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Combined Virtual Mobile Core Network Function Placementand Topology Optimization with Latency bounds
Andreas BaumgartnerVarun Reddy
Thomas Bauschert
Chair of Communication NetworksTechnische Universitat Chemnitz
October 2, 2015
Overview
1 Introduction
2 Problem Formulation
3 Performance Evaluation
4 Summary
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Overview
1 Introduction
2 Problem Formulation
3 Performance Evaluation
4 Summary
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Introduction
Placement decisions for virtualized network functions in a fullyvirtualized mobile core network scenario:
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Introduction
Mathematical optimization model:
� Find optimum topology for virtual mobile core network topology
� Find optimum embedding for virtual mobile core network
� Assure roundtrip time (RRT) delay bounds for service chains
VINO Project (BMBF funded)
Virtual Network Optimization
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Overview
1 Introduction
2 Problem Formulation
3 Performance Evaluation
4 Summary
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Problem Formulation
Problem StatementFind an optimum embedding with respect to embedding costs of thevirtual mobile core network on a physical substrate network
GoalMinimization of the overall link embedding costs and the costs forVNF placement on physical substrate nodes
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Problem Formulation
Approach
Virtual core network topology not given, but subject to optimization
� Do not focus on the embedding of a fixed topology but on theembedding of multiple service chains where each service chaincomprises a single RAN traffic aggregation point (TAP) as trafficend point
� Mixed Integer Linear Programming Formulation
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Problem Formulation
Considered LTE network functions and service chains
E-UTRAN EPC
S11
S1-MME
S1-U
S6
S5 SGi
MME
SGW PGW
HSS
IXP
TrafficAggregationPoint (TAP)
Control Plane Service Chain
User Plane Service Chain
S1-MME
S1-U
S5 SGi
Virtual SGW Virtual PGW Internet Exchange Point (IXP)
Virtual MME
S6
S11
Virtual HSS
������������������������������������
Virtual SGW
TrafficAggregationPoint (TAP)
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Problem Formulation
Consider Delay caused by:
� Propagation: Depending on link length→ linear
� Packet Forwarding/Queueing: Depending on node’s traffic utilization→ Non-Linear, typically convex curve
� Processing: Depending on CPU utilization→ Non-Linear, typically convex curve
M/M/1 model assumed for convex delay
curve
0 10 20 30 40 50 60 70 80 90
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
Node Utilisation (%)
Late
ncy
(ms)
M/M/1 Delayi=1i=2i=3i=4
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Problem Formulation
Given input data
� Physical (substrate) network: Directed graph (Ns , Ls)
� Capacity c(ns1,ns2) of every physical link (ns1, ns2) ∈ Ls
� Set of traffic aggregation points T ⊆ Ns
� Processing/Storage/Switching capacity of every node ns ∈ Ns , cmns
(m ∈ {pro,stor,bdw})� Link costs per occupied bandwidth unit: cost(nsi , nsj ) for (nsi , nsj ) ∈ Ls
� Basic node costs cost(ns) for ns ∈ Ns
� Cost per occupied pro, sto, bdw unit at node ns :
cost(x , ns), ∀x ∈ {pro,stor,bdw}
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Problem Formulation
Assumptions I
� Consider one virtual mobile core network for the embedding
� Single path routing
� Every node t ∈ T is a traffic aggregation point for RAN traffic with demand
dVNF,mt (VNF ∈ {SGW, PGW, IXP, MME, HSS},m ∈ {pro,stor,bdw}, t ∈ T )
� Only certain nodes are capable of hosting certain virtual network functionsVNF ∈ {SGW, PGW, IXP, MME, HSS}
suitVNFns =
{1 if VNF can be embedded on ns ,
0 else.
