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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