How to Design Mesh-restorable Networks V1

7/31/2019 How to Design Mesh-restorable Networks V1

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On the design of span- andpath- restorable meshnetworks

TRLabs Technical Report TR 2001-01

Release 1, November 2001It is intended that this document will be updated and grow in its coverage of additional

schemes. The next update will include the addition of design for shared backup path

protection schemes

Wayne D. Grover, John Doucette

TRLabs / University of Alberta


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Design of mesh-based transport networks Version 1, November 2001

2

I. Introduction

Brief Historical Background:

Accumulating experience with the planning and operation of ring-based transport

networks, and the advent of a DWDM-based optical networking layer has set the stage

for revisiting the mesh-restorable transport alternative following a decade in which rings

were the dominant approach for transport survivability.

The principle theoretical advantages of a mesh over ring-based transport are its greater

capacity efficiency (lower ratio of required spare to working capacity) and relative

simplicity in provisioning to satisfy growth and changes in demand pattern. Mesh-based

networking is also far more amenable to ideas of automated self-provisioning of new

service paths. A mesh is inherently more flexible than a committed set of rings.

On the other hand, two factors have often worked against industry-wide adoption of

mesh-based solutions in recent generations of technology (primarily the Sonet era). These

have been:

(i) the relatively poor economics of the past cross-connect devices (on which mesh

provisioning and restoration is based), relative to add-drop multiplexors (ADMs) onwhich rings are based, and

(ii) the typically slower restoration times which could be offered by mesh restoration

times (several hundred milliseconds opposed to the 50 msec benchmark of rings or

APS systems).

So what is different now? Why would a more capacity-efficient mesh imply

corresponding dollar-cost savings? One factor is optical networking technology based on

DWDM: The distance-dependent transmission costs for EDFAs, plus transmission-

related nodal termination and routing / switching equipment quantities, are high enough

to place a significant emphasis on capacity efficiency at the lightwave utilization level. In

the past nodal switching costs dominated and the truism was that transmission was nearly

free in comparison.

In addition, today, the optical transmission capacity (and associated line and nodal

transmission / cross-connecting gear) can sometimes barely even be provisioned quicklyenough to keep up with bandwidth needs. Regardless that the priceper bitkeeps going

down, the amount needed goes up as fast or more quickly so that the absolute yearly

capital expenditures on transmission equipment remain very significant: But even if the

cost-related argument for capacity efficiency was dismissed, it is still the case that more

revenue could be earned with an existing transmission base if less capacity has to be setaside for restoration.

This is one of the main reasons that mesh restoration stands ultimately to become more

cost-effective than rings, especially in a long-haul environment with rapid demand

growth.


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3) prepared by W. Grover TRLabs Copyright 2001 W. Grover [email protected]

2 : Basics of mesh - restorable networks

This section is intended to touch on the key concepts and issues of span- and path-

restorable networks. Section 3 goes on to show the design methods in detail.

Terminology

A transport network must inherently be treated as a multi-graph or capacitated simple

graph. The widespread practice of referring to almost anything that connects two entities,

at any layer either physical or logical, simply a link is not precise enough in this

environment. For capacitated design of transport networks it is helpful to have ways of

distinguishing between references to physical entities, logical entities, signal paths,

simple routes, etc. A link in a logical layer may actually be a signal path over a route

comprised of several spans in the physical layer for example. We therefore define thefollowing generic terminology for work on transport network design.

Link:A link is a logical pipe or connection between service layer devices such as a router or

telephone switch. In the transport layer each individual logical unit of transport capacity

between two adjacent nodes of the transport network is thus potentially part of a service-

layer link. For example, in a DWDM optically cross-connected transport network, a

single wavelength may be the unit capacity for forming service layer links. In a transport

network managed at the Sonet cross-connection layer the link unit may be the individual

STS1 or STS3c signal units managed. A link of capacity in the transport layers is often

also known as .a. capacity unit, bandwidth unit or a channel. These are discrete(integer) entities in either WDM or Sonet.

Span:

A span is the set of all transmission links (both working and spare) between two nodes at

which transport-layer signal management is performed and which share the fate in theevent of a physical cutof a facilities structure such as a cable of duct system.. There may

be several transmission systems operating in parallel, but all following the same physical

right-of-way or facilities structure (pole line, ducts, trenches, etc). A group of such

transmission systems, possibly of various types and rates, a logically represented in the

planning problem as one edge in the network graph and an associated capacity which is

the total provisioned capacity of all systems in the span in terms of whatever capacity

units at which the transport network is being provisioned and managed. A span is the

independent entity that physically undergoes a cut (if one occurs), not a link. For

planning purposes we assume any span cut fails all working and spare capacity on the

span.

