Combined Virtual Mobile Core Network Function Placement and Topology Optimization with Latency bounds

Transcription

1 Combined Virtual Mobile Core Network Function Placement and Topology Optimization with Latency bounds Andreas Baumgartner Varun Reddy Thomas Bauschert Chair of Communication Networks Technische Universita t Chemnitz October 2, 2015

2 Overview 1 Introduction 2 Problem Formulation 3 Performance Evaluation 4 Summary 2 of 31

3 Overview 1 Introduction 2 Problem Formulation 3 Performance Evaluation 4 Summary 3 of 31

4 Introduction Placement decisions for virtualized network functions in a fully virtualized mobile core network scenario: 4 of 31

5 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 5 of 31

6 Overview 1 Introduction 2 Problem Formulation 3 Performance Evaluation 4 Summary 6 of 31

7 Problem Formulation Problem Statement Find an optimum embedding with respect to embedding costs of the virtual mobile core network on a physical substrate network Goal Minimization of the overall link embedding costs and the costs for VNF placement on physical substrate nodes 7 of 31

8 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 the embedding of multiple service chains where each service chain comprises a single RAN traffic aggregation point (TAP) as traffic end point Mixed Integer Linear Programming Formulation 8 of 31

9 Problem Formulation Considered LTE network functions and service chains S6 HSS S1-MME Virtual MME S11 S Virtual HSS S1-MME Virtual SGW Control Plane Service Chain Traffic Aggregation Point (TAP) S1-U MME S11 S5 SGi IXP Traffic Aggregation Point (TAP) S1-U S5 SGi E-UTRAN SGW PGW EPC Virtual SGW Virtual PGW Internet Exchange Point (IXP) User Plane Service Chain 9 of 31

10 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 10 of 31 Latency (ms) 170 M/M/1 Delay 160 i=1 150 i=2 140 i=3 130 i= Node Utilisation (%)

11 Problem Formulation Given input data Physical (substrate) network: Directed graph (N s, L s) Capacity c (ns1,2 ) of every physical link (1, 2) L s Set of traffic aggregation points T N s Processing/Storage/Switching capacity of every node N s, c m (m {pro,stor,bdw}) Link costs per occupied bandwidth unit: cost(i, j ) for (i, j ) L s Basic node costs cost() for N s Cost per occupied pro, sto, bdw unit at node : cost(x, ), x {pro,stor,bdw} 11 of 31

12 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 d VNF,m t (VNF {SGW, PGW, IXP, MME, HSS}, m {pro,stor,bdw}, t T ) Only certain nodes are capable of hosting certain virtual network functions VNF {SGW, PGW, IXP, MME, HSS} { suit VNF 1 if VNF can be embedded on, = 0 else. 12 of 31

13 Problem Formulation Assumptions II Convex delay curves α i, β i, γ i, δ i Linearization parameters for the convex delay curve pro, max bdw, max z, z Big constants 13 of 31

14 Problem Formulation Variables I N s, VNF {SGW, PGW, IXP, MME, HSS}, t T Binary variable: True, if a virtual network function of type VNF is embedded on node for the traffic aggregation point t T f t,(vnf 1,VNF 2 ) (1,2 ) t T, (1, 2 ) L s, (VNF 1, VNF 2 ) {(TAB,SGW), (SGW,PGW),... } Binary variable: True, if the virtual link between (VNF 1, VNF 2 ) is embedded on the physical link (1, 2 ) for the demand of traffic aggregation point t T x t,vnf z(1, 2 ) Delay on the physical link from 1 to 2 14 of 31

15 Problem Formulation Variables II Delay caused by the processing of VNF for TAP t T on the physical node zn t,bdw s Delay caused by packet queueing for TAP t on the physical node un pro s, un bdw s Auxiliary variables for the utilization of the processing/forwarding resources at the physical node z t,vnf,pro 15 of 31

16 Problem Formulation Objective Function Minimize: a x ns cost() + b N s N s t T + c cost(1, 2) (1,2 ) L s t T VNF N v x {pro,stor,bdw} x t,vnf d VNF,x t cost(x, ) f t,(vnf1,vnf2) (1,2 ) d (VNF1,VNF2) t (VNF1,VNF2) L v 16 of 31

17 Problem Formulation Constraints I xn t,vnf s N s x t,vnf suit VNF suit VNF = 1 t T, VNF N v t T, N s, VNF N v (w, ) L s t T t T t T xn t,vnf s VNF N v xn t,vnf s VNF N v f t,(vnf1,vnf2) (w, ) (VNF1,VNF2) L v d VNF,pro t d VNF,stor t c pro c stor d (VNF1,VNF2) t c bdw N s 17 of 31

18 Problem Formulation Constraints II f t,(vnf1,vnf2) (1,2) d (VNF1,VNF2) t c(1, 2 ) (1, 2 ) L s t T (VNF1,VNF2) L v f t,(vnf1,vnf2) (w,1) (1,w) L s f t,(vnf1,vnf2) (1,w) = xn t,vnf1 s1 xn t,vnf2 s1 t T, 1 N s, (VNF1,VNF2) L v 18 of 31

