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Understand p -Cycles, Enhanced Rings, and Oriented Cycle Covers. Wayne D. Grover TR Labs and University of Alberta Edmonton, AB, Canada web site for related papers etc: http://www.ee.ualberta.ca/~grover/ ICOCN 2002, November 11-14, Singapore. Outline. What are p- Cycles ?

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understand p cycles enhanced rings and oriented cycle covers

Understand p-Cycles, Enhanced Rings, and Oriented Cycle Covers

Wayne D. Grover

TRLabs and University of Alberta

Edmonton, AB, Canada

web site for related papers etc: http://www.ee.ualberta.ca/~grover/

ICOCN 2002, November 11-14, Singapore

  • What are p- Cycles ?
    • Why do we say they offer “mesh-efficiency with ring-speed ?”
  • Why are p-cycles so efficient ?
  • Comparison to rings and “enhanced rings”
  • Comparison to orientedcycle-covering techniques
the context
The context
  • The domain for all that follows is the problem of network protection at the transport capacity layer.
  • i.e….
    • Layer 3 inter-router lightwave channels
    • OBS-service layer working channels
    • Direct transport lighpaths
    • any other services or layers employing lightwave channels or paths

All these sum to produce a certain number of working lightwavechannels on each span

Philosophy:Protect the working capacity directly and it doesn’t matter what theservice type is

rings fast but not capacity efficient
Rings... Fast,

but not capacity - efficient

upsr animation
UPSR Animation...

Working fibre


Tail-end Switch



Protection fibre




upsr oppr line capacity requirement
UPSR (OPPR)...line capacity requirement

A -> B


  • Consider a bi-directional demand quantity between nodes A, B: dA,B.- A to B may go on the short route- then B to A must go around the longer route
  • Thus, every (bi-directional) demand paircircumnavigates the entire ring.
  • Hence in any cross section of the ring,we would find one unidirectional instanceof every demand flow between nodes of the ring.
  • Therefore, the line capacity of the UPSRmust be:



B -> A



“ The UPSR must have a line rate (capacity) greater (or equal to)the sum of all the (bi-directional)demand quantities between nodes of the ring. “

4 fiber blsr or opsr
(4 fiber) BLSR…(or OPSR)

Working fibres





Protection fibres





blsr opsr line capacity requirement
BLSR …(OPSR) line capacity requirement
  • both directions of a bi-directional demand can follow the short (or long) route between nodes
  • “Bandwidth reuse”
  • The line capacity of the BLSR must be:

A -> B


B -> A





“ The BLSR must have a line rate (capacity) greater (or equal to)the largest sum of demands routed over any one span of the ring. “

a particular issue in multi ring network design
A particular issue in multi-ring network design...

Example of 3 (of 7) rings from an optimal design for network shown

Ring 8

Ring span overlaps

Ring 6

Ring 7

Ideally, BLSR-basednetworks would be 100% redundant.

Span overlaps and load imbalances mean in practice they can be up to 300% redundant

Mesh... Capacity - efficient ,

but (traditionally argued to be) slower,

and have been hampered by DCS / OCX port costs

concept of a span link restorable mesh network

span cut

30% restoration

70% restoration

100% restoration

Concept of a span- (link-) restorable mesh network

(28 nodes, 31 spans)

basics of mesh restorable networks

span cut

40% restoration

100% restoration

70% restoration

Basics of Mesh-restorable networks

(28 nodes, 31 spans)

basics of mesh restorable networks1
Basics of Mesh-restorable networks

Spans where spare capacity was shared

over the two failurescenarios ? .....

This sharing efficiency increases with the degree of network connectivity

“nodal degree”

p cycles fast and capacity efficient

Now we also have “ p-cycles “..

“ p-cycles “..



capacity efficient ....

protection using p cycles
Protection using p-cycles

If span i fails,p-cycle j provides one unit of restoration capacity



If span i fails,p-cycle j provides two units of restoration capacity



optimal spare capacity design typical results

i.e., “mesh-like” capacity

Optimal Spare capacity design - Typical Results
  • “Excess Sparing” = Spare Capacity compared to Optimal Span-Restorable Mesh
corroborating results cost239 european study network
Corroborating Results: COST239 European Study Network
  • Pan European optical core network
  • 11 nodes, 26 spans
  • Average nodal degree = 4.7
  • Demand matrix
    • Distributed pattern
    • 1 to 11 lightpaths per node pair (average = 3.2)
  • 8 wavelengths per fiber
  • wavelength channels can either be used for demand routing or connected into p-cycles for protection












corroborating results
Corroborating Results...