Route:A route is any contiguous sequence of spans. i.e., simply a geographically connected

walk over physically existing spans between any two nodes in the network.


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4

Path:

A path is a specific cross-connected concatenation of individual unit-capacity carrier

signals (links) following a route through the network. It is working paths that serve to

transport demand flows. Restoration path sets will be formed out of spare capacity units.

Reserve Network:

A term used to refer to the entire capacitated graph of spare capacity available for

restoration. A graph in which each edge has a limit to the flow that can cross the edge

(i.e., an edge capacity) is called a capacitated graph (as opposed to an uncapacitated

graph in which there are no such limits.)

"Span-restorable" mesh networks

The capacity-design of both span- and path- restorable networks is perhaps best

appreciated by starting with a look at the type of restoration re-routing mechanism that is

the basis for each class of network.

Span restoration re-routing In a network based onspan restoration1, cable cuts (or

single unit-capacity link failures) are restored by re-routing between the end-nodes of the

break directly. Thus, span restoration is like a locally applied set of detours around a

break in the road. Note, in this analogy that if the road or highway that is disrupted has

several lanes, there may be an independent detour path deployed for each lane of the

highway. There is no stipulation that all affected demands must travel as a group via a

single replacement route. Rather, the total amount of work capacity disrupted is

efficiently re-routed at the individual link capacity unit level of the associated bandwidth-

management layer.

A common misunderstanding about span-restorable mesh networks is the notion that

restoration is via a single two-hop route around the break, such route having enough

spare capacity to handle the entire working capacity of the failed span. It is important to

correct this for a proper assessment and appreciation of the potential benefits. More

generally in span restoration, each individual failed working link unit may take a different

restoration route, up to some hop limit (H) that can be considerable more that two hops.

This makes for a much greater opportunity for network-wide sharing of spare capacity.

Figure 1 illustrates the issue. More technically, the two-hop single-route restoration

model is just the special case of "H=2, fully bundled".

1 Other writers alternatively refer to this as "link restoration."


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a common, but misleading,portrayal of span restoration

the more general concept of spanrestoration permiting much greatersharing of network spare capacity

Figure 1: Different understandings of span restoration.

From Figure 1 it can be seen that there is a great deal more opportunity to share network

protection capacity on the right than on the left. In fact, through design controls on the

"hop (or distance) limit" parameter, a network operator can mediate a trade-off between

the maximum length of the restoration path-sets that would be acceptable against the total

investment in spare capacity required for restoration. Thus the fully bundled H=2 case on

the left above, gives the simplest re-routing characteristics, but uses the most sparecapacity. At higher hop-limits more complex patterns of re-routing arise, so as to

maximize spare capacity sharing. At a "threshold" hop-limit the theoretical minimum of

spare capacity is reached. Restoration path-sets even at this highest hop limit, however,

are typically not as complex as the example on the right, which is intended mainly as an

example of the generality of the re-routing that is possible.

Although the example may look complex, the path-sets in span restoration are always

algorithmically specified. Theoretically the ideal restoration path-set is equivalent to a

solution of the (single-commodity) max-flow problem between the immediate end nodes

of the failed span (the custodial nodes). In practice this is very closely approximated by

a type of k-shortest paths (ksp) re-routing [2]. The literature in graph and routing theorycontains many variants of "k-shortest paths", many of which are for scheduling and

project management applications on uncapacitated graphs, and may include looping -to

enumerate successive route-lengths. The model to approximate max-flow for span

restoration is, however, specifically the set of k non-looping link-disjoint paths of

successive length up to the maximum number of paths feasible or required for restoration.

Note that link-disjointness refers here specifically to disjointness at the unit-capacity of

transport management. This means that no unit-capacity linkcan be used in more than

one path, but any number of restoration paths can share the same span, up to the spare

capacity limit of the span. In other words the paths are not span-disjoint, but as a set have

to respect the capacitation of all spans. The ksp path-set can thus be thought of as the


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6

process of finding "all the paths feasible on the shortest route, followed by all the paths

feasible on the second shortest route not using any spare links from the first set, followed

by the set of feasible paths on the third-shortest replacement route not using and spare

links of the first or second set of paths, etc." (up to the maximum allowed hop- ordistance-limit). The paths are link-disjoint (i.e., they are discrete and feasible under the

capacities present) but are notlimited to being span-disjoint.

