1362 IEEE COMMUNICATIONS LETTERS, VOL. 22, NO. 7, JULY 2018

Multicast Virtual Network Services Embeddingfor Improved Disaster Recovery Support

Mahsa Pourvali, Hao Bai, Jorge Crichigno , and Nasir Ghani

Abstract— Multicast virtual network (MVN) cloud serviceshave tight restrictions in terms of coverage, delay, delay variation,and reliability. However large disasters impose key challenges,and there are no known solutions that incorporate stochasticmulti-failure risk into the MVN embedding process. Hence, thisletter presents novel proactive “risk-aware” MVN mapping algo-rithms to improve resiliency and also incorporate efficiency. Sim-ulation results show that the proposed schemes yield substantialperformance gains versus existing MVN survivability methods.

Index Terms— Multicast virtual networks, disaster recovery.

I. INTRODUCTION

CLOUD providers are using virtualization techniques tobuild flexible services over physical substrates. For

example, virtual network (VN) services provide flexible com-puting and storage topologies for clients. Multicast VN (MVN)services are also emerging for streaming and real-time appli-cation support [1]. These offerings embody more specializeddemand models (than VN) but offer more flexibility thanmulticast connections (coverage, end-point variability).

Now regular multicast connection routing (with fixed nodes)can be treated as a NP-hard Steiner tree problem (least-cost spanning tree). However MVN services require addednode-level reservation and flexible node mappings. Hencethese demands can be treated as specialized VN requests thatonly specify source/terminal nodes and delay/delay variationconstraints, i.e., no explicit VN links. Now recent studieshave addressed MVN embedding and survivability [1]- [5].Namely [2] presents optimization and heuristic schemes forsingle node failures, limiting mappings to certain sites. Singlefailure MVN node recovery is also studied in [3]. Howeverlarge disasters can cause multiple substrate node and linkfailures, posing key concerns for MVN embedding. Hencestudies have also looked at multi-failure MVN recovery,e.g., [4] uses pre-defined risk regions to compute disjointworking/protection mappings (costly, inefficient). Also [5]presents a post-fault heuristic for multi-failure MVN re-mapping. However this scheme provisions demands as mul-tiple point-to-point unicast connections (connection overlap,low efficiency).

Overall, most multi-failure MVN survivability schemesimplement backup protection and do not use multicast trees

Manuscript received January 21, 2018; revised February 19, 2018; acceptedFebruary 20, 2018. Date of publication April 3, 2018; date of current versionJuly 10, 2018. The associate editor coordinating the review of this paperand approving it for publication was V. Eramo. (Corresponding author:Nasir Ghani.)

M. Pourvali, H. Bai, and N. Ghani are with the Electrical Engineer-ing Department, University of South Florida, Tampa, FL 33620 USA(e-mail: nghani@usf.edu).

J. Crichigno is with the College of Engineering and Computing, Universityof South Carolina, Columbia, SC 29208 USA.

Digital Object Identifier 10.1109/LCOMM.2018.2822739

to improve efficiency. Hence this study proposes novel “risk-aware” heuristics to improve multi-failure MVN disasterrecovery by proactively incorporating a-priori stochastic multi-failure models of vulnerable regions [6], [7]. These solu-tions also setup logical MVN trees. Note that optimizationmethods are not considered due to space constraints. Thesemethods require more complex mixed integer linear pro-gramming (MILP) models, posing high complexity for largenetworks. Instead the focus is to build a base framework for“risk-aware” working MVN mapping. This letter is organizedas follows. Section II introduces the notation, and Section IIIdetails the MVN embedding schemes. Simulations are thenpresented in Section IV followed by conclusions in Section V.

II. NETWORK MODEL & NOTATION

The overall notation is presented first, see also Fig. 1.

A. Physical Network Model

The cloud infrastructure is given by a graph Gs = (Vs,Es),where Vs is the set of physical datacenter nodes and Es isthe set of physical links. Without loss of generality, datacenterresources are generalized to a single dimension, and hence themaximum resource capacity of node v ∈ Vs is R�

v (albeit thiscan be stratified into multi-dimension vectors). Meanwhile thebandwidth capacity of a physical link e ∈ Es is B�

e, its costis c(e), and its delay is d(e). Hence for an end-to-end pathroute P, the total delay, d(P), is the sum of all of its linkdelays. The end-to-end path cost, c(P), can also be computedlikewise.

