Aalborg Universitet
Restoration mechanism for the N2R Topological Routing Algorithm
Gutierrez Lopez, Jose Manuel; Pedersen, Jens Myrup; Cuevas, Ruben; Madsen, Ole Brun
Published in:
Seventh International Conference on Networking, 2008. ICN 2008
DOI (link to publication from Publisher):
10.1109/ICN.2008.43
Publication date:
2008
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Gutierrez Lopez, J. M., Pedersen, J. M., Cuevas, R., & Madsen, O. B. (2008). Restoration mechanism for the
N2R Topological Routing Algorithm. In Seventh International Conference on Networking, 2008. ICN 2008 IEEE.
https://doi.org/10.1109/ICN.2008.43
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Restoration Mechanism for the N2R Topological Routing Algorithm
Jose M. Gutierrez
Department of Electronic Systems
Aalborg University
jgl@es.aau.dk
Jens M. Pedersen
Department of Electronic Systems
Aalborg University
jens@es.aau.dk
Ruben Cuevas
Departamento de Telem
´
atica
Universidad Carlos III de Madrid
rcuevas@it.uc3m.es
Ole B. Madsen
Department of Electronic Systems
Aalborg University
obm@es.aau.dk
Abstract
The topological routing over N2R structures has been
studied and implemented using different techniques. An
implemented algorithm achieves good performance and a
restoration mechanism has been added to the algorithm to
obtain higher reliability. This paper introduces the concept
of restoration, when failures occurs, being able to reroute
the packets to the destination when the main path is not
available. The goal is prove that there is an easy and ef-
ficient method for restoration in case of a failure of any el-
ement.
1 Introduction
Topological routing is an alternative to traditional rout-
ing methods, based on tables. It allows for very fast restora-
tion, and is particularly well suited for large-scale commu-
nication where table updates can be time consuming and
introduces significant overheads. Topological routing is un-
derstood as follows:
At a given address scheme, from any node any packet can
be routed given only knowledge of the addresses of the cur-
rent node and the destination node, with no routing tables
involved [1].
Several studies has demonstrated the potential of N2R
networks for a degree three structure [2] and the feasibil-
ity of topological routing on many different regular topolo-
gies [1], [3] and [4] (Grid and Honeycomb), including N2R
[5], [6] and [7]. The N2R topology and the previous stud-
ies are explained and summarized in the following Section
2. The N2R (Network with 2 Rings) structure is a type of
generalized Double Ring structure, where inner ring links
do not physically interconnect neighbor nodes.
Future networks will demand better characteristics for
the different services supported. Those characteristics can
be related to reliability and a number of other performance
metrics. Wired networks (such as fibre optic networks) have
the handicap of the possible physical cable cuts which im-
plies the loss of connectivity between nodes [8]. Therefore,
for topological routing being a feasible option for real net-
works, a mechanism against failures is required to achieve
high performance networks capable of supporting future de-
mands. The failure problem has been treated in [7] from the
Path Protection perspective.
This paper treats the failure issue on the topological rout-
ing environment of the N2R networks from a new point of
view, “Path Restoration” [9] and [10]. The goal is to an-
alyze the potential, feasibility and performance of restora-
tion on N2R networks. This method has been successfully
implemented on other topologies with interesting results
(Grid [3], Honeycomb [4]). Restoration basically consist
on, in case of failure, the possibility of automatically rerout-
ing the packets surrounding the failure element to reach the
destination. Due to the more complex structure of the N2R
than the Grid or Honeycomb an algorithm for applying a
restoration mechanism is challenging. The solution must
be simple, so the delay at each node is minimized due to
the routing tasks, and the path obtained should be relatively
short for capacity and performance optimization. A priori,
the main problem to be solved is the avoidance of infinite
loops (the packet is routed forming a loop and is not possi-
ble to reach the destination).
The previous algorithm “Balanced Algorithm” [5] (in-
troduced in Section 2.2) has been modified to apply a
restoration mechanism. The implemented modification is
simulated in order to obtain values of traditional parame-
ters as delay, diameter and average distance to analyze the
potential Structural Quality of Service (SQoS) offered by
this kind of topologies, a number of metrics and properties
related with the logical structure of the network [9]. The
results are compared with other solutions to document the
feasibility, advantages, disadvantages and the potential for
applying this new method.
The structure of the rest of the document is as follows.
Section 2 treats the definitions, the proper notation and pre-
vious studies explanations concerning this topological rout-
ing issue. Section 3 introduces the modification of the pre-
vious algorithm to be able to implement a restoration mech-
anism. In Section 4 the proposed algorithm is simulated
and the results are exposed. Finally, Section 5 presents the
conclusions extracted from this paper.