For many planning and study purposes dealing with span-restorable networks, the "k-

shortest paths" (ksp) path-sets for span restoration can be found by an O(nlogn) algorithm

[11] that generates restoration paths, up to the number feasible or needed in each case.2

A

related point for clarification is that while the ksp reference model for span restoration

finds its paths in a sequentially increasing iterative manner, we do not mean to suggest or

imply that the actual real-time restoration protocols work the same way. For instance a

distributed span-restoration protocol may actually find all paths at once without iteration

and be equivalentin terms of path number and path length total to algorithmic ksp,without being based on a direct iterative ksp approach [12].

Capacity design for span restoration: A "span-restorable mesh network" is one in which

the spare capacity allocation across the network is sufficient to allow this type of re-

routing behavior to provide 100% restoration of any single span cut. An input parameter

when we design the spare capacity of a mesh network is the maximum hop or distance

limit that one considers acceptable for restoration in the network. Hop counts, H, are

typically in the range of 5 to 10 for many networks at the level at which the network can

be viewed as a mesh - more will be said about this later. This is the concept of a meta-mesh abstraction for the case of networks with extensive chain segments.

Hmin H*

Full

restoration

infeasibleTotal

spare

capacity

Design Hop Limit, H

Figure 2: How mesh network spare capacity depends on hop limit.

2 Here, n is the number of nodes in the network.


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Figure 2 illustrates how the optimum spare capacity decreases with increasing hop count

for eligible restoration routes, up to a threshold limit. In specifying a hop count for the

design there are two main considerations: H should be sufficiently high so as to enable

achievement of the theoretical minimum of spare capacity. As the hop count isconceptually increased from the minimum starting value (of two), a network first reaches

a state where 100% restorability becomes feasible. (Not all networks will even be

restorable, regardless of capacity, under the pure H=2 deflection re-route model discussed

above.) Further increases in H allow full restorability to be satisfied with decreased total

spare capacity, because the sharing of spare capacity on each span over separate failure

scenarios is increasing, until the threshold hop limit, H* , is reached. Thereafter increases

in H provide no further reduction in total spare capacity.

As a matter of study design, some preliminary tests can determine H* and the detailed

capacity designs conducted using that value, as long as it is not excessive from a practical

restoration distance standpoint or from the standpoint of computational complexity of thedesign formulations that follow.

"Path-restorable" mesh networks

If we return to the analogy of re-routing around a multi-lane highway section that is

under repair,path restoration is more like planning a completely different route before

setting out on the journey, as opposed to following the regular route up to the break then

taking a local detour. In the transport network context it is thus equivalent to rapid tear-

down and re-provisioning of new end-to-end paths (which avoid the break) for every

affected O-D pair simultaneously. Path restoration thus distributes the impact of failures

and the recovery effort more widely over the network as a whole and therefore generally

permits greater efficiency in spare capacity design. Theoretically this offers even lower

network spare capacity requirements for 100% restorability, but it comes at the price of a

quite significant escalation in both design and real-time reconfiguration complexity. A

simple illustration of the concept, in contrast to span restoration, is shown in Figure 3.


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8

Figure 3: Example of path restoration

The solid lines in Figure 3 show the pre-failure working path routings. The dashed lines

show what is called "stub-release" - the surviving portions of the pre-fail path up to and

following the break are released back into a pool of effectively spare capacity for

restoration. (Otherwise these stub-segments of the pre-failure paths are like unusable

deadwood that in fact get in the way and can even block restoration sometimes. In the

example the top path retraces its path up to the break (using a left to right orientation)

then takes a completely different path the rest of the way to its destination. The next

lower path takes a completely disjoint route end-to-end.

With path restoration the key technical issue is that to have an assurance of 100%

restoration within the relatively even lesser amount of spare capacity in a path-restorable

network, one must globally solve for the correct co-ordination amongst restoration path-

sets for individual origin -destination (O-D) pairs. The issue is sometimes referred to as

the "mutual capacity" problem : in the worst case up to N (N-1)/2 O-D pairs may

simultaneously want to make use of the limited spare capacity available on one span out

in the body of the network. A small example can be based on the figure above. This is

Figure 4 below.


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Figure 4: Illustrating the importance of stub release in path restoration.

Say the top path in Figure 4 took the alternate route shown (relative to Figure 3.) This

route may be equally good (short) from the point of view of this O-D pair alone, but as

can be seen below, would block out the second path (assuming the available spare

capacity can just support the initial path-set above.)

Therefore the allocation of spare links on every span must be made so that all required

restoration paths are feasible at once. If a spare link on one span is allocated to one O-D

pair, which may have several diverse options for re-routing, another O-D with fewerrouting options may be frozen out and fail to obtain full restoration. A set of

independently determined shortest replacement paths for each O-D in isolation does not

provide this property at all.