B. Multicast Virtual Network (MVN) Demand Model

The MVN demand model consists of a source node, s,and a set of destination terminals, D = {di}, requestingdatacenter (computing, storage) resources and interconnectingbandwidth connections. It is assumed that node mappingsare geographically-constrained to improve end-point servicedistribution, as done in [2]. Namely location sets (regions)are specifed, i.e., a source can only be mapped to a subsetof physical nodes, locs ⊂ Vs, and likewise a terminal di

can only be mapped to a subset of physical nodes, locdi ⊂Vs (Fig. 1). All MVN nodes require r datacenter resources,and all MVN terminals require b bandwidth connectivity tothe source. Hence the full MVN demand tuple is given by(s, locs,D, {locdi}, δ, γ, r, b), where δ is the maximum delayand γ is the maximum delay variation.

C. Multi-Failure Outage Model

A stochastic model is used to characterize disasters withmultiple correlated spatial/temporal failures. Namely, U ={u1, u2, . . .} defines a set of a-priori risk events, ui. Here each

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POURVALI et al.: MVN SERVICES EMBEDDING FOR IMPROVED DISASTER RECOVERY SUPPORT 1363

Fig. 1. Notational overview.

event has an occurrence probability, p(ui), and an associatedrisk region containing a set of nodes/links that can potentiallybe affected. As per [6], [7], the events are assumed to berare and hence treated as independent and mutually-exclusive,i.e.,

∑∀ui∈U p(ui) = 1. Without loss of generality, disaster

regions are also assumed to be non-overlapping herein. Hencea uniform conditional failure probability, ω (v), is defined fora physical node v ∈ Vs falling in event ui region. A uniformconditional failure probability, ω (e), is also defined for aphysical link e ∈ Es falling in event ui region (note thatoverlapping regions can be handled by summing over all ui).

III. MVN EMBEDDING SCHEMES

Three polynomial-time MVN embedding heuristics are pre-sented. A base scheme is first defined to minimize resourceusage. Next, a risk-minimization strategy is defined to lowernode/link failures. However only focusing on risk can yieldless efficient MVN links [7]. Hence a hybrid strategy is alsopresented. All schemes follow a common approach, Fig. 2. Thefirst step prunes non-feasible physical nodes/links (insufficientresources). The request is then provisioned iteratively bysetting up a (virtual) MVN tree to map the MVN source andterminals and route interconnecting link connections. This treeis denoted by T = (Tv,Te), where Tv = {s,D} are the treenodes, and Te are the tree edges, Fig. 1.

All schemes initialize T to (Tv,Te = {∅}) and map theroot s to a feasible node, v ∈ locs, as per the desired objective,Fig. 2. Functions are then called to iteratively embed MVNterminals and connect them to the tree, i.e., Fig. 3 (MRU, MRFschemes) and Fig. 4 (HRR scheme). These functions scan allunmapped terminals di ∈ (D − Tv) and compute a mappingcost for all feasible embedding locations in v ∈ locdi :

costm = (ε)costnv + (1 − ε)costtv (1)

where costnv is the node mapping cost, costtv is the treeupdate cost, and ε is a weighting factor, i.e., 0 ≤ ε ≤ 1.Here costtv is the cost of the path route to connect a nodeto the current tree, T (candidate paths must meet delayconstraints). Now the node mapping and tree update costsdepend upon the particular scheme’s objective (detailed next).

