification strategy (Fig. 9b) with improved mappingefficiency and low mapping cost. The potential weaknessof MMPC relies on its performance in terms of acceptanceratio, especially when the resource in PN becomes scarce.

Two theorems of the proposed MMPC algorithm arepresented as follows:

Theorem 1. After the mapping of a virtual node, u, and all itsvirtual leaf nodes (if exists) onto the physical network withMMPC, the sum of the physical path length between thephysical nodes mapped onto, u, and the other physical nodesmapped onto the leaf nodes of node, u, is optimum locally.

Fig. 11. The substrate network topology.

0.8

0.9

1

1.1

orm

aliz

ed m

appi

ng ti

me

MMPCconventional 2-phase mapping

Proof. Given any virtual node, u 2 InD [ S; k leaf nodes,v ið1 6 i 6 kÞ of u in a VN request, and the mapping of thevirtual link lv ½u;v i� onto the physical link ispT ½MNðuÞ;MNðv iÞ�, since the MMPC conducts the paths con-vergence step by step following the direction from the leafnodes to the roots, which equals to MNðuÞ is the closestcommon root of MNðv iÞ if the mapping is valid. Therefore,the sum of lengths of all mapped physical paths (from indi-vidual destination nodes to source node),

Pki¼1pT ½MNðuÞ;

MNðv iÞ�, is locally optimum.Taken an example shown in Fig. 10, the node r1 is the

common root of n1;n2 and n3 which are found throughpath convergence (e.g. step1-step2-step3-step4). Supposethat there exists another node, r2, is the closer commonroot (i.e. with a smaller number of hops) of the three nodesthan that of r1 in the PN (e.g. step1-step2-step3), which isequivalent to r2 can be firstly detected and returned by thealgorithm than r1. However, this contradicts our assump-tion that r1 is found as the common root based on ourassumption. h

2 4 6 8 10 12 14 16 18 200.6

0.7

Set division parameter δ

N

Benefits of automatic IN identification

upper bounder of δ

Theorem 2. The time complexity of MMPC isOðjDj � ðjV j þ jEjÞÞ, where jDj represents the quantity of end-users in VN request, jV j represents the quantity of physicalnodes and jEj represents the quantity of physical links in PN.

2.2

MMPC

Fig. 12. Normalized mapping time vs. d.

Proof. To prove the time complexity of MMPC asOðjDj � ðjV j þ jEjÞÞ equals to certify that the upper boundcomplexity is OðjDj � ðjV j þ jEjÞÞ [18].

Fig. 10. An example scenario of path convergence.

Upper bound: Let’s consider the worst situation that allthe destination nodes need to traverse the entire physicalnodes and links in PN to find their corresponding videoservice supplier (intermediate node or source node), whichmeans a destination node will traverse jV j þ jEj times inPN. Thus the upper bounder of MMPC is OðjDj � ðjV j þ jEjÞÞ.Therefore, the time complexity of MMPC is OðjDj � ðjV jþjEjÞÞ. h

2 4 6 8 10 12 14 16 18 201.5

1.6

1.7

1.8

1.9

2

2.1

Set division parameter δ

Nor

mal

ized

map

ping

cos

t

conventional 2-phase mapping

upper bound of δ


Fig. 13. Normalized mapping cost vs. d.

1 2 3 4 5 6 7 8 9 101.7

1.8

1.9

2

2.1

2.2

k in MDC VN request

Nor

mal

ized

map

ping

cos

t

MMPCconventional 2-phase mapping


Fig. 15. Normalized mapping cost vs. k.

1 2 3 4 5 6 7 8 9 100.6

0.7

0.8

0.9

Video service type k in MDC VN request

Nor

mal

ized

map

ping

tim

eMMPCconventional 2-phase mapping


Fig. 14. Normalized mapping time vs. k.

0 500 1000 1500 20000.5

0.6

0.7

0.8

0.9

1

Acc

epta

nce

ratio

Time

conventional 2-phase mappingMMPC

Fig. 16. Normalized acceptance ratio.


5. Performance assessment and simulation results

5.1. Experimental configuration and performance metrics

This section implements the MMPC algorithm and eval-uates its performance through extensive simulation exper-iments in terms of its acceptance ratio, mapping time andmapping cost for a range of network scenarios. The MMPCalgorithm (VN request mapping with automatic intermedi-ate nodes identification) is assessed by using the classicaltwo-phase VN mapping algorithm (VN request mappingwithout automatic intermediate nodes identification) asthe comparison benchmarks. The evaluation environmentis shown as follows:

� CPU: Intel Core i7 920.� MEMORY: Kingston DDR3 1333 2G X 3.� OS: Linux Ubuntu version 10.10.� COMPILER: gcc version 4.5.0.