The problem is still solvable of course. Formally, the solution to the multiple O-D pair

simultaneous re-routing problem is a multi-commodity maximum flow (MCMF) problem

with constraints on amounts of each commodity [3]. Optimal solution to this problem is

NP-hard (compute time rises exponentially with problem size) whereas for span

restoration the re-routing problem is practically and indeed optimally solvable in low-

order "polynomial time" (O(n2) for ksp or O(n

3) for strict max-flow).

3 : Design Theory and AMPL / CPLEX Details

Span restorable networks

In this section we look at the design of span-restorable mesh networks using a basic "arc-

path" type of optimization formulation first promoted by Meir Herzberg, then of Telestra

(Australia), in 1994 [4]. We present an extension of Herzberg's work that includes joint

optimization of the working path routing along with spare capacity placement. This is


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10

logically the version of the span-restorable mesh design problem that most directly

corresponds to the ring-based status-quo in the sense that BLSR / OPSR ring

functionality is a form of span restoration (not path restoration or 1+1 APS) and, in ring-

based networking, we always have to plan the routing of working paths in concert withthe protection structures being employed (as opposed to pure shortest path routing of the

workers independent of the protection capacity).

This basic formulation is later referred to as the "joint", span-restorable, design case and

it may be solved with or without optimized chain sub-networks through changes in the

basic model that will be described. The basic model to follow does not treat chain sub-

networks in the "optimized" manner described above. That follows as an enhancement to

the basic model.

Basic Model for Optimal Capacity Design: Joint, Span-restorable, no chain bypass.

Parameters:Cj Cost of each unit of capacity on span j

Li Target Restoration level for span i (Li = 1 assumed henceforth)S Number of spans in the network

Pi Number of eligible routes for restoration of span i (discussed below)

wj Number of working links (capacity units) on span j

i,jp Equal to 1 if pth eligible route for span i uses span j

D Total number of O-D pairs with non-zero demand

dr Number of demand units for O-D pair rQr Number of eligible working routes available for demand pair r

jr,q Equal to 1 if qth eligible route for demands between O-D pair ruses spanj

Variables:fi

p Restoration flow assigned to pth eligible restoration route for span i

sj Number of spare capacity units placed on span j

gr,q Working capacity assigned to the q th eligible working route for demand pair r

wj Number of working capacity units on span j

1

( )s

j j j

j

Minimize C w s=

+ (1)

Subject to:

iiP

p

p

i Lwfi

=1

.,...,2,1 Si = (2)

,

1

iPp p

j i j i

p

s f=

jiSji = .,...,2,1),( (3)

=

=r

Q

q

rqr dg1

, .,...,2,1 Dr= (6)

, ,

1 1

rQDr q r q

j j

r q

g w= =

= .,...,2,1 Sj = (7)


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Constraint set (2) ensures that restoration for span failure i meets the target level.

Constraints (3) force sufficient spare capacity on each span j such that the sum of the

restoration paths routed over that span is met for every failure span i. The largest

simultaneously imposed set of restoration paths imposed in a span effectively sets theminimum si value on each span in the solution.

The constraint set (6) ensures that all working demands are routed. The constraints in (7)

generate the logically required working capacity required on each spanj to satisfy thesum of all pre-failure demands routed over it.

AMPL Model for Modular Joint Span restorable design

An AMPL model that implements the above formulation is shown below. The AMPL

model shown is actually suitable for the general case ofmodularmin-costdesign. In themore general, modular, design case the family of available transmission module sizes and

corresponding per-span costs for each module can be entered in the parametersZmodCap[m] and Cost[m , j]where {1... }m M is the mth module size andj is the spanindex.


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# Joint Modular Span-Restorable Design Model

# This model is designed to jointly optimize the routing of working

# paths and spare capacity placement Modularity is included in the basic

# model. If a family of modular capacity sizes does not pertain

# simply provide the data file with a single module of size 1 which will be

# equivalent to the non-modular design.

# SETS

set SPANS; # (set of all spans)

set REST_ROUTES{i in SPANS};

# (set of all restoration paths for each span failure i)

set MODULES; # (set of all types of capacity modules)

set DEMANDS; # (set of all demand pairs or node pairs)

set WORK_ROUTES{r in DEMANDS};

# (set of all working routes for each demand pair r)

# PARAMETERS

param bypass{i in SPANS} symbolic;

param Cost{m in MODULES, j in SPANS};

# (cost (or distance as a surrogate)of module types on span j)

param DemUnits{r in DEMANDS};

# (number of demand units between node pair r)param Level{i in SPANS};

# (the minimum required restoration level on span i)

param ZModCap{m in MODULES}; # (capacity of module type m)

param Delta{i in SPANS, j in SPANS, p in REST_ROUTES[i]};

