The strength of routing Schemes. Main issues Eliminating the buzz: Are there real differences between forwarding schemes: OSPF vs. MPLS? Can we quantify.

The strength of routing Schemes

Main issues

Eliminating the buzz:

• Are there real differences between forwarding schemes: OSPF vs. MPLS?

• Can we quantify them?

Outline

• Define packet forwarding paradigms:– Vanilla IP, OSPF, MPLS, general bifurcation

• Compare their relative strength:– upper and lower bounds on performance ratio

• A centralized heuristic for vanilla IP forwarding– control is centralized anyway– achieves good performance

Packet forwarding in practice

• Vanilla IP– forward all packets destined to some addr. to a

selected shortest path

• OSPF– like above, but allow equal splitting when

multiple shortest paths exist

• MPLS– pre-select routes for flows.

Forwarding Modelling

• Network as a graph: G(V,E), |V|=n, |E|=m.

Nv – the set of neighbors of node v. ce >0 – the capacity of link e E D={di,j} – the demand matrix

• Routing assignment: R: V4 [0..1],

φu,v(i,j) is the relative amount of (i,j)-flow that is routed from a node u to a neighbor v. 1. For all u,i,jV: Σv Nu φu,v(i,j)=1

2. For all u,i,j,vV, v Nu: φu,v(i,j)=0

source invariance

• A routing assignment R is source invariant if it does not depend on the source:

φu,v(i1,j) = φu,v(i2,j) φu,v(j)

• Unrestricted Splitable Routing (US-R)• Restricted Splitable Routing (RS-R)

– Split over at most L outgoing links

– Special case: Unsplittable flow problem (RS-R1)

• Standard IP Forwarding (IP-R)– Source invariant RS-R1

• OSPF Routing (OSPF-R)– Source invariant routing assignments splitting flow

evenly among next hops.

Routing Paradigms

u,jV, vNu : φu,v(j)=1

u,j,v,v’V, if φu,v(j)>0 and φu,v’(j)>0 then φu,v(j)= φu,v’(j)

How packets are splitted?

• Option 1 (basic): packet sprinkler– each packet chooses next hop with prob. φu,v(j)

– may cause reordering hurts performance.

• Option 2 (flow-cached): hashing– each flow is hashed to next hop with prob. φu,v(j)

– may not result in splitting at desired ratios – can we afford double hashing/buckets at core?

Performance Measures

Decide on an allocation matrix– say use max-min fairness

• Min Congestion– congestion factor (CF) = link flow / link capacity– hard constraint: congestion 1, – soft constraints minimize the penalty

• Max Flow (MF)

Hardness Result

IP-R is NP even for a single destination!

Hardness Result

• node i has demand ai

• node x is connected to dest with capacity B

• node y is connected to dest with capacity ai -B

1 2 3 n…

x y

dest

• nodes 1,2,…,n are connected to nodes x and y with

infinite capacity Equiv. to subset sum:The partition can be made if the max cong. = 1.

Comparison between paradigms

Lower Bound on ratio:Example that shows the ratio is at least as high as

(f(n))

Upper Bound on ratio:Show that a ratio of, at least, O(g(n)) can always

be achieved.

• If f(n)=g(n) the bound is tight (g(n)).

IP-R vs RS-R1 and OSPF-R

• Lower bound Ω(N)– IP-R: single path

• CF=N

– RS-R1: separate routes• CF=1

– OSPF-R: divide equally• CF=1

• Upper bound O(N)– IP-R can use the highest

flow of RS-R1/OSPF-R

1 2 3 n…

x

dest

… n

IP-R vs RS-R1 and OSPF-R

• Lower bound Ω(N)– IP-R: single path

• CF=N, MF=1

– RS-R1: separate routes• CF=1, MF=N

– OSPF-R: divide equally• CF=1 , MF=N

• Upper bound O(N)– IP-R can use the highest

flow of RS-R1/OSPF-R

1 2 3 n…

x

dest

… n

• N flows, each carry a unit demand

• OSPF-R– use single path thruput is 1

– use two paths thruput is 2

– use more - still limited by 2 (due to the first split)