Overall, the nodes v ∈ locdi with lower mapping costs areadded to T first (Figs. 3, 4). Note that cost values are set tozero for physical links in Te since re-using them does notadd to resource cost. Similarly, the risk values for all physicalnodes (links) added to Tv (Te) are also set to zero. Considerthe details.A. Minimum Resource Usage (MRU) Scheme

The MRU scheme lowers node and link capacity usageand provides a baseline. First, the MVN source is mappedto a feasible physical node with the maximum free resources,R�

v, to balance load (line 13, Fig. 2). Next, the embeddingfunction, Fig. 3, adds terminals to the MVN tree based uponresource usage. As per Eq. 1, the mapping cost, costm, hastwo components, i.e., node mapping cost, costnv , and treeupdate cost, costtv. Since this scheme focuses on resourceminimization, costnv is inversely-proportional to the availablenode resources. The latter costnv is set to the hop count ofthe (delay-constrained) shortest path, Pv , connecting nodev to T, i.e., c(Pv) (line 7, Fig. 3). To pursue resourceminimization, link costs are also set to unity, i.e., c(e) = 1.

B. Minimum Risk Failure (MRF) Scheme

The MRF scheme reduces risk by leveraging a-priori multi-failure state. Now in order to translate the failure probabilitiesinto additive metrics for shortest-path algorithms, modifiedlogarithmic node and link failure risks are computed as [8]:

ξ(v) = log1

1 − p(ui)ω(v)(2)

ξ(e) = log1

1 − p(ui)ω(e)(3)

where ui is the (non-overlapping) region containing thenode or link. Here MVN failures will depend upon the riskassociated with the MVN nodes and MVN link connections.Now the risk for a MVN node is equal to the modified logarith-mic failure risk of its mapped physical node, i.e., ξ(v), and therisk for a MVN link is equal to the modified logarithmic failurerisks of all traversed physical route nodes/links, i.e., path risk:

ξ(Pv) =∑

e∈P

ξ(e) +∑

v∈P

ξ(v) (4)

1364 IEEE COMMUNICATIONS LETTERS, VOL. 22, NO. 7, JULY 2018

Fig. 2. MVN embedding schemes (resource, risk, hybrid).

Hence the MRF scheme maps the MVN source to a feasiblelocation with the lowest failure risk (line 15, Fig. 2). Theembedding process in Fig. 3 then adds MVN terminals to Tper risk-based node costs. The mapping cost in Eq. 1 is setto the logarithmic node failure risk, i.e., costnv = ξ(v) (line 9,Fig. 3). Also, the tree update cost for node v in Eq. 1 is setto the logarithmic path failure risk of the (delay-constrained)lowest-risk path to the tree, Pv , i.e., ξ(Pv) (line 11, Fig. 3).

C. Hybrid Resource and Risk (HRR) Scheme

The HRR scheme jointly incorporates risk and resourceusage. A feasible mapping is first chosen for the MVN sourceto minimize a joint cost, i.e., logarithmic node failure riskand resource usage (line 17, Fig. 2). MVN terminals are thenembedded via the function in Fig. 4 using a joint mapping costwith two parts. Namely, cost1m pertains to resource usage:

cost1m = (ε)costn,1v + (1 − ε)costt,1v (5)

where costn,1v is inversely-proportional to node resource usage,

costt,1v is the hop count of the (delay-constrained) shortestphysical path, c(Pv), that connects node v to the tree, and εis a fractional weighting factor, 0 ≤ ε ≤ 1. Meanwhile, cost2mpertains to risk and is computed as follows:

cost2m = (ε)costn,2v + (1 − ε)costt,2v (6)

where costn,2v is equal to the logarithmic node failure risk,

costt,2v is equal to the logarithmic path failure risk of the delay-constrained lowest-risk path, ξ(Pv), connecting node v to thetree, and ε is defined above. Also, the HRR scheme differs inits MVN node mapping (lines 11-12, Fig. 4). Namely, it ranksnodes by increasing cost1m values, i.e., resource-based nodemapping and tree update costs. The top l nodes are then

Fig. 3. MRU/MRF_TREE embedding function.

Fig. 4. HRR_TREE embedding function.

searched to find the one with the lowest cost2m, i.e., risk-basednode mapping and tree update costs. The k-shortest paths arethen computed from this node to the tree, and the path withlowest risk chosen (lines 15, Fig. 4).

D. Complexity Analysis

The MRU and MRF schemes process all valid terminallocations to compute feasible paths to the tree. This oper-ation has a complexity of O(|D|3|locd|). Given a shortestpath bound of O(|Es|log (|Vs|)), these schemes are ofO(|D|3|locd||Es|log(|Vs|)). The HRR scheme also checksall MVN terminals and locations but uses the k-shortest pathalgorithm, i.e., O(k|Es||D|log(|Vs|)). This yields a highercomplexity bound of O((|D||locd| + k)|D|2|Es|log(|Vs|)).

