1. TRLabs & University of Alberta
p-Cycles
W. D. Grover
TRLabs & University of Alberta
© Wayne D. Grover 2002, -2006

2. Background and Motivation
“ Ring “
A. 50 msec restoration times
B. Complex network planning and growth
C. High installed capacity for demand-served
D. Simple, low-cost ADMs
E. Hard to accommodate multiple service classes
F. Ring-constrained routing
“Mesh”
G. Up to 1.5 sec restoration times
H. Simple, exact capacity planning solutions
I. well under 100% redundancy
J. Relatively expensive DCS/OXC
K. Easy / efficient to design for multiple service classes
L. Shortest-path routing
“ Shopping list” : A, D, H, I, L (and K) please...keep the rest

3. Relative Characteristics of Known Schemes
1+1 APS, Rings
100% redundancy: “the dividing line”
Capacity Redundancy
p-Cycles
Mesh Span Restoration
Shared Backup Path Protection (SBPP)
True Mesh Path Restoration
Restoration Times

4. p-Cycles

5. p-Cycles - an “on-cycle” failure
loopback
Reaction to an “on-cycle” failure is logically identical to a unit-capacity BLSR loopback reaction
“on-cycle” spans have both working and spare capacity like a BLSR

6. p-Cycles - a “straddling span” failure
Break-in
Reaction to a straddling span failure is to switch failed signals onto two protection paths formed from the related p-cycle
Straddling spans have two protected working signal units and have no spare capacity

7. How much difference can this make ?x2
A lot !
Re-consider the example:
It consumes 13 unit-hops of spare capacity
It protects one working signal on 13 spans and two working on 9 spans
i.e., spare / working ratio = 13 / (13*1 + 9*2 )
= 42%
A fully-loaded Hamiltonian p-cycle reaches the redundancy limit, 1/(d-1)

8. Example of a whole p-cycle network design
Working span capacities arising from one unit of demand on each node-pair: 8 1 5 6 9 4 10 7 3 2 13 11 14
Total working capacity: 158 units

9. Design Solution: 53.8 % overall redundancy
p-Cycle Copies
A 1
B 1
C 1
D 2
E 2
Total: 7
Total protection capacity: 85 units Redundancy: 53.8% Optimal configuration dynamically computable or self-organized

10. ADM-like nodal device for p-cycle networking

11. Summary: 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 based on ADM-like nodal devices
a unit-capacity p-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
-> mesh capacity efficiency
Only two nodes do any real-time switching for restoration
protection capacity is fully pre-connected
switching actions are known prior to failure
-> BLSR speed
“pre-configured protection cycles”  p - cycles

12. p-Cycle Capacity Design
If span i fails, p-cycle j provides one unit of restoration capacity i j
If span i fails, p-cycle j provides two units of restoration capacity j i

13. Optimal Spare capacity design with p-cycles

14. Basic (non-joint) p-cycle Design Model “p-cycle SCP”
Min cost of spare capacity
P=set of candidate cycles, index j
=1 if span k in cycle j (parameter)
Number of unit copies of cycle j to build as a p-cycle (solution variable).
xij =1 if span i on-cycle to cycle j.
xij =2 if span i straddles cycle j.
xij =0 if neither of above.

15. AMPL Model to Implement p-Cycle SCP (1)
# p-cycle SCP IP Model for AMPL - Version December-2001 by John Doucette
# Copyright (C) 2001 TRLabs, Inc. All Rights Reserved.
# This is an AMPL model for determining the minimum-cost p-cycle network design.
# This model optimizes p-cycles only... working capacity is provided as inputs.
# SETS
#****************************
set SPANS; # Set of all spans.
set CYCLES; # Set of all candidate cycles.
# PARAMETERS
param Cost{j in SPANS}; # Cost of each unit of capacity on span j.
param Work{j in SPANS}; # Number of working links placed on span j.
param Xpi{p in CYCLES, i in SPANS} default 0;
# Number of paths a single copy of cycle p provides for restoration of failure of span i (2 if straddling span, 1 if on-cycle span, 0 otherwise).
param pCrossesj{p in CYCLES, j in SPANS} := sum{i in SPANS: i = j and Xpi[p,j] = 1} 1;
# Equal to 1 if cycle p passes over span j, 0 otherwise. i.e. if Xpi[p,j] = 1, then cycle p crosses span j.

