1. Span-restorable Mesh Network Design
ECE Module 11
Span-restorable Mesh Network Design
W. D. Grover
TRLabs & University of Alberta
© Wayne D. Grover 2002, 2003, 2004

2. Key ideas and vision behind “mesh” restoration
(1) many real networks are highly mesh-like in their topology
(2) for restoration, generalized re-routing over the graph can permit greater sharing of spare capacity
the redundancy will go down in proportion to the average nodal degree
(3) the network can be its own computer for the real-time solution of the restoration re-routing problem
the network can self-organize restoration pathsets is a split-second
without any external control or databases
(4) if a network is mesh-oriented it is more flexible and adaptable to unforeseen patterns of demand
the network can continually self-organize its mapping of physical transmission to logical transport configuration to suit time-and-spatially varying demand patterns
Real
Less capacities are required... <100% can be achieved.
self-organize restoration pathsets... dynamic
future-proofing...
More.. yes. Capable to handle multiple failure with higher availability
Why do we study ring networks?? Drawback. Lower restoration speed.
Ring networks have been deployed for years. Standardized technology.

3. A look at some real network topologies
32-node Italian backbone transport network

4. A look at some real network topologies
Belgian national transport network
(Belga nodes, 59 spans)

5. A look at some real network topologies
“COST 239” European Community project model
( 19 nodes, 40 spans)

6. A look at some real network topologies
“Bellcore” (New-Jersey LATA) (LATA = local access and transport area)

7. A look at some real network topologies
“MCI” North American continental backbone
(homeomorphism of topology only)

8. A look at some real network topologies
Level (3) North American continental backbone

9. Concept Animation- Span-restorable Mesh networks
(28 nodes, 31 spans)
span cut
30% restoration
100% restoration
70% restoration

10. Basics of Mesh-restorable networks
(28 nodes, 31 spans)
100% restoration
span cut
40% restoration
70% restoration

11. Basics of Mesh-restorable networks
Spans where spare capacity was shared
over the two failure scenarios ? .....
This sharing efficiency increases with the degree of network connectivity
“nodal degree”

12. Basics of Mesh-restorable networks
Mesh networks require less capacity as graph connectivity increases

13. Span restoration: some details
The set of working paths severed by a span cut are restored by substitution of a set of local replacement paths between the end nodes of the failed span.
The restoration path-set is equivalent to single-commodity max-flow routing or k-shortest paths routing between failure end nodes within the surviving portion of the reserve network.
The number of paths crossing any span must respect the discrete spare capacity on the span.
A network employing a span restoration mechanism and an optimally designed (e.g., minimal capacity) reserve network that just supports the target level of restorability by that mechanism is what we mean by “a span-restorable mesh network”.

14. Basics of Mesh-restorable networks

15. A lower-bound on achievable redundancy
Consider two idealizations:
(1) restoration is “end node limited”
i.e., the min cut governing restoration path number is at one or the other of the custodial nodes
(2) node has span degree d
(3) all wi are equal at the node
mesh equivalent of the ‘perfect balance’ notion with rings
then:
d spans in total
if any one span fails, the total spare capacity on the surviving (d-1) spans must be >= to w.
hence....
redundancy = (node) d
OCX W

16. Sakauchi’s “min-cut max-flow” approach for spare capacity design
(Ref: H. Sakauchi, et al., “A self-healing network with an economical spare-channel assignment”, IEEE GLOBECOM ‘90, pp , 1990.)
S.t.
Where:
S = set of all spans
ci = cost of a spare link on span i.
si = number of spare links assigned to span i.
Ci = set of “partial cutsets” relevant to restoration of span i.
= 1 if span j is a member of the cth partial cutset relevant to restoration of span i , 0 otherwise.
c = an individual cutset in the set Ci
wi = the number of working links on span i (working demands are routed prior to solving for the spare capacity.)