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Problem Formulation
Assumptions II
� Convex delay curves
� αi , βi , γi , δi Linearization parameters for the convex delay curve� zpro, max
ns , zbdw, maxns Big constants
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Problem Formulation
Variables I
� x t,VNFns ∀ns ∈ Ns ,VNF ∈ {SGW, PGW, IXP, MME, HSS}, t ∈ TBinary variable: True, if a virtual network function of type VNF isembedded on node ns for the traffic aggregation point t ∈ T
� ft,(VNF1,VNF2)(ns1,ns2)
∀t ∈ T , (ns1, ns2) ∈ Ls , (VNF1,VNF2) ∈{(TAB,SGW), (SGW,PGW), . . . }Binary variable: True, if the virtual link between (VNF1,VNF2) isembedded on the physical link (ns1, ns2) for the demand of trafficaggregation point t ∈ T
� z(ns1, ns2) Delay on the physical link from ns1 to ns2
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Problem Formulation
Variables II
� z t,VNF,prons Delay caused by the processing of VNF for TAP t ∈ Ton the physical node ns
� z t,bdwns Delay caused by packet queueing for TAP t on thephysical node ns
� uprons , ubdwns Auxiliary variables for the utilization of the
processing/forwarding resources at the physical node ns
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Problem Formulation
Objective FunctionMinimize:
a ·∑ns∈Ns
xns · cost(ns) + b ·∑ns∈Ns
∑t∈T
∑VNF∈Nv
∑x∈{pro,stor,bdw}
x t,VNFns · dVNF,x
t · cost(x , ns)
+ c ·∑
(ns1,ns2)∈Ls
cost(ns1, ns2) ·∑t∈T
∑(VNF1,VNF2)∈Lv
ft,(VNF1,VNF2)(ns1,ns2)
· d (VNF1,VNF2)t
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Problem Formulation
Constraints I
∑ns∈Ns
x t,VNFns · suitVNFns = 1 ∀t ∈ T ,VNF ∈ Nv
x t,VNFns ≤ suitVNFns ∀t ∈ T , ns ∈ Ns ,VNF ∈ Nv
∑(w ,ns )∈Ls
∑t∈T
∑(VNF1,VNF2)∈Lv
ft,(VNF1,VNF2)(w ,ns )
· d (VNF1,VNF2)t ≤ cbdwns∑
t∈T
∑VNF∈Nv
x t,VNFns · dVNF,prot ≤ cprons∑
t∈T
∑VNF∈Nv
x t,VNFns · dVNF,stort ≤ cstorns ∀ns ∈ Ns
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Problem Formulation
Constraints II
∑t∈T
∑(VNF1,VNF2)∈Lv
ft,(VNF1,VNF2)(ns1,ns2)
· d (VNF1,VNF2)t ≤ c(ns1, ns2) ∀(ns1, ns2) ∈ Ls
∑(ns1,w)∈Ls
ft,(VNF1,VNF2)(w ,ns1)
− ft,(VNF1,VNF2)(ns1,w) = x t,VNF1ns1 − x t,VNF2ns1
∀t ∈ T , ns1 ∈ Ns , (VNF1,VNF2) ∈ Lv
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Problem Formulation
Constraints III
αi + βi · uprons ≤ z t,VNF,prons + (1− x t,VNFns ) · zpro,maxns
z t,VNF,prons ≤ zpro,maxns · x t,VNFns ∀ns ∈ Ns ,VNF, t ∈ T , i ∈ I
γi + δi · ubdwns ≤ z t,bdwns + (1− f tns ) · zbdw,maxns
z t,bdwns ≤ zbdw,maxns · f tns ∀ns ∈ Ns , t ∈ T , i ∈ I
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Problem Formulation
Constraints IV
∑ns∈Ns
∑VNF∈Nv
z t,VNF,prons +∑
(ns1,ns2)∈Ls
∑lv∈Lv
f t,lv(ns1,ns2)· z(ns1, ns2) +
∑ns∈Ns
z t,bdwns ≤ duser
∀t ∈ T ,∀Nv , Lv
∑ns∈Ns
∑VNF∈Nv
z t,VNF,prons +∑
(ns1,ns2)∈Ls
∑lv∈Lv
f t,lv(ns1,ns2)· z(ns1, ns2) +
∑ns∈Ns
z t,bdwns ≤ dcontrol
∀t ∈ T ,∀Nv , Lv
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Problem Formulation
Constraints V
x t,VNFns , xns , ft,(VNF1,VNF2)(ns1,ns2)
, f tns , xns ∈ {0, 1}
z t,VNF,prons , z t,bdwns ∈ R+ ∀t ∈ T ,VNF ∈ Nv , ns ∈ Ns , (VNF1,VNF2) ∈ Lv , (ns1, ns2) ∈ Ls
Nv = {TAP,SGW,MME,HSS,PGW,IXP}Lv = {(TAP,SGW), (SGW,TAP), (TAP,MME), (MME,TAP), (SGW,PGW), (PGW,SGW),
(SGW,MME), (MME,SGW), (PGW,IXP), (IXP,PGW), (MME,HSS), (HSS,MME)}
Nv = {TAP,SGW,PGW,IXP}
Lv = {(TAP,SGW), (SGW,TAP), (SGW,PGW), (PGW,SGW), (PGW,IXP), (IXP,PGW)}
Nv = {TAP,MME}, {MME,HSS}, {MME,SGW}
Lv = {(TAP,MME), (MME,TAP)}, {(MME,HSS), (HSS,MME)}, {(MME,SGW), (SGW,MME)}
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Overview
1 Introduction
2 Problem Formulation
3 Performance Evaluation
4 Summary
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Performance Evaluation
Performance Evaluation using network topology examples fromSNDlib
