=Paper=
{{Paper
|id=Vol-1830/Paper58
|storemode=property
|title=Computer Network Reliability Analysis of a Dual Ring Network: Federal University of Technology, Minna (Gidan Kwanu Campus) As a Case Study
|pdfUrl=https://ceur-ws.org/Vol-1830/Paper58.pdf
|volume=Vol-1830
|authors=Godwill Udoh,Caroline Alenoghena,Bala A. Salihu
}}
==Computer Network Reliability Analysis of a Dual Ring Network: Federal University of Technology, Minna (Gidan Kwanu Campus) As a Case Study==
https://ceur-ws.org/Vol-1830/Paper58.pdf
International Conference on Information and Communication Technology and Its Applications
(ICTA 2016)
Federal University of Technology, Minna, Nigeria
November 28 – 30, 2016
Computer Network Reliability Analysis of a Dual Ring Network:
Federal University of Technology, Minna (Gidan Kwanu Campus) As a Case Study
Godwill Udoh, Caroline Alenoghena, and Bala A. Salihu
Department of Telecommunication Engineering, Federal University of Technology Minna, Nigeria
godwilludoh@gmail.com-mail,carol@futminna.edu.ng, salbala2000@hotmail.com
Abstract—In the reliability analysis of computer networks Different set of algorithms are employed in reliability
there are different approaches to tackling the task. For dual analysis of computer networks. The algorithms used can be
ring networks, k-terminal reliability is preferred and used in grouped into two:
this work. A concise description of the campus network studied
is given. In this work a reliability analysis of a computer A. Path/Cut Enumeration:
network is done using K-terminal reliability measure to give an
This entails the listing of all the simple paths that exist
index for comparison and define network performance
indicators that affect the reliability of the computer network.
between the end nodes. This represents a complete set of
.In the reliability evaluation, the terminal stations/nodes are favorable non-disjoint events. Simple paths are links in the
seen as to be made up of different critical components and is network that connect set of nodes while prime cut sets are
treated as such. Plots of reliability index against these links in the network which when disconnected cause the
components of the stations show very low values when priority network to fail. The simple paths are considered as sets of
is placed on only one node as is the case in the understudied favorable events while the prime cuts as set of unfavorable
network. Different parameters affect the reliability of the events. Reliability analysis entails summing the terminal
network and are evaluated in the work. reliabilities of these paths which is an indication that each
node communicates with a designated node. To obtain the
Keywords-reliability analysis; computer network; reliability computer network reliability, the inclusion-exclusion
index; network reliability; k-graphs; dual rings techniques of path and cuts is carried out. Boolean algebra
also offers efficient techniques that can be used to do this.
B. Case analysis:
I. INTRODUCTION Case analysis uses the method of graph decomposition.
Present day communication is centered on computer This entails the creation of subsets from the pathsets, either
networks, thus, the design of reliable computer networks is around a reference edge or around a number of
much needed. Reliability analysis of a computer- edges/links/paths. A reference edge is simply the node from
communication network gives “worthiness test” of the which the factoring is referenced. When more than one edge
infrastructure or relevant components that constitute the is considered, graph decomposition is restricted to a
computer network and as such, seeks to evaluate the conservative policy as against an exhaustive one. Using a
relevance of the computer network to its intended design conservative policy minimizes the number of disjoint events
expectations.In evaluating the relevance of a computer in the analysis. Disjoint events are simple paths that are not
network, service indicators like Quality of Service (QoS) connected or have common node. This decomposition
often come into consideration. Reliability is a prominent simplifies the analysis and helps cancel out occurrence of
index in achieving high QoS performances of parallel links.
telecommunications networks. Effective reliability design
also aids resource managements. Effective reliability design II. REVIEW OF RELATED WORKS
technologies in developed countries employ “end-to-end Most of the works reviewed evaluate the reliability of
reliability” measure. In catering for factors shaping the understudied Networks by the methods of minpaths and
distribution of economic activities, progress process of mincuts. A minpath is the shortest distance/path/ number of
network facilities and disparity of reliability at inter-regional hops between nodes needed to keep them up and
level, “one-to-all” measure is employed in developing communicating while mincut is the smallest break in the
countries link/network that renders the link/network ineffective. An
Most computer network reliability problem is primarily aggregation of paths between nodes is called pathsets while
resolved by calculatingthe probability that some specific set an aggregation of cuts in the network is called cutsets.
of nodes in understudied network can “talk” to one another at As a network enlarges and nodes increase, the number of
a given time. minpaths and mincuts increase exponentially. Effective
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
analysis of these sets needed to keep the network up or down The reliability of a network component is the
via optimization methods help in estimating the reliability of probability that it is operative at any given point in
understudied networks. time.