16. AMPL Model to Implement p-Cycle SCP (2)
Continued…..
# VARIABLES
#****************************
var p_cycle_usage{p in PCYCLES} >=0 integer, <=10000; # Number of copies of p-cycle p used.
var spare{j in SPANS} >=0 integer, <=10000; # Number of spare links placed on span j.
# OBJECTIVE FUNCTION
minimize sparecost: sum{j in SPANS} Cost[j] * spare[j];
# CONSTRAINTS
subject to full_restoration{i in SPANS}: Work[i] <= sum{p in PCYCLES} Xpi[p,i] * p_cycle_usage[p];
subject to spare_capacity_placement{j in SPANS}: spare[j] = sum{p in PCYCLES} pCrossesj[p,j] * p_cycle_usage[p];

17. Optimal Spare capacity design - Typical Results
“Excess Sparing” = Spare Capacity compared to Optimal Span-Restorable Mesh
i.e., “mesh-like” capacity

18. Understanding why p-cycles are so efficient...
Spare
p-Cycle …with same spare capacity
UPSR or BLSR
Working Coverage
9 Spares cover 29 working channels on 19 spans
9 Spares cover 9 Workers
“the clam-shell diagram”

19. Further comparing p-cycles to rings

20. A Priori p-Cycle Efficiency: AE(p)
AE (p) measures a cycle’s potential to provide protection relationships for working channels
SC,p = # on cycle
SS,p = # straddlers
ci = unit cost of i
Xp,i = 1 if on cycle
Xp,i = 2 if straddler
SS,p = 3
SC,p = 9
AE(p) = 1.67
SS,p = 4
SC,p = 10
AE(p) = 1.80

21. Demand-weighted p-Cycle Efficiency: Ew(p)
Ew(p) measures a cycle’s actual efficiency in providing protection relationships for uncovered working channels
Xp,i = 1 if on cycle
Xp,i = 2 if straddler
wi = working on i
ci = unit cost of i 1 3 2 4
AE(p) = 1.67
Ew(p) = 1.56 1 3 2 4
AE(p) = 1.67
Ew(p) = 1.44

22. Self-organization of the p-cycles ...
p-cycles certainly could be centrally computed and configured.
based on the preceding formulation
However, an interesting option is to consider if the network can adaptively and continually self-organize
- a near-optimal set of p-cycles within itself,
- for whatever demand pattern and capacity configuration it currently finds.

23. Self-organization of the p-cycles
Based on an extension / adaptation of SHN™ distributed mesh restoration algorithm
“DCPC” = distributed cycle pre-configuration protocol
Operates continually in background
Non-real time phase self-organizes p-cycles
Real time phase is essentially BLSR switching
p-cycles in continual self-test while in “storage”
Centralized “oversight” but not low-level control
Method is autonomous, adaptive
Networks actual state on the ground is the database

24. Key concepts of DCPC protocol
Node roles:
Cycler node state , Tandem node state
DCPC implemented as event-driven Finite State Machine (FSM)
Nodal interactions are (directly) only between adjacent nodes
Indirectly between all nodes (organic self-organization)
via “statelets” on carrier / optical signal overheads
Three main steps / time-scales / processes
Each nodes act individually, “exploring” network from its standpoint as cycler node.
All nodes indirectly compare results
Globally best p-cycle is created

25. Overview of DCPC protocol

26. How DCPC discovers “best p-cycles” (2)

27. How DCPC discovers “best p-cycles” (1)

28. DCPC Performance studies

29. Illustrating the Real time phase

30. Adapting p-cycles to the IP-layer …

31. IP Network Restoration
IP Networks are already “Restorable”
Restoration occurs when the Routing protocol updates the Routing Tables
This update can take a Minute or more - Packets are lost until this happens
Speed-up of IP Restoration is needed
Not losing packets would be great too
Also some control over capacity / congestion impacts needed
p-cycles proposed as “fast” part of a fast + slow strategy that retains normal OSPF-type routing table re-convergence
dfsdf

32. Span versus Node Restoration Restoration Layer-Strategy Choice
Unavailability of Spans/Nodes in the Different Layers
Feasibility of IP Restoration in the Different Layers

33. IP p-Cycle Properties p-Cycles are Virtual Circuits
Consume Zero Capacity until used
Well suited to MPLS-like Emerging Standards
p-Cycles are Pre-planned
Centrally or Distributed (~DCPC)
Designed prior to Failure
At Failure, a p-Cycle requires no time to Setup or Use
p-Cycles can restore Node and Span Failures

34. IP-layer p-cycles
Network setup: logical p-cycle establishment in routing tables.
p-cycles are established as “virtual circuits” using MPLS or a small number of “reserved” IP addresses
(2) Real-time phase: nodal p-cycle behavior:
encapsulation,
deflection,
re-introduction

35. Operation of IP-layer p-cycles
Insertion of an IP packet into a p-cycle
If the packet’s normal routing table entry indicates forwarding into a now-dead port, encapsulate the packet with the “p-cycle address” for dead neighbour router, route encapsulated packet (I.e, into p-cycle)
The IP packet is encapsulated in a p-cycle packet and routed along the p-cycle