Considered Scenarios
� I: Given IXP nodes and givennodes for VNF placement
� II: Given IXP nodes, every nodecan host any type of VNF
� III: Every node can be IXP nodeand host any type of VNF
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Performance Evaluation
Example: Nobel-EU network (28 nodes, 41 links)
� Node costs with respect of the GDP of the specific country
� Each node is assumed to be a traffic aggregation point (TAP)
� Traffic demand scales with number of Internet users in the specificcountry
� Different utilization scenarios realized by a global demand scaling factor k
� Signal propagation speed 0.67 · clight (fiber connections)
� Linearized M/M/1 delay curve for processing and switching (Centralbuffer model)
� Use of Python/CPLEX 12.5 on Intel i7-3930K CPU, 64Gbyte RAM
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Performance Evaluation
VNF placement and TAP allocation example
P HMS
P HMS
PS
P HMS
P HMS
P HMS
P HMS
X
XAmsterdam
Frankfurt
Zagreb
Brussels
Budapest
Dublin
Copenhagen
Zurich
k = 3, dcontrol = duser = 25 ms
PS
XX
P HMS
P HMS
P HMS
P HMS
Copenhagen
Amsterdam
Brussels
London
Dublin
Zagreb
k = 3, dcontrol = duser = 50 ms
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Performance Evaluation
Scenario I
0.5 1 1.5 2 2.50
10
20
30
40
50
Demand scaling factor k
Op
tim
alit
yG
ap(%
)
Fixed IXP and VNF placement locations
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
0.5 1 1.5 2 2.50
2000
4000
6000
Demand scaling factor k
Com
pu
tati
onT
ime
(s)
Fixed IXP and VNF placement locations
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
Optimality gaps and solution times for different demand scaling factors anddelay bounds, Scenario I.
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Performance Evaluation
Scenario II
1 2 3 4 50
10
20
30
40
50
Demand scaling factor k
Op
tim
alit
yG
ap(%
)
Fixed IXP locations
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
1 2 3 4 50
2000
4000
6000
Demand scaling factor k
Com
pu
tati
onT
ime
(s)
Fixed IXP locations
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
Optimality gaps and solution times for different demand scaling factors anddelay bounds, Scenario II.
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Performance Evaluation
Scenario III
1 2 3 4 50
10
20
30
40
50
Demand scaling factor k
Op
tim
alit
yG
ap(%
)
No restrictions for IXP/VNF placement
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
1 2 3 4 50
2000
4000
6000
Demand scaling factor k
Com
pu
tati
onT
ime
(s)
No restrictions for IXP/VNF placement
d = 25ms
d = 30ms
d = 40ms
d = 50ms
d = 60ms
Optimality gaps and solution times for different demand scaling factors anddelay bounds, Scenario III.
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Overview
1 Introduction
2 Problem Formulation
3 Performance Evaluation
4 Summary
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Summary
MILP formulation for virtual mobile core network embedding
� Finding optimum virtual network topology together with it’s embeddingon a given physical substrate network
� Delay bounds are considered for each specific service chain and subchain
� Solvable in reasonable time with standard CPLEX settings for moderatenetwork sizes
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Summary
Ongoing work
� Consider robustness of VNF placement with respect to trafficvariation (robust optimization)
� Consider robustness of VNF placement with respect to substratenetwork failures (reliability)
� Develop mathematical model for service chain embedding withindata centers
� Consider control and user plane separation (SDN controllerplacement)
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