# (equal to 1 if pth restoration route for failure of span

# i uses span j and 0 otherwise)

param Zeta{j in SPANS, r in DEMANDS, q in WORK_ROUTES[r]};

# (equal to 1 if qth working route for demand between node pair r

# uses span j and 0 otherwise)

# VARIABLES

var flowrest{i in SPANS, p in REST_ROUTES[i]} >=0, =0, =0, =0, =0, = sum{p in REST_ROUTES[i]} Delta[i,j,p] * flowrest[i,p];

subject to modularity{j in SPANS}:

spare[j] + work[j] = sum{m in MODULES} nmodules[j,m] * ZModCap[m];

subject to demands_routed{r in DEMANDS}:

sum{q in WORK_ROUTES[r]} gwrkflow[r,q] = DemUnits[r];

subject to working_capacity{j in SPANS}:

work[j] = sum{r in DEMANDS, q in WORK_ROUTES[r]} Zeta[j,r,q] *

gwrkflow[r,q];

# END


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Concept of Eligible routes and their generation:

To implement the above formulation, one needs a pre-processing step, usually with

custom programs, to enumerate the sets of "eligible" working and restoration routes. The

ideal is to represent all distinct routes for restoration up to the threshold hop (or distance)limit between adjacent node pairs on the network graph for span restoration, and the set

of all distinct routes up to a corresponding allowance in excess of the shortest path for

each O-D pair, for routing of working paths.

The complete sets of all such paths are, however, strictly O(S 2dH

) where Sis the number

of spans, His the hop limit, and dis the average node degree. So in practice, unless thehop limits are low, one typically has to limit the number of eligible restoration routes to a

target number for each relation, say to 10 or 20, or adopt a technique of artificially

reducing the hop limit and supplementing the resulting route-set with an explicit set of k-

successively shortest distinct routes without any hop limit [6].

In our recent studies, a further improved strategy for populating the route-sets has been

used. In this approach, the hop limit is adaptively determined for each span failure

scenario, or each working path to be routed, so that a minimum target number of distinct

eligible routes are found. For example, it might be desired to solve a joint span-restorable

design formulation where there are at least 10 distinct working path choices for each O-D

pair and 20 eligible restoration routes for every span failure scenario. The program that

identifies such routes takes each failure case individually and first conducts a complete

depth-first search for all distinct routes between the relevant end nodes, with an

arbitrarily high initial hop limit, for instance 3/4 of all the nodes in the network. This is

typically a large file, written to disk as a temporary working file3. The routes in this

complete list are then sorted by increasing mileage. The required number of routes for theformulation are then taken from the top of the sorted list, and the highest hop limit

amongst these routes is recorded. The temporary file for that O-D pair or span failurescenario is then deleted and the process repeated for the next failure or working O-D pair.

In the case of joint span-restorable designs, the eligible route policy for the result is then

denoted by the minimum numbers of eligible routes found this way. N1, is the number of

distinct eligible working routes consider for each O-D pair, and N2 is the number of

distinct eligible restoration routes considered for each failure scenario.

The above is a practical and effective procedure for formulating the optimization problem

with minimum time spent in source-code development, but it is acknowledged that the

formulations are solved to optimality with respect to the set of generated routes. Only by

implicitly or explicitly considering all possible routes can we strictly claim absolute

optimality of the solution. Advanced optimization techniques such as column generation

embedded within branch-and-bound could be developed in future to solve the

formulation exactly without the need to generate all of the candidate paths. This is an area

of suggested further research.

3 Writing the routes to a temporary file before sorting and selecting is a practical albeit brute-force way of achieving the

desired end with relatively little time spent programming (i.e., elapsed project time as opposed to computing

efficiency). A more elegant approach for production use would be to keep a distance-sorted linked list during the depth

first search


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14

Path-restorable Design

The path restorable design formulation described here is one in which working paths are

first shortest-path routed (independent of the spare capacity design problem i.e., it is anon-joint design), and stub-release is assumed.

mCj

Parameters and variables path-restorable capacity design(in the master formulation)*

rxi

,r qg

D

,r q

j

S

mnjrd

jw

0

,s

i j

,prf

i

,,rp

i j j

s

riP

rQ

* some variables become pre-computable parameters in the variations that follow

Input data

Intermediate (internal)variables

Design output variables

Cost of mth modulesize on span j.

Set of all point to pointdemand quantities, indexed

by r

amount of demand onrelation r

Set of all spans between

mesh cross-connection points

Set of eligible workingroutes for relation r

Encodes routes in= 1 if span j is in qth route

for relation r

rQ

Set of eligible restorationroutes for relation r

upon failure i.