IV. PERFORMANCE EVALUATION

The schemes are evaluated using simulation models for a24 node/86 link network with 5 risk regions, Fig. 5. Nodeshave 100 units capacity and links have 10,000 units bandwidth.All random MVN requests have 7-12 nodes, and location

POURVALI et al.: MVN SERVICES EMBEDDING FOR IMPROVED DISASTER RECOVERY SUPPORT 1365

Fig. 5. 24 node/86 link network topology with 5 a-priori risk regions.

subsets are randomized with 2 nodes (non-overlapping). MVNnodes require 1-10 units capacity, and MVN links require50-1,000 units bandwidth (uniform). Delay and delay variationbounds are set to 6 and 3 sec, respectively, and requestshave infinite duration (realistic long-standing demands). Riskregions are randomly selected, and affected nodes/links areuniformly failed. Tests are done for medium-to-heavy loadsand averaged over 10 runs. Results for the single failure REALscheme [3] are also presented as it is the most comparable,i.e., versus full MVN protection [4] or post-fault MVN re-mapping [5].

Pre-fault blocking rates are first plotted in Fig. 6. The REALscheme gives the highest blocking as it routes multiple unicastconnections. Meanwhile the MRU scheme gives the lowestblocking as it focuses on efficiency, i.e., notably lower thanMRF scheme. The hybrid HRR scheme achieves a very goodtradeoff, closely tracking the MRU scheme. Net revenue isgauged next, defined as a function of total revenue, cost, anddisruption penalties [8], i.e., revenue for MVN demand T is:

R(T) = ψ∑

e∈Te

bI(e) + (1 − ψ)∑

v∈Tv

rI(v) (7)

where I(e) and I(v) are the revenue per unit of bandwidthand node resource, respectively, and ψ is a weighting factor,0 ≤ ψ ≤ 1. Also, the cost of mapping a tree T is [8]:

C(T) = π∑

e∈Te

χTe ∗ C(e) + (1 − π)

∑

v∈Te

ΥTv ∗ C(v) (8)

where χTe is the amount of bandwidth allocated to tree link e,

ΥTv is the amount of resources allocated to tree node v, C(e)

and C(v) are the unit bandwidth and unit node resource costs,respectively, and π is a weighting factor, 0 ≤ π ≤ 1. Also,the disruption penalty for an affected MVN request is [8]:

P(T) = ∑

e∈Te

b(e) ∗ P(e) + (1 − )∑

n∈Tv

r(n) ∗ P(n) (9)

i.e., P(e) and P(n) are unit node and link penalties, and is a weighting factor, 0 ≤ ≤ 1. Hence net revenue istotal revenue adjusted by total mapping cost and disruptionpenalty averaged over time [8]. Results are plotted in Fig. 7with all node and link costs/revenues/penalties set to unityand weighting factors to 0.5, i.e., uniform weighting for allparameters (carrier settings may vary). Findings show that theMRU and REAL (MRF) schemes give the highest (lowest)revenues. The HRR scheme closely tracks the MRU scheme,i.e., within 2% at heavy loads and over 70% above MRUscheme. Finally, failure rates are plotted in Fig. 8, i.e., fraction

Fig. 6. MVN blocking rate (pre-fault).

Fig. 7. MVN revenues (post-fault).

Fig. 8. MVN failed ratio (post-fault).

of unrecoverable demands. The “risk-based” MRF schemegives the best reliability, but the REAL scheme performs theworst. Meanwhile the HRR scheme achieves a good median,reducing failures to below 50% at heavy loads. Note thatfull protection-based multi-failure MVN schemes also yieldsimilar failure rates for equivalent MVN sizes [4].

V. CONCLUSIONS & FUTURE WORK

Novel embedding schemes are proposed to improve mul-ticast VN (MVN) mapping under multiple stochastic fail-ures. Results show that joint risk and resource minimizationachieves a good tradeoff between reliability and efficiency.

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