1. Span-restorable Mesh Network Design
E E
Span-restorable Mesh Network Design
W. D. Grover
TRLabs & University of Alberta
© Wayne D. Grover 2002,

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. Basics of Mesh-restorable 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 (sample result)

13. Span restoration: what we mean
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. Design Objective: Span Restorable Mesh Networks
Given a transport network with known working capacities, how much spare capacities should we place on each span so than the network is 100% restorable to a single span failure? 4 3 9
How much spare capacity do we need for each span? 4
Working capacities of each span are known 2 2 15 11 7 8 5 5 2 4

16. A simple 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

17. 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

18. 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

19. Solving Herzberg’s SCP ...
Input Parameters to Solvers
Working capacities
of each span i wi
Shortest path routing
Set of eligible restoration
routes for each span failure i
Pi, i,j p
Restoration routes finder for all network spans
c i
Unit cost for each span i
Output (Variables) from Solvers
Spare capacities
of each span i
s i
LPsolve
Restoration Flow p
f i p
LPsolve

20. Herzberg’s approach - technical aspects
working paths are routed prior to this formulation --> (provides the wi’s)
A separate program finds “all distinct routes” for each failure scenario based on the depth-first search algorithm (DFS).
DFS may be limited by a hop - count, a distance limit, any other operational criterion.
These become the “eligible routes” for restoration.
“Eligible routes” are not a priori decisions about the restoration routes to be taken for each failure…they only represent the routes available for restoration flow assignment.
There are
S restorability constraints (equalities) and S(S-1) spare capacity generating inequality constraints.
~ variables - but controllable via eligible routes.
Yields restoration path-set details along with reserve network spare capacity.
The LP relaxation sometimes acts unimodular but this is data-dependent. Solution as IP often solves quickly enough or a “repair” procedure can be devised for fractional outcomes when solved as LP.

21. Threshold value ( for the network shown )
How hop-limit affects complexity and solution quality in Herzberg’s formulation
( 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

22. Some practical notes re: “hop limit” concept
In practice,
hop limits can easily be converted to mileage limits or combined hop / distance limits in generating the eligible route-sets for the formulation.
the basic idea of a single network-wide hop limit can evolves into approaches such as adapting hop limits per span (and per working route in the joint formulations) so as to assure a minimum representation of route diversity, within a computational “budget” for numbers of variables and constraints.

23. (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

24. (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.

25. 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

26. Some recent Research Comparisons on effect of design modularity
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.
Post-Modularized (PMSC)
Modular-aware
(MSCP)
Joint-modular
(MJCP)
Working
Path
Shortest Path
Shortest Path
Joint Modular
Routing
Spare
IP Formulation
Integer, but non-modular
Modular on Totals
Capacity
(Spare + Working)
Placement
True
Modularity
Rounded Up *
On Totals
Modular Design
Notes
Existing Benchmark
A compromise
No approximations
* rounding rule = least cost combination of modules such that meets the wi+si requirement, under the same economy-of-scale model as the MSCP and MJCP trial cases.

27. Experimental Design
Each formulation implemented in AMPL Modeling System
Solved in CPLEX Linear Optimizer 6.0.
Used 9 test networks of various sizes (below).
The number of eligible working and restoration routes is controlled by hop-limit strategies.
Eligible working routes restricted to 5 to 20 per demand.
Eligible restoration routes similarly restricted for each failure scenario.

28. Experimental Design (2)
Five module sizes = {12, 24, 48, 96, and 192 wavelengths}.
Module costs follow three progressively greater economy-of-scale models
notation for economy of scale models : 3x2x --> “3 times capacity for 2 times cost”
Cost
Module
Module
Module
Module
Module
Model
Size 12
Size 24
Size 48
Size 96
Size 192
3x2x
120
186
288
446
690
4x2x
120
170
240
339
480
6x2x
120
157
205
268
351

29. Results - “modular aware” spare capacity placement (MSCP)*
* Relative to the least-cost post-modularized design (PMSCP) with the same series of module costs

30. Results - “joint modular” capacity placement (MJCP)*
* Relative to the least-cost post-modularized design (PMSCP) with the same series of module costs

31. Spontaneous Topology Reduction
Unexpected finding
Happens with strong economy of scale scenarios
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. Summary of Results Post-Modularized Design (PMSCP):
14 % to 37% levels of “excess” (above design working and spare) capacity arises from efficient post-modularization into the {12, 24, 48, 48, 192} set.
“Modular-aware” Spare Capacity Design (MSCP):
Moderate levels of excess capacity (9% to 30%, average 19.4%).
Moderate cost savings (up to 6%).
Joint Modular Design (MJCP):
Minimal excess capacity (~1 to 4.7%).
Highest cost savings (~6 to 21%, average 10.7%).
“Spontaneous Topology Reduction” observed (~ 24% of spans for 6x2x)