= 1 if span j is in pth routefor relation r upon failure i

Stub releasequantity on span j

from failure i

Amount of demand loston relation r for

failure i

No. of operatingworking and spare

links (channels)on span j

No. of modules oftype m to install

on span j for min cost

mZCapacity of mth

module size

Working andrestoration

routingsolutions


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m m

j j

m j

Minimize C n

M S

Cost of modules of all sizes placed on all spans

Master formulation for path-restorable capacity design

S. t.

;i r S D, ,r q r qiq

rg xi

=rQ

Defines the amount of damaged working flow

for each relation under each failure scenario

,

r

r q r

q

g d

=Q

r D

, ,r q r q

j j

r q

g w

= rD Q

j S

All demands must be routed

Working capacity on spans must be adequate

(1)

(2)

(3)

Master formulation for path-restorable capacity design (2)

, , ,

0

,

0

r q r q r q

j ir q

gs

i j

=

rD Q

With stub release

Without stub release

2( , )i j

i j

S

rP

,

p i

p rrf xii

= ;i r S D

0

rP

, ,,,

pr i

rp rpf s sji i i jj

D

Restorability of working flows for each relation

Spare capacity on spans must be adequate(see note on stub release)

=

+M

m

mm

jjj Znws1

j S Modularity of installed capacity

(4)

(5)

(6)

(7)

As presented, this is a universal or master formulation that allows for (i) modularity, (ii)

joint optimization of working path routing, (iii) stub release or non-stub release.

The master formulation requires as inputs:


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(a)point-to-point demand matrix (or list)

(b)set of eligible distinct working routes for every (O-D) pair, r

(c)set of eligible distinct restoration routes for every (O-D) pair, rfor each failure scenario i .

It solves for:

(a) the amount of working flow on each working route for each O-D pair(working flows may be split over several routes)

(b)the working, spare, (and module) capacity totals on each span

(c) the composite restoration path-set for all affected demands in each

failure scenario

One may represent specific problems variants as follows:

(a) If an integer but non-modular capacity design is desired, change theobjective function to cost-weighted sum of spares (and / or working, if

joint) and drop the set M, and the related module number variables and

Constraint (7).

(b)If a non-joint design is desired, drop (1), (2), (3), (6) and pre-computeall of the xi

rdamage coefficients (from the known routings) as

constants. Also pre-compute all the stub-release spare capacity

quantities according to (6).

(c) If stub-release is not desired: drop (6) and set all stub release sparecapacity return values to zero.


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A note on Joint path-restorable networks: In a prior study of six different test

networks it was found that while the aspect ofjointdesign was in all cases quite

significant ( 15 to 28%) in reducing total capacity for thespan-restorable designs, it was

very much more marginal in the difference it made in thepath-restorable designs (only afew percent improvement relative to the corresponding non-joint cases).

# AMPL Model for non-joint path-restorable design with stub release

set SPANS;

set DEMAND_PAIRS;

# Set of all non-zero demand pairs as read in from dat file

param span{SPANS} symbolic;

# whereas the SET SPANS is an indexing of spans that exist, span[j]

# is the actual NAME of the jth span in the set.

param Cost{j in SPANS};

# DESCRIPTION OF WORKING DEMANDS AND THEIR NORMAL ROUTING

param DemUnits{r in DEMAND_PAIRS} default 0;

# Number of demand units between node pair r.

set WORK_ROUTES{r in DEMAND_PAIRS};

set WORK_ROUTE_VECTORS{r in DEMAND_PAIRS, p in WORK_ROUTES[r]} within {j in

SPANS};

param Work_Route_Vectors{r in DEMAND_PAIRS, p in WORK_ROUTES[r], j in

WORK_ROUTE_VECTORS[r,p]} symbolic;

# N.B. Everywhere in this model a route is specified as a sequence

# of the names of spans that comprise the route. This is a more# compact form that replaces the prior encoding of routes by 1 / 0

# representation of span membership in a routes for every span of

# the network


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set DEMANDS_AFFECTED{i in SPANS}

:= {r in DEMAND_PAIRS : exists {p in WORK_ROUTES[r], j in WORK_ROUTE_VECTORS[r,p]}

Work_Route_Vectors[r,p,j] = span[i] };

# This builds a set of the demand pairs that are damaged by each possible spanfailure i

param Stub_release {i in SPANS, j in SPANS: span[i] span[j]}

:= sum {r in DEMANDS_AFFECTED[i]: exists {p in WORK_ROUTES[r], k in

WORK_ROUTE_VECTORS[r,p]} Work_Route_Vectors[r,p,k] = span[j] } DemUnits[r] ;