5.1.1. Substrate networkThe substrate network topology in the experiments is

generated by using GT-ITM tool [19], as illustrated inFig. 11, which is organized by 300 nodes with the averagenode degree of 8, resulting 1159 physical links for the PN.

The CPU capacity of physical node and physical link band-width are generated following a uniform distribution from60 to 100.

5.1.2. Virtual network requestIn the evaluation, the virtual network mapping results

are generated with the number of multicast tree end-usersvaries from 10 to 30, and type of required video services kvaries from 1 to 10 in individual VN requests, respectively.The CPU and bandwidth requirements of virtual nodes andlinks are uniformly distributed in the range of 3 and 5.

5.1.3. Performance metricsThe performance of MMPC algorithm is assessed with

three metrics: (1) mapping cost, which is defined previ-ously in Eq. (6), assuming that only CPU capacity and band-width are considered and both CPU capacity andbandwidth are equally weighted ða1 ¼ a2 ¼ 0:5Þ; (2)acceptance ratio, which is defined as

ACRatio ¼ accepted VN requestsentire VN requests

ð8Þ

and (3) mapping time in terms of computation time, mea-sured in milliseconds (ms).

5.2. Simulation result

5.2.1. Mapping performance vs. d and kFigs. 12 and 13 present the normalized result (mapping

time and mapping cost with %95 confidence interval) ofMMPC with automatic intermediate nodes (INs)identification against the conventional 2-phase VN mappingalgorithm with intermediate nodes preprocessing, respec-tively. The VN requests used in these two experiments arewith the same scale and delivered service type k, but differ-ent set-division parameter d. The time consumed by MMPCrises rapidly along with the increase of d which is propor-tional to the number of physical paths needed to be con-verged by the path-convergence function and suchconvergence contributes the majority of the time cost. Themapping cost of MMPC decreases due to the fact that thenumber of intermediate nodes that are potentially to beused is inversely proportional to the value of d. As a result,

0 500 1000 1500 20000.6

0.65

0.7

0.75

0.8

0.85

0.9

Time

Nor

mal

ized

ave

rage

map

ping

tim

e


Fig. 17. Normalized average mapping time.


it leads to the declination of the total length of all mappedphysical paths, and hence the mapping cost. Comparativelyspeaking, the time consumption and mapping cost of theconventional 2-phase VN mapping algorithm is less signifi-cant along with the increase of d. Figs. 14 and 15 present an-other set of normalized result where the used VN requestsare with the same scale and the set-division parameter d,but different delivered service type k. We can find the ser-vice type k has less effect on both MMPC and conventionalVN mapping algorithm compared with the parameter d, be-cause the increase of k contributes a small number of inter-mediate nodes with fixed d, and the time consumption andmapping cost of identifying intermediate nodes are gener-ally small. It can be concluded that the parameter d is thedominate factor of mapping time and cost. It is should benoted that the value of d needs to be appropriately selectedto achieve the best combination benefits in terms of bothmapping time and cost.

5.2.2. Mapping performance in dynamic scenariosThe following simulation experiments are carried out to

evaluate the mapping algorithm performance in terms ofacceptance ratio, average mapping time and mapping costfor the network scenarios with the dynamic VN request ar-rival pattern. It is assumed that the arrivals of multicast VN

0 500 1000 1500 20001.6

1.7

1.8

1.9

2

2.1

2.2

Time

Nor

mal

ized

ave

rage

map

ping

cos

t


Fig. 18. Normalized average mapping cost.

requests follows the Poisson distribution with the meaninter-arrival time of 10 time units, and the life time ofVNs follows exponential distribution with the mean timeof 100 time units. All simulations are carried out for 2000time units with random-scaled VN requests to obtain stea-dy state performance measurements. Fig. 16 presents theacceptance ratio result of MMPC in comparison withthe conventional two-phase mapping approach against thesimulation time. The result shows that the acceptance ratioof MMPC is slightly lower than that of the two-phase algo-rithm (< %10) mainly due to the fact that the mappingperformance will be degraded if no appropriate intermedi-ate nodes or source node can be found by path conver-gence. While the two-phase algorithm enables locationadjustment for the intermediate nodes generated by pre-processing in PN until a feasible VN mapping is identified.Figs. 17 and 18 illustrate the average mapping time andaverage mapping cost for the MMPC algorithm and two-phase mapping against the simulation time. It is can beseen that MMPC has the better performance on averagemapping time and mapping cost than the two-phase algo-rithm. This because the MMPC algorithm can automaticallyidentify the intermediate nodes upon the receipt of VN re-quests to carry out the VN mapping, and hence the time toidentify the intermediate nodes can be minimized (seeFig. 9). Also, the intermediate node identification processis locally optimized, which significantly reduces theobtained VN mapping cost (see Theorem 1).

