The strength of routing Schemes. Main issues Eliminating the buzz: Are there real differences...
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Transcript of The strength of routing Schemes. Main issues Eliminating the buzz: Are there real differences...
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.