17. Recall: the “max-flow = min-cut” concept6 B C 20 6 6 A F 6 20 8 D E 26 32 20 26 12
the “min-cut” = 12
Hence --> no routing solution can provide more than 12 units of flow between A -F (i.e., this is the “max-flow”)

18. How Sakauchi uses this: sizing the cutsets to support restoration
Illustrating the “partial cutsets” relevant to restoration of span (1-2):
Corresponding constraints:
C1: s1-3 + s1-4 + s1-5  w1-2
C2: s3-4 + s1-4 + s1-5  w1-2
C3: s4-5 + s1-5  w1-2
C4: s4-5 + s1-5 + s2-5  w1-2
C5: s2-5  w1-2 C 1 w
1-2 2 1 s C
1-3 5 s 3
2-5 C s 2
1-4 s
3-4 4 5 s
4-5 C C 3 4

19. Sakauchi’s method - technical aspects
Number of cuts of graph is O(2 S)
Have only S variables but S O(2 S-1) partial cutset constraints in a complete (fully constrained) formulation
> hence row generation (in the primal) methods have been used.
Row generation:
Each added row represents a new partial cutset constraint for a span that is not yet fully restorable.
Uses a separate program to test for full restorability (formulation itself has no explicit expression of restorability for built-in infeasibility detection.)
Sakauchi used the N-1 basic cuts of a graph in the initial tableau.
Venables provided composite strategy for incident cutset constraints in initial tableau plus targeted discovery of “most relevant” additional cutset constraints.
Other practical aspects:
Can run as LP with rounding up at each iteration
Don’t get (or control) restoration path-sets
Corresponds to perfect max-flow restoration routing

20. “Incident cutset “ constraints:
Venables strategy for initializing Sakauchi’s cut- dimensioning approach
(Ref: B. Venables, M.Sc.thesis, “Algorithms for near optimal design of mesh-restorable transport networks”, University of Alberta, Fall )
“Incident cutset “ constraints:
s2  w0
s3 + s1  w0
s5 + s7  w2
s0  w2
s6 w4
s1  w4
s4  w6
s5 + s8 + s3  w6
s3 + s0  w1
s4  w1
s6 + s5 + s8  w3
s0 + s1  w3
s7 + s2  w5
s6 + s8 + s3  w5
s5 + s2  w7
s8  w7
s6 + s5 + s3  w8
s7  w8

21. Venables strategy for discovering new cut-set constraints
si values after first LP iteration
1 path s t
remove edges saturated by the restoration routing trial (or at zero in the LP)
1 path
1. Run restoration routing algorithm to find an un-restorable span.
2. Inspect the restoration path-set for that span (available as a result from 1.)
3. Remove saturated edges from the graph.
4. Each combination of disconnected sub-graphs in which two subgraphs remain, one containing s, the other t, defines a new cutset constraint.
5. Done when step 1. Finds all spans fully restorable.
Next cut-set constraint:
s7 + s3 +s6 >= w5
(also: s0 + s7 >= w5 )

22. Herzberg’s “arc-path” hop-limited approach
(Ref: M. Herzberg, and S. Bye, “An optimal spare-capacity assignment model for survivable networks with hop limits,” Proc. IEEE GLOBECOM ‘94, pp , 1994.)
Subject to:
Restorability :
Spare capacity :
Where:
S, ci, si, wi are as before
Pi is a set of “eligible routes” for restoration of span i
is an assignment of restoration flow for span i to the pth eligible route
encodes the eligible restoration routes: = 1 if span j is in the pth eligible route for restoration of span i

23. Understanding the span-restorable mesh spare capacity problem
(Based on Herzberg’s approach)
Total spare capacity (minimize)
All other spare capacities
Failure scenarios
Failure scenarios
Greatest
requirement on all spans
si values
Failure scenarios
Flows over eligible routes
Failure scenarios
Network structure
Flows simulta-
neously imposed on any span
Represented in the eligible route - defining information input

24. Threshold hop-limit effect
( Total spare capacity, total number of eligible restoration routes )
Minimum spare
Threshold value ( for the network shown )
Below the design threshold hop-limit, solution quality is affected.
Above the threshold hop limit, computational difficulty grows unnecessarily

25. Representing networks in a “.snif” file
Date:
File Name: bellcore.snif
Network: New Jersey LATA area from 1993 publication ...
Program: Jointspandatprep.exe followed by AMPL JointSCP.mod
Node Xcoord Ycoord
Span NodeA NodeB Distance Working Spare
..... to last span entry (28 here)
snif = TRLabs standard network interface file
Notes:
- x,y node co-ordinates are optional to support graphical display applications
- working and spare quantities may or may not be present depending on use or stage of design processing
Input format for the restoration routes finder software