5.2.3. Case studiesFinally, we further assess the MMPC algorithm and val-

idate the previous results by using a realistic campus net-work [20], which consists of 18 distribution switches and28 departments (with 10–30 end-users), illustrated inFig. 19. We consider that end-users in different depart-ments demand different video services and adopt the sameparameters of multicast VN requests in terms of scale, ar-rival pattern and life time as used in the previous experi-ments. Figs. 20–22 give the MMPC performance results interms of acceptance ratio, average mapping time and

Fig. 19. A university campus network topology.

0 500 1000 1500 20000.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1A

ccep

tanc

e ra

tio

Time


Fig. 20. Normalized acceptance ratio.

0 500 1000 1500 20000.45

0.5

0.55

0.6

0.65

0.7

0.75

Time

Nor

mal

ized

ave

rage

map

ping

tim

e


Fig. 21. Normalized average mapping time.

0 500 1000 1500 20001.2

1.3

1.4

1.5

1.6

1.7

1.8

Time

Nor

mal

ized

ave

rage

map

ping

cos

t

2-phase conventional mappingMMPC

Fig. 22. Normalized average mapping cost.


average mapping cost against the conventional two-phasemapping algorithm. It can be seen that similar results aredemonstrated which confirms our previous conclusionsobtained from experiments with the random networktopology.

6. Conclusion and future work

In this paper, we presented a novel VN mapping algo-rithm, MMPC with automatic intermediate node identifica-tion, for addressing multicast virtual network mappingproblem to enable the delivery of MDC based video services.The suggested algorithmic solution solves the mappingproblem through the adoption of a path convergence ap-proach with the primary aim of minimizing the mappingcost and improving the mapping efficiency. The perfor-mance of MMPC algorithm is assessed through extensivesimulation experiments for a range of network scenariosin comparison with some existing algorithms and the out-come demonstrates its effectiveness and efficiency in termsof acceptance ratio, average mapping cost and mappingtime.

The future work can be taken following two directions:we are interested in further accessing the performance ofthe proposed MMPC algorithm in the NetFPGA-based testbed to obtain more insights. In addition, we further explorethe potentials of improving the algorithm design, e.g. mak-ing the identified intermediate nodes to take further roles(e.g. load balance) during the VN mapping and exploringthe advanced mechanisms of Video on Demand (VOD)from which our work can benefit. More insights and resultswill be reported in our future publications.

Acknowledgement

This work is supported by the National Basic ResearchProgram of China (973Program) under the Grant No.2012CB315900, the National High-tech Program of China(863 Program) under the Grant No. 2011AA01A107, theNational Natural Science Foundation of China (Nos.61070157, 61070213 and 51107113), and the ZhejiangProvincial Natural Science Foundation of China underGrant (No. Y1111192).

References

[1] CISCO Visual Networking Index: Forecast and Methdology, 2009–2014, 2010. <http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/whitepaperc11-481360ns827NetworkingSolutionsWhitePaper.html>

[2] J. Apostolopoulos, T. Wong, Wai-Tian Tan, Susie Wee, On multipledescription streaming with content delivery networks, in: Proc. ofIEEE INFOCOMM02, New York, USA, 2002, pp. 23–27.

[3] W. Szeto, Y. Iraqi, R. Boutaba, A multi-commodity flow basedapproach to virtual network resource allocation, in: Proc. of IEEEGlobal Telecommunications Conference (GLOBECOM’03), SanFrancisco, CA (USA), 2003, pp. 3004–3008.

[4] J. Fan, M. Ammar, Dynamic topology configuration in service overlaynetworks – a study of reconfiguration policies, in: Proc. of IEEEINFOCOMM06, Barcelona, Spain, 2006, pp. 1–12.

[5] Y. Zhu, M. Ammar, Algorithms for assigning substrate networkresources to virtual network components, in: Proc. of IEEEINFOCOMM06, Barcelona, Spain, 2006, pp. 1–12.

[6] M. Yu, Y. Yi, J. Rexford, M. Chiang, Rethinking virtual networkembedding: substrate support for path splitting and migration,SIGCOMM Comput. Commun. Rev. 38 (2) (2008) 17–29.