2 Background
The development of the topological routing on N2R
structures already has some results to start with. Therefore,
this Section exposes the important ideas required to under-
stand the whole concept of this paper. Subsections 2.1 - 2.4
introduce the basic properties of N2R structures, Balanced
Algorithm, failure solutions and Restoration mechanisms:
2.1 N2R Structure
The number of nodes in the N2R structure is any positive
even integer larger or equal to 6. These rings each contain
the same number of nodes (p). Links in the outer ring and
the links interconnecting the two rings can be described in
the same way as the DR structure, but links in the inner ring
are interconnecting node I
i
and node I
(i+q )modp
, where q
is a positive integer. To avoid forming two separated net-
works in the inner ring, q must fulfil gcd(p, q) = 1 (Greatest
Common Divisor), also q is evaluated from 1 to p/2 [2].
2.2 Balanced Algorithm (BA)
The first approach concerning the issue of topological
routing was to implement an algorithm which could route a
packet with no path information as routing tables or headers
containing the complete path from any source to any desti-
nation nodes [6]. A second study proposed several algo-
rithms to improve the results in terms of path distances and
path completion time. The best solution found was named
“Balanced Algorithm” which did not obtain the best results
in path distances nor path completion time but those values
had not a significant difference with the optimal [5]. The
trade off between these two parameters was the best among
the studied and therefore the one used to continue the work.
As a brief explanation, what the algorithm basically does
is to calculate three distances to reach the destination. These
distances are based on the following three types of transmis-
sions: Using the outer ring, the inner ring clockwise or the
inner ring counterclockwise.
The only required information to be able to find these
values is the destination address. The current node address,
p and q is assumed as implicit information at every node.
The shortest of these three possibilities is selected and
the packet is forwarded using the link related to that option.
At the next node the procedure starts all over again until
the destination node is reached. For further information and
deep explanations it is recommended to see [5]. The solu-
tion proposed in this paper for a reliable topological routing
is based on this algorithm.
2.3 Failure Problem
The failure problem concerning N2R topological routing
schemes already has two proposed solutions:
-Pre-calculated paths, this solution is brute force based
and it requires long computational executions. In order to
use the pre-calculated paths, routing tables are required at
every node which implies tables look-up delays. The larger
the network, the longer is that delay. This solution is not
applicable on topological routing.
-Path protection mechanism [7], this solution was imple-
mented for topological routing as the first approach on the
failure protection. When a failure occurs, the algorithm is
capable of rerouting the packets, from the source node, us-
ing an independent path of the original one. For this method
it is required to notify to the source node the unavailability
of the original path to execute the algorithm for the alter-
native path. Therefore, there is a transition time (when a
failure occurs but the source does not know about it yet)
when the network might not be protected.
These two options will be compared with the new pro-
posal of restoration to be able to find the best solution for
the failure problem on these environments.
2.4 Path Restorati on
Path restoration methods have been implemented on dif-
ferent regular topologies topological routing methods [3],
[4], [9] and [10]. This method requires small tables at the
nodes to introduce the failure elements. When a failure oc-
curs, the neighbors of the failure element introduce on their
tables the failure element. When any packet is tried to be
forwarded using that failure element, the path restoration
mechanism is able to reroute the packet surrounding the
failure and the destination can be reached. The failure ta-
bles are very simple and the maximum number of entries is
two. The nodes are degree three, hence, if there are three
neighbor elements failing at the same time, the node is iso-
lated, and there is no need for three entries in the table.
3 Algorithm
The implemented algorithm, capable of supporting fail-
ures by path restoration, is based on the previous BA al-
gorithm. The main goal is to implement a simple mecha-
nism to minimize the routing tasks executed by every node
to minimize the delay. At the same time, the paths obtained,
when failure occurs, should be as short as possible to opti-
mize the capacity of the global network.
The procedure, in principle, is quite simple. The BA al-
gorithm calculates the best link to forward the packets (the
shortest path). The modification consists, when there is a
failure, on calculating the second best link to forward the
packet. This calculation does not imply difficult changes on
the BA and it is based on the same distances described in
Subsection 2.2. The algorithm can be implemented in two
ways:
Separated Algorithms at the failure neighbor, Option
1: The original path algorithm is executed always, even
when there is an entry on the table. If the failure element
in the table is the same as the one calculated for the original
path to forward the packet, the algorithm is executed again
calculating the second best link.
Unique algorithm at the failure neighbor, Option 2:
The restoration algorithm is executed at any node with some
entry on its table. Hence, the two best links are always cal-
culated at this type of nodes, even though there will be oc-
casions when it is not necessary. If the failure element is
not the best link to forward the packet, the best path is not
blocked, and the calculation of the second link is not neces-
sary.
The two options will be analyzed and discussed in Sec-
tion 4. The result of the two options will be the same path,
but one will be faster than the other, reducing the delay. At
the neighbor nodes of the failure it is possible to reroute the
packet using the incoming link since it might be the best
option. After this point, the packet is not allowed to travel
backwards. At these nodes, also the same issue about how
to apply the restoration method as at the neighbors of the
failure can be discussed. For the moment, without consid-
ering which of the two options is used, the next example,
illustrated in Fig. 1, explains the procedure. The protec-
tion path obtained with the Protection mechanism [7] is pre-
sented as well to discuss some of the differences between
the two techniques.