36. Operation of IP-layer p-cycles
IP Packet
Routing Table
p-Cycle Packet Encapsulation
p-cycle Packet

37. Operation of IP-layer p-cycles
Insertion of an IP packet into a p-cycle…
The p-cycle packet packet contains the IP packet two new fields:
The ID of the p-cycle on which the packet belongs
The cost of the original pre-failure path for the IP packet

38. Operation of IP-layer p-cycles
Router Processing of a p-cycle packet arrival
(a) the router checks if it has a routing entry (with a functional port) for the encapsulated IP packet’s destination;
if no, continue the packet along the p-cycle
(b) If yes to (a), test ;
is cost of local “continuing route” option >= cost in p-cycle packet (I.e., from the encapsulation point);
If yes, continue along the p-cycle.
If no, remove the IP packet from the p-cycle packet and route it “normally” from this node.

39. Operation of IP-layer p-cycles
Failed Link
Router
Data De-Encapsulation
Data Encapsulation
p-cycle
(a) On-Cycle Failure (1 restoration Path)
(b) Straddling Failure (2 Restoration paths)

40. Capacity Planning for Span Restoration with p-cycles
Integer Program Formulation
chooses a set of p-cycles to restore all Span failures
Failed working demands may be re-routed over all available p-cycles
User-defined input constraint on number of p-cycles in the design
Objective: Minimize the Max Restoration-induced total flow on any span (i.e., min (max (oversubscription))
subject to:
The maximum over-subscription is over all Span Failures
Every span failure is “covered”
Hop count limit is respected
Design limiting number of p-cycles

41. Illustrating restoration-induced “over-subscription” of capacity
9/12
3/6
Pre-Failure flow
4.5/6
10.5/12
“Straddling” Failure Flow lost = 3
Split 1.5 units each way around p-cycle
Max subscription = 10.5/12 = 0.875
12/6
“On-Span” Failure Flow lost = 9
9 units around p-cycle
Max (over-) subscription = 12/6 = 2
Installed capacity

42. Some sample results Integer Program design results
Run in “Bellcore” network
Minimally provisioned to be fully mesh- span restorable

43. Sample Result
This set of five p-cycles producing  20% over-subscription for any IP span restoration
Allowed 15 design p-cycles,  max over-subscription goes to  2%

44. Router Failure Restoration using “Node-Encircling” p-Cycles
Node Encircling p-Cycles. Each Node has a p-Cycle dedicated to its failure
For each Node, a p-Cycle is chosen which includes all logically “Adjacent” Nodes but not the Protected Node
Other Nodes
Encircled Node
Node-Encircling p-cycle

45. Router Restoration using “Node-Encircling” p-Cycles
Node Failure
p-Cycles are Virtual Circuits/Protection Structures which can redirect Packets around Failures
Plain IP is Connectionless but p-Cycles can be realized with MPLS, IP Tunneling/Static Routes

46. Key concept / extension of basic p-cycles: “node encircling” p-cycles
An “encircling” p-cycle for node k includes all nodes that are logically adjacent (directly connected) to node k but not node k itself.
“Encircling” p-cycles may be visually (graphically) apparent as such, may require a Figure 8, and / or may be non-apparent, I.e., logically, but not graphically encircling.
A special case of “Figure-8’ing” is when the Figure 8 loop is logically required to go down and back the same span, to include one or more degree 2 sites.
The important property is that the encircling structure “intercepts” all transiting flows through the subject node.
Examples of each case follow...

47. Router Restoration using p-Cycles p-Cycle Examples
Simple, Apparent
Simple, Non-Apparent
Non-Simple (Segment)
Non-Simple (Figure “8”)
final demo .....

48. Operation of node-encircling p-cycles
Encapsulate IP
Packet Routing (Pre-Failure)
Path Cost = 3 IP
P-Packet
But …
Failure IP

49. Operation of Node-encircling p-cycles
P-packet continues along p-cycle until the local path cost is less than at entry
At which point the IP packet is “unencapsulated” and routed as usual
1 unit of cost per link
(Infinite) > 3 IP IP
(2) < 3 !
(3) == 3
P-Packet
P-Packet

50. Concluding Comments
p-cycles offer new approaches to both WDM and IP-layer transport
“ mesh-like efficiency with ring-like speed ”
Capacity-planning theory
for 100% span restoration in WDM / Sonet with mesh sparing
for controlled worst-case over-subscription in IP-layer
“Node-encircling” p-cycles
fast integrated restoration against either router or link-failures
Nortel has implemented span-restoration via IP p-cycles
~ 10 msec restoration time, no packet loss in their experiments
Ongoing studies:
Integrated planning of composite node / link restoration p-cycles
Availability analysis of p-cycles