Is Multipath Routing Really a Panacea?

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  • Is Multipath Routing Really a Panacea?

    Deep Medhi

    Computer Science & Electrical Engineering DepartmentUniversity of Missouri-Kansas City, USA

    dmedhi@umkc.eduin association with Xuan Liu, Sudhir Mohanraj, and Micha Pioro

    Supported in part by NSF Grant # CNS-0916505

    CNSM Keynote: 11 November 2015

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  • Keynote dedicatedin memory ofKaren Medhi

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  • Manhattan, NY

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  • Going between Two points in Manhattan, NY

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  • Going between Two points in Manhattan, NY: one path

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  • Going between Two points in Manhattan: two paths

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  • Going between Two points in Manhattan: three paths

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  • Going between Several points in Manhattan, NY

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  • Going between *ANY* two points in Manhattan, NY

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  • Question:

    At instant of time, is multipath routing beneficial?

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  • What Multipath Routing is NOT

    Take one path in the morning, another path in the evening thisis NOT multipath routing

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  • Multipath Routing: A Common Belief

    Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

    An alternative considered in this context is single-pathrouting (non-split routing of the demands). Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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  • Multipath Routing: A Common Belief

    Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

    An alternative considered in this context is single-pathrouting (non-split routing of the demands). Many ISPs prefer (for troubleshooting)

    Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

    MPR-SPR

  • Multipath Routing: A Common Belief

    Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

    An alternative considered in this context is single-pathrouting (non-split routing of the demands). Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.

    Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

    MPR-SPR

  • Multipath Routing: A Common Belief

    Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

    An alternative considered in this context is single-pathrouting (non-split routing of the demands). Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?

    Taking a Traffic Engineering Perspective...

    MPR-SPR

  • Multipath Routing: A Common Belief

    Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

    An alternative considered in this context is single-pathrouting (non-split routing of the demands). Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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  • A 3-node Example: Single Demand (Commodity)

    1

    3

    2

    10

    10

    10Capacity

    15

    Traffic Volumebetween 1 and 2

    Easy to see that 15 units of traffic would need to be splitbetween the paths 1-2 and 1-3-2.

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  • 3-node example: All pairs with traffic

    1

    3

    2

    Capa

    city =

    10Capacity = 10

    Capacity = 15

    Traffic = 5

    Traffic = 7Traffic

    = 10

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  • Min Cost Routing: (i) Illustration for 3-node network: all pair traffic

    Linear Programming Formulation:Minimize x12 + 2 x132 + x13 + 2 x123 + x23 + 2 x213

    subject to

    d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 = 0x123 >= 0x23 >= 0x213 >= 0End

    1

    3

    2

    Capa

    city =

    10

    Capacity = 10

    Capacity = 15

    Traffic = 5

    Traffic = 7Traffic

    = 10

    For each pair, the first (direct) path is cheaper than the second path.Solution: x12 = 5, x13 = 10, x23 = 7 3 positive path-flows

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  • 3-node example: All pairs with traffic

    1

    3

    2

    Capa

    city =

    10Capacity = 10

    Capacity = 15

    Traffic = 5

    Traffic = 7Traffic

    = 10

    Is it possible for each pair to use both the direct and alternatetwo-link paths with positive flows at optimality?

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  • Min Cost Routing: (ii) 3-node net (swap path cost)

    Minimize 2 x12 + x132 + 2 x13 + x123 + 2 x23 + x213subject to

    d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 = 0x123 >= 0x23 >= 0x213 >= 0End

    1

    3

    2

    Capa

    city =

    10

    Capacity = 10Capacity = 15

    Traffic = 5

    Traffic = 7Traffic

    = 10

    Note: same traffic demand and link capacity as before; the path cost in objective ischanged. Solution: x12 = 1, x132 = 4, x13 = 3.5, x123 = 6.5, x23 = 4.5, x213 = 2.56 positive path-flows

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  • Is there a connection?

    1) How does the number of positive flows at optimality relate tothe size of the problem?2) Does the objective function matter?

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  • Two Letters to Remember for the Rest of the Talk

    D : Number of demands in a Network

    L : Number of Links in a Network

    NOTE:D = N(N 1)/2 if every pair has traffic (bidirectional) in aN-node network

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  • Two Letters to Remember for the Rest of the Talk

    D : Number of demands in a Network

    L : Number of Links in a Network

    NOTE:D = N(N 1)/2 if every pair has traffic (bidirectional) in aN-node network

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  • D + L result: Min Cost Routing Multi-CommodityNetwork Flow

    minx0

    dD

    pPd

    dp xdp (1a)pPd

    xdp = hd , d D (demand) (1b)dD

    pPd

    dp`xdp c`, ` L (capacity) (1c)

    hd : traffic for demand ID d D (#(D) = D)c`: link capacity (#(L) = L)dp: unit path cost of path p for demand ddp`: link-path indicator 0/1

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  • Min Cost Routing Multi-Commodity Network Flow

    minx0

    dD

    pPd

    dp xdppPd

    xdp = hd , d D (demand)dD

    pPd

    dp`xdp c`, ` L (capacity)

    D + L property

    In vertex solutions in Linear Program, there are at most D + L positivepath-flows. (Proof skipped)

    Corollary: There are at most L demands that require more than onepositive path-flow

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  • Quick Review: Feasible Region and vertices for a linear program

    Objective

    Feasible Region

    Optimal Vertex

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  • Consider again the following illustration for the 3-nodemulti-commodity example:

    d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213

  • CorollaryIf the optimization problem (1) is feasible, then at most L trafficpairs will have more than one path with non-zero flows atoptimality.

    Proof:

    From the theorem, we know that there are D + L non-zero flowvariables. Since there are a total of D pairs, at least one pathfor each pair must carry the traffic load. This then leaves uswith at most D + L D = L pairs that has more than one pathswith non-zero flows.

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  • CorollaryIf the optimization problem (1) is feasible, then at most L trafficpairs will have more than one path with non-zero flows atoptimality.

    Proof:

    From the theorem, we know that there are D + L non-zero flowvariables. Since there are a total of D pairs, at least one pathfor each pair must carry the traffic load. This then leaves uswith at most D + L D = L pairs that has more than one pathswith non-zero flows.

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  • Traffic Engineering Objectives (besides min costrouting)

    Commonly used traffic engineering objectives for IP, MPLS,SDN networks:

    Network Load Balancing (Minimize Maximum utilization),also known as Congestion MinimizationAverage Delay (Minimize Average Network Delay)

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  • Load Balancing Optimization: LP Formulation

    min{x0,r}

    r

    subject to pPd

    xdp = hd , d DdD

    pPd

    dp` xdp c`r , ` L

    xdp 0, p = 1, 2, ...,Pd ,d = 1, 2, ...,D

    (3)

    Note: introduced a new variable r (load balancing variable)

    We again have D + L constraints.

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  • LB: load balancing

    minx0,r

    rpPd

    xdp = hd , d DdD

    pPd

    dp`xdp c`r , ` L

    xdp 0, p = 1,2, ...,Pd , d = 1,2, ...,D

    D + L 1 property

    In vertex solutions, there are at most D + L 1 positive path-flows.There are at most L 1 demands that require more than one positivepath