The restoration path is exactly the same as the original
one until a failure blocks the shortest path (in fact, the same
algorithm is executed). When the original path is blocked,
the second best link is used to forward the packet, to able
to reach its destination. The protection path is quite differ-
ent. The protection path is calculated from the source node,
and it is significantly shorter due to the knowledge from the
source node that the original path is blocked. This protec-
Figure 1. N2R(8,3) example
tion path calculation has two main differences:
1) This method is applicable when the source node
knows about the failure, in the transition time (since the fail-
ure occurs until the source receives the information about
it) it is not possible. The failure notification requires some
managing tasks besides the routing method itself, but the
result gives shorter distances since the path can be modified
from the source and not from the failure point.
2) The algorithm is significantly more complex, the exe-
cution time is double the original BA. The restoration mech-
anism is simpler and faster, in Section 4 the execution times
values obtained for the simulation are presented.
At the time of simulating the algorithm, some problems
were found at specific configurations. The problem is the
commented infinite loops, the packet gets stuck on infinite
loops and is not able to reach the destination. The problem
can be solved by adding some conditions to avoid this loop.
The loops are likely to take place when any of Conditions
(1) or (2) is fulfilled, being F
e
the failure element, N
c
the
current node and O
r
the outer ring. Both conditions include
the locations of the failure, therefore, in these cases, infor-
mation about where the failure is must be included in the
packet, it can be just one flag (1 bit).
p + 1
q
= 0 & F
e
∈ O
r
& N
c
> p (1)
F
e
∈ O
r
& N
c
> p & p > 30 (2)
4 Simulation
The simulation of the algorithm was performed varying
the value of p from 5 to 100 (200 nodes in total) and test-
ing at each of these values all the possible configurations
(possible q values). It is important to mention that the al-
gorithm works for any of these configurations, but for the
graphical representations, only one q is chosen for each p.
These q are the optimal (best result on diameter and average
distance) for the original path obtained at [5]. The proce-
dure is to simulate failures on the nodes and the algorithm
simulates transmissions from all the nodes to all the nodes.
The simulation covers the failure of all the nodes in the net-
work, one at a time, to obtain a deterministic result. When a
node fails, three of the links in the network are unavailable
instead of one when there is a link failure. Therefore, the
nodes failures are studied to give the worse case when an
element fails, important to define the limitations of the net-
work. In real wired networks, the links are more likely to
fail than the nodes, hence, the distance values can be shorter
than the presented ones, but never longer.
The graphs in Figs. 2-5 illustrate the comparison be-
tween the average distances and diameters of the precalcu-
lated paths, protection and restoration option and the exe-
cution time
1
at every node and path completion time of the
protection and restoration mechanisms. All the values rep-
resented correspond to the paths obtained when the shortest
one is not available and the Protection mechanism results
are extracted from [7]. The execution time and path com-
pletion time correspond to the delay caused by the routing
tasks, there are other factors that might have influence on
the delay. These other factors are not included since they
are independent of the routing method, therefore they do
not affect the comparisons treated in this paper.
Figure 2. Diameters
The first of the parameters discussed is the diameter of
the paths (maximum distance between any pair of nodes).
The diameter values are always interesting to define the
limitations of the network. Fig. 2 illustrates the compari-
son between the diameters of the precalculated, protection
and restoration paths. As predicted, the diameter values ob-
tained for the proposed restoration mechanism are longer,
mainly due to the commented fact that there is no path mod-
ification until the failure is reached. Therefore, there is part
of that path that could be found as a waste of resources.
Below, at the completion time analysis, the benefits of this
1
The execution time was obtained under the same conditions as the BA,
since depending on the machine where these algorithms are executed the
result will vary. It is assumed though that the proportion will be main-
tained. The machine used is a Genuine Intel(R) CPU T2050 @1.60 GHz
(2 CPU) and 1GB of RAM. The Software used is PHP and MySQL
Figure 3. Average path distances
Figure 4. Path completion time
mechanism will be discussed. When p > 50 (more than
100 nodes) some peaks can be identified at certain values of
p. These out of proportion peaks are mainly due to a prob-
lematic link decision at the time of routing the packet. The
decision is taken as the second shortest path, the problem is
that this option also includes the failure element. This de-
cision is corrected along the path but with the consequence
of very long distances. This problem can be predicted us-
ing the information about the location of the failure (due
to Condition (2) this information is added to packet so it
does not represent an addition of information) but the al-
gorithm becomes more complex, this modification will be
called “Restoration (fixed)”, included in Fig. 2.
Fig. 3 presents the average distance of the different op-
tions, as the diameter in Fig. 2, and the results are similar
and the same conclusions can be extracted. In this case, the
difference between the Restoration and Restoration (fixed)
is not very significant. To see the effect of the path distances
over the delay, Fig. 4 presents the average path and diam-
eter completion times of the Protection mechanism and the
two Restoration mechanisms. The results are very interest-
ing, the Restoration mechanisms are faster than the Protec-
tion one. This fast execution allows to have lower delays
in transmissions even though the distances are longer. The
only exception is the diameter completion time for those