See: Schupke et al… ICC 2002

Schupke found p-cycle WDM designs could have as little as 34%redundancy for 100%span restorability

understanding why p cycles are so efficient
Understanding whyp-cycles are so efficient...


p-Cycle…with same spare capacity


Working Coverage

9 Spares cover 29 working on 19 spans

9 Spares cover 9 Workers

“the clam-shell diagram”

efficiency of p cycles
Efficiency of p-Cycles

(Logical) Redundancy =

2 * no. of straddling spans + 1* no. on-cycle spans


no. spans on cycle


7 spans on-cycle,

2 straddlers :

7 / ( 7 + 2*2) = 0.636

Limiting case: p-cycle redundancy = N / ( N 2 - 2N)

the unique position p cycles occupy
The Unique Position p-Cycles Occupy

Path rest, SBPP

p -cycles: BLSR speedmesh efficiency


Span (link)rest.

200 ms


“50 ms”


50 %

100 %

200 %


summary of important features of p cycles
Summary of Important Features of p-Cycles
  • Working paths go via shortest routes over the graph
  • p-Cycles are formed only in the spare capacity
  • Can be either OXC-based or on ADM-like nodal devices
  • a unit-capacityp-cycle protects:
    • one unit of working capacity for “on cycle” failures
    • two units of working capacity for “straddling” span failures
  • Straddling spans:
    • there may be up to N(N-1)/2 -N straddling span relationships
    • straddling spans each bear two working channels and zero spare
  • Only two nodes do any real-time switching for restoration
    • protection capacity is fully preconnected
    • switching actions are known prior to failure
and how they differ from p cycles

Another recent development:

--> “Enhanced Rings”

..and how they differ from p-cycles

to understand enhanced rings consider
To understand “enhanced rings..”consider

If the fill level of the two “working fibers” at the span overlap is 50% each then the overall LA-SLC arrangement is 300% redundant !

i.e., (total protection + unused working) _________________________

used working

enhanced rings
“Enhanced” rings...

Idea is to allow the two “facing” rings to share switched access to a single common protection span.

So, the cross-sectional view becomes:c

Now, redundancy = 2 / 1 = 200%

is an enhanced ring the same as a p cycle
Is an enhanced ring the same as a p-cycle ?...
  • No, because there is still a requirement for at least a matching amount of working and protection capacity on every span.
  • In other words protection is still only provided and used in the “on-cycle” ring-like type of protection reaction.
  • In contrast if the same problem is addressed with p-cycles, the troublesome span can be treated as:

no protection fibers at all on straddling span:

redundancy = 1 / 1 = 100%


no need to equip two working fibers if load does not require protection:

redundancy ~ 0%

oriented cycle double covers

Another recent approach to reduce undesirable span overlaps in ring-based network design ...

Oriented cycle double-covers

bi directional cycle covers
Bi-directional Cycle Covers
  • Consider the problem of “covering” all spans at a node with conventional bi-directional rings, without causing a span overlap...

At an even degree node…there is no problem

Even-degree node Odd degree node

bi directional cycle covers1
Bi-directional Cycle Covers
  • Now consider the same problem of covering at an odd-degree nodec

At an odd degree node…no bi-directional ring cover exists that does not involve a span overlap

Even-degree node Odd degree node

but with unidirectional oriented cycle covers
But with Unidirectional (Oriented) Cycle Covers

…you can always cover both even and odd nodes without the equivalent of a ring span overlap...

examples of undirectional ring covers...

Even-degree node Odd degree node

(A mirror image set providesbidirectional W,P)

The unidirectional ring coveravoids any double-coverage !

Equivalent to the bidirectional cover

so are oriented cycle covers the same as p cycles
So are Oriented Cycle Covers the same as p-cycles ?
  • No…because they still only protect in an on-cycle way.
  • The result is to get to ring-protection at exactly the 100% redundancy lower limit.
  • In an optimum oriented cycle cover every span will have exactly matching working and protection fibers.
  • P-cycles involve spans that have 2 working and zero protection fibers, which will never be found in an oriented cycle cover.
  • p-Cycles offer a promising new option for efficient realization of network protection
    • are preconfigured structures
    • use simple BLSR-like realtime switching
    • but are mesh-like in capacity efficiency
  • Other recent advances can be superficially confused with p-cycles:
    • enhanced rings reduce ring network redundancy by sharing protection capacity between adjacent rings
    • oriented cycle (double) covers adopt a undirectional graph cycle-covering approach to avoid span overlaps
  • Neither involves straddling spans; spans with working but no spare capacity
    • Both aim to approach their lower limits of 100% redundancy from well above 100%
    • p-cycles are well below 100% redundancy