19 Problem Formulation Constraints III α i + β i u pro z t,vnf,pro z t,vnf,pro z pro,max x t,vnf + (1 xn t,vnf s ) zn pro,max s N s, VNF, t T, i I γ i + δ i u bdw z t,bdw z bdw,max z t,bdw ˆf t + (1 ˆf t ) z bdw,max N s, t T, i I 19 of 31

20 Problem Formulation Constraints IV z t,vnf,pro N s VNF Ñ v z t,vnf,pro N s VNF ˆN v + (1,2 ) L s + (1,2 ) L s f t,lv (1,2 ) l v L v f t,lv (1,2 ) l v ˆL v z(ns1, ns2) + z(ns1, ns2) + zn t,bdw s N s zn t,bdw s N s d user t T, Ñv, L v d control t T, ˆN v, ˆL v 20 of 31

21 Problem Formulation Constraints V x t,vnf, x ns, f t,(vnf 1,VNF 2 ) (1,2 ), ˆf t, x ns {0, 1} zn t,vnf,pro s, zn t,bdw s R + t T, VNF N v, N s, (VNF 1, VNF 2 ) L v, (1, 2 ) L s N v = {TAP,SGW,MME,HSS,PGW,IXP} L v = {(TAP,SGW), (SGW,TAP), (TAP,MME), (MME,TAP), (SGW,PGW), (PGW,SGW), (SGW,MME), (MME,SGW), (PGW,IXP), (IXP,PGW), (MME,HSS), (HSS,MME)} Ñ v = {TAP,SGW,PGW,IXP} L v = {(TAP,SGW), (SGW,TAP), (SGW,PGW), (PGW,SGW), (PGW,IXP), (IXP,PGW)} ˆN v = {TAP,MME}, {MME,HSS}, {MME,SGW} ˆL v = {(TAP,MME), (MME,TAP)}, {(MME,HSS), (HSS,MME)}, {(MME,SGW), (SGW,MME)} 21 of 31

22 Overview 1 Introduction 2 Problem Formulation 3 Performance Evaluation 4 Summary 22 of 31

23 Performance Evaluation Performance Evaluation using network topology examples from SNDlib Considered Scenarios I: Given IXP nodes and given nodes for VNF placement II: Given IXP nodes, every node can host any type of VNF III: Every node can be IXP node and host any type of VNF 23 of 31

24 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 specific country Different utilizatiocenarios realized by a global demand scaling factor k Signal propagatiopeed 0.67 clight (fiber connections) Linearized M/M/1 delay curve for processing and switching (Central buffer model) Use of Python/CPLEX 12.5 on Intel i7-3930k CPU, 64Gbyte RAM 24 of 31

25 Performance Evaluation VNF placement and TAP allocation example S P M H S P M H Copenhagen Copenhagen Dublin S P M H Dublin S P S P M H S P M H X Brussels Zurich S P M H X Amsterdam X London Frankfurt Brussels S P M H Zagreb Budapest S P M H k = 3, dcontrol = duser = 25 ms 25 of 31 S P S P M H X Amsterdam Zagreb S P M H k = 3, dcontrol = duser = 50 ms

26 Performance Evaluation Scenario I Fixed IXP and VNF placement locations Fixed IXP and VNF placement locations 50 d = 25ms d = 25ms d = 30ms d = 30ms Optimality Gap (%) d = 40ms d = 50ms d = 60ms Computation Time (s) d = 40ms d = 50ms d = 60ms Demand scaling factor k Demand scaling factor k Optimality gaps and solution times for different demand scaling factors and delay bounds, Scenario I. 26 of 31

27 Performance Evaluation Scenario II Fixed IXP locations Fixed IXP locations 50 d = 25ms d = 25ms d = 30ms d = 30ms Optimality Gap (%) d = 40ms d = 50ms d = 60ms Computation Time (s) d = 40ms d = 50ms d = 60ms Demand scaling factor k Demand scaling factor k Optimality gaps and solution times for different demand scaling factors and delay bounds, Scenario II. 27 of 31

28 Performance Evaluation Scenario III No restrictions for IXP/VNF placement No restrictions for IXP/VNF placement 50 d = 25ms d = 25ms d = 30ms d = 30ms Optimality Gap (%) d = 40ms d = 50ms d = 60ms Computation Time (s) d = 40ms d = 50ms d = 60ms Demand scaling factor k Demand scaling factor k Optimality gaps and solution times for different demand scaling factors and delay bounds, Scenario III. 28 of 31

29 Overview 1 Introduction 2 Problem Formulation 3 Performance Evaluation 4 Summary 29 of 31

30 Summary MILP formulation for virtual mobile core network embedding Finding optimum virtual network topology together with it s embedding on 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 moderate network sizes 30 of 31

31 Summary Ongoing work Consider robustness of VNF placement with respect to traffic variation (robust optimization) Consider robustness of VNF placement with respect to substrate network failures (reliability) Develop mathematical model for service chain embedding within data centers Consider control and user plane separation (SDN controller placement) 31 of 31