# Stub_release[i,j] is the amount of surviving working capacity on

# span[j] that is in a stub of a working route severed

# by failure of span [i]

# ELIGIBLE ROUTES FOR PATH-LEVEL RESTORATION OF O-D PAIRS

set REST_ROUTES{r in DEMAND_PAIRS};

set REST_ROUTE_VECTORS{r in DEMAND_PAIRS, p in REST_ROUTES[r]} within {j in SPANS};

param Rest_Route_Vectors{r in DEMAND_PAIRS, p in REST_ROUTES[r], j in

REST_ROUTE_VECTORS[r,p]} symbolic;

# There is one set of restoration routes, indexed within each set

# by dummy variable p, for each r. (r,p) is subsequently

# used directly as a tuple so that AMPL will index over only the

# (r, p) combinations actually presented in the data file.

# The DAT file will present params Rest_routes[r,p,j] which will be

# for each relation r, a set of horizontal lists

# numbered locally by p, each list being a vector of span names

# that are included in the pth eligible route for relation r.

# VARIABLES

var rest_flow {i in SPANS, r in DEMAND_PAIRS, p in REST_ROUTES[r]} >=0, =0, = sum {r in DEMANDS_AFFECTED[i], p in REST_ROUTES[r]: exists {k in

REST_ROUTE_VECTORS[r,p]} Rest_Route_Vectors[r,p,k] = span[j]} rest_flow[i,r,p] -

Stub_release[i,j];

# END


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Note that in both of the AMPL models presented above, an essentially arbitrary upper

bound of 10000 (links) is used on the spare capacity variables to ensure the bounds were

not active in the solution. In future one might be able to improve the solution times with

tactics to tighten these initial bounds. One suggestion would be to start with a set ofbounds that are generated by application of a simple "max-latching" heuristic such as

described in [13] (for the case of span restorable design). Max-latching always produces a

feasible but over-capacitated reserve network, which may be suitable for use as a set of

upper bounds span spare capacities in the AMPL models.

Stub release: Figure 10 illustrates how the surviving stub segments of the failed paths

are detected for generation of the 0sij

stub release quantities in the above formulation. In

the non-joint case these can be handled as a set of computed parameters, as shown in the

AMPL model above. In the jointly optimized case the stub release quantities and all the

associated working path routing indicators become additional variables in the problem.

How the stub-release quantities are detected / generated

O D

Relation r

Route q

Failure span i

Other span j Working flow g r,q

,

1r q

j =

, 1r qi =

Span j enjoys a stub release credit

of spare capacity = g r,q for any failureon span i such that:

, ,( 1) ( 1)r q r qj i true = = =I

Figure 10: How stub release following failure generates free spare capacity to include in

the restoration problem.


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20

References

[1] Telecommunication Network Planning, B.Sanso, P. Soriano (editors), Kluwer

Academic Publishers, 1999, pp. 169-200.

[2] D.A. Dunn, W.D. Grover, M.H. MacGregor, A comparison of k-shortest paths and

maximum flow methods for network facility restoration, IEEE Journal on Selected

Areas in Communications, Jan. 1994, vol. 12, no. 1, pp. 88-99.

[3] R.R. Iraschko, W.D. Grover, A Highly Efficient Path-Restoration Protocol for

Management of Optical Network Transport Integrity,IEEE Journal on Selected Areas inCommunications, vol.18, no.5, May 2000, pp. 779-794.

[4] M. Herzberg and S. J. Bye, "An Optimal Spare-Capacity Assignment Model for

Survivable Networks with Hop Limits",IEEE GLOBECOM '94, 1994.

[6] R. R. Iraschko, M. H. MacGregor, W. D. Grover, "Optimal Capacity Placement for

Path Restoration in STM or ATM Mesh-Survivable Networks",IEEE/ACM Transactions

on Networking, Vol. 6, No. 3, pp. 325-336, June 1998.

[11] M.H. MacGregor, W.D. Grover, Optimized k-shortest paths algorithm for facility

restoration, Software - Practice & Experience, Vol. 24(9), Wiley & Sons, Sept. 1994,pp.823-834.

[12] W.D. Grover, Self-organizing Broad-band Transport Networks,Proceedings ofthe IEEE: Special Issue on Communications in the 21st Century, vol. 85, no.10, October

1997, pp. 1582-1611.

[13] W.D. Grover, V. Rawat, M. MacGregor, A Fast Heuristic Principle for Spare

Capacity Placement in Mesh-Restorable SONET / SDH Transport Networks,

Electronics Letters, vol.33, no.3, Jan. 30, 1997, pp.195-196.