[7] N. Chowdhury, M.R. Rahman, R. Boutaba, Virtual networkembedding with coordinated node and link mapping, in: Proc. ofIEEE INFOCOMM09, Rio de Janeiro, Brazil, 2009, pp. 783–791.

[8] Jens Lischka, Holger Karl, A virtual network mapping algorithmbased on subgraph isomorphism detection, in: Proc. of ACMSIGCOMM09, Barcelona, Spain, 2009.

http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/whitepaperc11-481360ns827NetworkingSolutionsWhitePaper.html




[9] I. Houidi, W. Louati, D. Zeghlache, A distributed virtual networkmapping algorithm, in: Proc. of IEEE ICC2008, 2008, pp. 5634–5640.

[10] M. Chowdhury, F. Samuel, R. Boutaba, PolyViNE: policy-based virtualnetwork embedding across multiple domains, in: Proc. of the secondACM SIGCOMM workshop on Virtualized infrastructure systems andarchitectures, 2010, pp. 49–56.

[11] B. Lv, Z. Wang, et al., A hierarchical management architecture forvirtual network mapping, in: Proc. of Internet Technology andApplications, 2010.

[12] F. Ilhem, A.S. Nadjib, et al., VNE-AC: virtual network embedding Al-gorithm based on ant colony metaheuristic, in: Proc. of IEEE ICC,Kyoto, 2011.

[13] D. Pompili, L. Lopez, C. Scoglio, Multicast algorithms in serviceoverlay networks, in: Proc. IEEE INFOCOMM06, Barcelona, Spain,2006, pp. 1–3.

[14] L. Lao, J.H. Cui, M. Gerla, Multicast service overlay design, in: Proc.International Symp. on Performance Evaluation of Computer andTelecommunication Systems (SPECTS’05), Philadelphia PA, USA,2005.

[15] G.N. Rouskas, I. Baldine, Multicast routing with end-to-end delayand delay variations constraints, IEEE J. Sel. Areas Commun. 15 (3)(1997) 346–356.

[16] S. Kapoor, S. Raghavan, Improved multicast routing with delay anddelay variation constraint, in: Proc. of Global Telecomm. Conf.(GLOBECOM00), San Francisco, USA, 2000, pp. 476–480.

[17] S.M. Banik, S. Radhakrishnan, C.N. Sekharan, Multicast routing withdelay and delay variation constraints for collaborative applicationson overlay networks, IEEE Trans. Parallele Distrib. Syst. 18 (3) (2007)421–431.

[18] T.H. Cormen, et al., Introduction to algorithms second edition, ISBN:0-262-03293-7, 2001, pp. 222-230.

[19] E.W. Zegura, K.L. Calvert, S. Bhattacharjee, How to model aninternetwork, in: Proc. of IEEE INFOCOMM, 1996.

[20] R.G. Ingalls, M.D. Rossetti, et al., Evaluation of secure peer-to-peeroverlay routing for survivable SCADA system, in: Proc. of the 2004Winter Simulation Conference, Urbana, USA, 2004.

Yuting Miao is currently pursuing his Ph.D. atCollege of Computer Science, Zhejiang Uni-versity, PRC. His research area is P2P networksand network virtualization.

Qiang Yang (IET, IEEE member) received hisM.S. and Ph.D. degrees both in Telecommuni-cation from University of London UK in 2003and 2007, respectively. Afterwards, he workedas a postdoctoral research fellow at the Elec-trical and Electronic Engineering Dept., Impe-rial College London UK. Dr. Yang is now anAssistant Prof. of the College of ElectricalEngineering, Zhejiang University, PRC. Hisresearch interests are in the areas of computernetworks and distributed computing, complexnetwork modeling, control and optimization.

Chunming Wu, received his Ph.D. in Com-puter Science from Zhejiang University in1995, and currently is a full Professor of Col-lege of Computer Science at Zhejiang Univer-sity. His research fields include Internet QoSprovisioning, reconfigurable network tech-nology, virtualization network and artificialintelligence.

Ming Jiang received his Ph.D. in ComputerScience from Zhejiang University in 2004, andcurrently is an Associate Professor of Collegeof Computer Science at Hangzhou dianziUniversity. His research interests are inInternet QoS provisioning, the differentiatedservices network, and Internet congestioncontrol.

Jinzhou Chen is currently in completion of hisM.S. in Computer Science from Zhejiang Uni-versity, PRC. His work has covered Next gen-eration networking and its testbedimplementation.

Documents

Multicast virtual network mapping for supporting multiple description coding-based video applications