26. “Transportation-like” variant of the mesh spare capacity problem
Partly for completeness, and partly because of the “special structure” (unimodularity) of the classic “transportation” problem.
This approach also allows formulation without pre-processing to find either cutsets or eligible restoration routes.
N.B.: for this we switch to node-based indexing and implicitly directional flow variables.
s.t.:
Restorability:
- source = sink :
- flow transhipment nodes :
Spare capacity :

27. Technical aspects of the “transportation-like” problem formulation
Generates
2 S(S-1) flow variables plus S capacity variables
S sets of { 2 source-sink and (N-2) flow conservation constraints } ~ i.e., O(SN) = O(S2)
O(S2) spare capacity constraints.
Advantages:
compact formulation (in the sense of no pre-processing required)
each failure scenario presents a transportation-like flow sub-problem (however, these are all coupled under a min spare objective)
unimodular nature of transportation problem.
Disadvantages:
AMPL / CPLEX memory for ~ O(S2) constraints on O(S2) variables
no direct knowledge of restoration path-sets from solution
no hop or distance-limiting control on restoration
implicitly assumes max-flow restoration mechanism
“blows up” in later “joint” or path-restorable problem formulations

28. (1) Adding modularity (and economy of scale)
Ref: J. Doucette, W. D. Grover, “Influence of Modularity and Economy-of-scale Effects on Design of Mesh-Restorable DWDM Networks”, IEEE JSAC Special Issue on Protocols and Architectures for Next Generation Optical WDM Networks, October 2000.
Before….
To make it modular….
same
same
Plus:
= cost of mth module size on span j
= number of modules of size m on span j
= capacity of mth module size

29. (2) Additions for “joint” working and spare optimization
= the set of all (active) O-D pairs
= an individual O-D pair (“relation r”)
= the set of “eligible working routes” available for working paths on relation r.
= the total demand for relation r.
= the amount of demand routed over the qth eligible route for relation r.
= 1 if the qth “eligible working route” for relation r crosses span j.

30. Optimizing the working path routes with spare capacity placement
modular “joint” capacity (working and spare) placement (MJCP)
Cost of modules of all sizes placed on all spans
All working span capacities must be fully restorable
Spare capacity on spans must be adequate
Only modular totals are possible
new
All demands must be routed
Working capacity on spans must be adequate

31. Spontaneous Topology Reduction under Economy of Scale
PMSCP (benchmark)
MJCP (joint design) 48 24 24 48 24 48 12 48 24 48 24 24 48 48 96 48 48 48 24 24 48 24 48 24 24 24 48 24
9n17s2 - 6x2x 48 48 24
Total Capacity = 504
Total Cost = 2861
Total Used Spans = 17
Total Capacity = 612
Total Cost = 2595 (9.3% savings)
Total Used Spans = 13 (23.5% reduction)
Class question: Why is this happening - explanation?

32. Generating the “eligible route” sets
Two types of route - sets can be needed:
(1) “all distinct routes” up to a hop or distance limit (or both) for restoration each prospective span failure
Needed for both joint and non-joint span-restorable mesh design.
These routes are all between nodes that are adjacent in the pre-failure graph.
Require S sets of such routes, typically up to hop or distance limit H
(2) distinct route sets for working path routing
Needed in addition for the joint working and spare formulations - in addition to routes (1)
Require ~ N2/2 sets of such routes (each O-D pair)
Typically delimited by hop or distance limit in excess of the shortest path distance.
Rationing / budgeting of route-set sizes may be required.
Then also need strategies for selecting / sampling which routes to represent

33. Overall strategy for generating route-sets needed in formulations
One practical approach can be to generate a “master database” of all distinct routes up to some “high” hop limit
can take a long time … and produce a large file
but, it is a one-time effort for any number of studies on the same topology.
Once the master route-set is available, the route representations for specific problem formulations can be generated by filter programs according to almost any desired specification..
e.g.
all routes under 3,000 miles or six hops, except for ...
all routes that exclude nodes {…} or spans {…}
routes up the hop limit that provides at least 15 per span (or OD pair).
a set of routes that visit no node more than x times
the first 15 routes when sorted by increasing length
etc.
Possible project idea: statistical “sampling” of master route-sets for practical formulations