• RS-R1 can do N

• Lower bound Ω(N)

N-1

1 11

N-2N-3

1

OSPF-R vs. RS-R1

Max Flow (basic)N

N

• N flows, each carry a unit demand

• OSPF-R– to max. throughput must

split the flows– max thruput is log N– given log* N stages: max

thruput is 2

• RS-R1 can do N

• Lower bound Ω(N)

N-1

1 11

N-2N-3

1

OSPF-R vs. RS-R1

Max Flow (flow-cached)N

N

N-1

1 11

N-2N-3

• N flows, each carry a unit demand

• OSPF-R– use single path CF=N

– use two paths CF=N/2 on the down link

• RS-R1 can do CF=1

• Lower bound Ω(N)

N-1

1 11

N-2N-3

1

OSPF-R vs. RS-R1

Congestion Factor (both cases)N

N

What do we have thus far?

• IP-R vs. RS-R1 and OSPF-R (N) in both criteria.

• OSPF-R vs. RS-R1 O(N) in all criteria and cases.

• But, we sometime used fairly complex topologies!

• What if topologies are simple? or very simple?

A Simple Topology

S D

1

2

3

L

wlog, the link capacities are C1 C2 CL

• OSPF-R– cl non-decreasing use all links from l* and above.

– throughput is given by: (L- l* +1) cl* = C/ ln L

OSPF-R vs. RS-R1

Max Flow (basic)

LlLlL

Ccl

1,ln

1

1

• OSPF-R– cl non-decreasing use all links from l* and above.

– throughput is given by: (L- l* +1) cl* = C/ ln L

OSPF-R vs. RS-R1

Max Flow (basic)

LlLlL

Ccl

1,ln

1

1

• OSPF-R– cl non-decreasing use all links from l* and above.

– throughput is given by: (L- l* +1) cl* = C/ ln L

• RS-R1 can achieve C

• Lower bound Ω(log L)• We can also show that for any capacity allocation

OSPF-R can achieve, at least, C/ ln L, hence (log L)

OSPF-R vs. RS-R1

Max Flow (basic)

LlLlL

Ccl

1,ln

1

1

Hn-ln n

5 10 15 20 25 30

0.625

0.65

0.675

0.7

0.725

0.75

A centralized heuristic for vanilla IP forwarding

• Aim: improve performance of centrally controlled IP networks.

• Why centralized?– networks are centrally controlled anyway: IPNC.

• Static weight setting sucks!

21 n

21 n

sources

destinations

A centralized heuristic for vanilla IP forwarding

• Aim: improve performance of centrally controlled IP networks.

• Why centralized?– networks are centrally controlled anyway: IPNC.

• Static weight setting sucks! dynamic link weights adjustment

Link Weights

• The family of exponential weights:

• Proved to perform well by [AAP93] for related problems.

• [Fortz, Thorup,2000] used a piece-wise linear approximation of it.

control the routing sensitivity to load.

)( ee flowce

Algorithm

Input: network topology & demand matrix

Output: forwarding tables

1. sort flows

2. initialize link weights

3. for every flow in sort order

4. route flow along SP with IP constraint

5. adjust weights

Simulation Setting

– Two types of random networks: Flat & Inet – demand di,j {1,2,3…}. D = Σi,j di,j – Demand matrices

• Destinations – uniformly chosen• Sources – uniformly or Zipf-like chosen (param.=.5)

– Link capacities – all 1– Infinite bandwidth requirements – Three heuristics: rand, sort, dest– α=β/D, β=0,1,20,100,D

Total Flow

• When =D (Max Sensitivity) the flow increase by 30-50%

• All other cases, the total flow is almost the same.

• Even =1 improved performance significantly with almost no penalty in added flow.

Histogram - Inet, Zipf

Inet, Zipf

Summary

• At least, in theory OSPF cannot compete with MPLS abilities.

• In practice vanilla IP may be enough if you have central control.