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Appendix A:

The joint span-restorable mesh design

process


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22

Overview of the files and programs involved

Netname.snf

Netname.ptp

Netname.cst

JointSpanDATprepNetname.dat

Netname..hpd

Netname.hpr

AMPL

Netname.MPS

CPLEX

Figure A1: Relationships of files and programs for a jointly optimized mesh capacity

design

Format and Function of SNF, PTP, and CST input files

Format of Standard Network Interface File (SNF)

Example:

Date: 1 July 2001

File Name: TopoTrial2.snf

Network: Netname

Program: This SNF file was created by hand as an input file for

JointSpanDATprep

Node Xcoord Ycoord

1 42.6525 73.76

2 33.7489 84.38

3 30.2669 97.742

4 39.2903 76.61

5 42.3583 71.06

6 42.8864 78.87

7 35.2269 80.84

.... (etc)


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50 40.7608 111.9

51 38.6272 90.2

52 41.0533 73.54

53 36.3361 102.07

54 27.9472 82.46

55 42.45 80.02

56 39.7458 75.54

Span NodeA NodeB Distance Working Spare

1 21 44 490 0 0

2 44 31 112 0 0

3 31 47 11 0 0

4 47 48 54 0 0

5 48 21 481 0 0

6 49 50 1205 0 0

7 49 39 200 0 0

8 39 44 667 0 0

9 21 22 406 0 0

10 22 50 500 0 011 13 50 653 0 0

..... (etc)

53 26 1 225 0 0

54 1 5 206 0 0

55 5 41 47 0 0

56 41 16 72 0 0

57 16 52 79 0 0

58 52 30 48 0 0

59 30 29 11 0 0

60 29 40 40 0 0

61 40 36 50 0 0

62 36 56 28 0 0

63 56 4 74 0 064 4 12 39 0 0

66 30 12 322 0 0

Format of Point-to-Point Demand File (PTP)

171

0 1 2 2

1 1 3 2

2 1 4 1

3 1 5 34 1 6 2

5 1 7 1

6 1 8 1

7 1 9 1

8 1 10 2

9 1 11 2

10 1 12 3

.... etc

164 15 19 1

165 16 17 12

166 16 18 15

167 16 19 7


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168 17 18 11

169 17 19 12

170 18 19 9

Format of Span Cost File (CST)

span unitcost fixedcost

1 490 0

2 112 0

3 11 0

4 54 0

5 481 0

6 1205 0

7 200 0

8 667 0

9 406 0

10 500 0

11 653 012 33 0

13 93 0

14 360 0

15 942 0

16 364 0

17 573 0

18 207 0

19 291 0

20 256 0

....

55 47 0

56 72 0

57 79 058 48 0

59 11 0

60 40 0

61 50 0

62 28 0

63 74 0

64 39 0

Generating the AMPL DAT file for the problem

The usage of program JointSpanDATprep is:

JointSpanDATprep NetName MinWRoute MinRRoute

where : "NetName" is the project name of the network for which the span-restorable

design is being generated. MinWRoute is the minimum number of eligible workingroutes to be generated for each demand pair . MinRRoute is the minimum number of

eligible restoration routes to be generated for each span failure. Default values are 10 and

20, respectively.


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Program JointSpanDATprep automatically uses NetName to identify and open its

corresponding input files: NetName.snf, NetName.ptp, and NetName.cst which should be

prepared the respective file formats documented elsewhere in this Appendix. The

NetName.* files may be placed in the same directory as the instance of programJointSpanDATprep.exe that is being run, in which case no specification has to be

given. More generally the NetName.* files can be in any directory as long as the path is

given in the command line, as in the example below.

Program JointSpanDATprep also uses the keyword NetName to create output filesNetName.dat, NetName.hpr, and NetName.hpd. NetName.dat is the main output- the AMPL

DAT file to go with AMPL model file JointSpanMesh.mod. Ancillary output files

NetName.hpr and NetName.hpd document the restoration route hop-limits used for each span

failure and the working route hop-limits used for each demand pair, as required to

satisfy the MinRRoute and MinWRoute specifications when calling JointSpanDATprep.

Example:

If compiled as an executable for Windows or NT you could use the following command

line:

JointSpanDATprep.exe C:\directory\subdirectory\Netname 5 15

where files Netname.snf, Netname.ptp, and Netname.cst are present in

C:\directory\subdirectory\). The program will then create the appropriate output

files in the same directory. If you don't enter any path then it will perform all of its

operations in whatever directory JointSpanDATprep.exe resides.

Documents

How to Design Mesh-restorable Networks V1