Genetic algorithm as an optimization tool was used in The Channel Capacity, C, is fixed and C » B (where
evaluating the reliability of networks [1]-[3] [4]. B is the provisioned Bandwidth/Capacity for the
Wei-Chang Yeh [5] in his work used Particle Swarm Network).
Optimization and Monte Carlo Simulation in analyzing the Failure of any electronic component in a station,
pathsetsinorder to evaluate the reliability including the power supply, causes the station to fail
Monte Carlo simulation was also employed in [6] [7] [8] Network reliability does not include the probability
to analyze the pathsets/cutsets inorder to evaluate the for failure of attached hosts since they are external to
reliability understudied network. the understudied communication ssubnetwork.
Wei Hou [9] in his thesis, analyzed the reliability of
networks with software and hardware failures. He developed The components used to define the node in the
models; MORIN – Modelling Reliability for Integrated understudied network are the link, port and station itself. The
Networks and SAMOT – Simplified Availability Modeling station define the system health and caters for power issues
Tool, with which he used in analyzing the Network. in the node. Failure/success probabilities of these component
Boolean reduction technique was also used in evaluating are independent of each other but have an overall effect on
the reliability of understudied network [10] – [14] the state of the node.
Mathematical Analysis are also employed in the The port comprises the transmitter, receiver and the
reliability analysis of networks [15] – [17]. inbound/outbound link used in effecting self-healing when a
An overview of works reviewed shows that little has fault occurs.
been done on reliability analysis of Ring topology networks
(this might be a ripple-effect from the fact that most A. Describing the Understudied Network
computer networks implement the mesh topology for its The School’s campus network understudied (Federal
obvious advantages). University of Technology, Minna; GidanKwanu campus), as
Earlier works seem to use survivability, availability, at time of research has 9 nodes (RAD ETX-1002) and 11
susceptibility, connectivity and reliability interchangeably. terminal stations (RAD ETX-201). All the nodes have a
These mentioned parameters are distinct and a field of study port/Terminal station/leaf that serves the complex they are
on themselves. located. The nodes (which are basically DAS –Dual
Modern communication networks are made up of reliable Attachment Station) form the backbone of the network. The
components and failed components are quickly repaired. terminal stations or leafs on the branches are basically SAS –
Multiple connections which allow for rerouting of messages Single Attachment Station. The Campus Network is a Dual
in the event of a network failure is also a common feature. Core, full-Duplex, Bi-directional Ring Network. For the
With the afore-stated in mind, it is important to take into purpose of analysis, we are considering it as a dual ring
account the connection ports, links and state of the nodes network having 9 DAS as nodes. We implement the K-
(this should cater for issues of power supply, equipment Terminal Reliability measure in evaluating the reliability of
malfunctioning and working environment) in the reliability the dual ring.
analysis of computer networks.
B. K –Terminal Reliability
A good index for measuring the utilization of a computer
network reflects the fact that network usually fails gradually
III. MODELING THE NETWORK
and that some nodes and/or links are more important than
Models used to describe computer networks help to others. The measure also should not be based on traffic
define a frame in which the network could be studied. From patterns. Terminal, “capacity-related”, and “travel-time
papers researched, the common model used for Computer related” reliability measures are possible measures that
Network is the Stochastic Model. satisfy the stated prerequisites.
A stochastic network [18] describes a physical system in Terminal Reliability is the probability that there is an
which each node and/or each edge (directed or undirected) end-to-end connection between atleast two nodes in a
fails statistically independently with a number representing computer network needed to keep the network up and
the non-failure probability such that failures of any network running. There are basically 3 variants; K-Terminal, 2-
elements do not affect another network element in same Terminal and All-Terminal Reliabilities.
network. With this model, the network reliability analysis The common measures of reliability problems when
problem consists of measuring the probability given applied to computer networks are mainly specialized cases of
failure/operation probabilities for edges/nodes and the link k-terminal reliability. This is defined as the probability that
connectivity [19]. a path exists which connects k terminals (nodes) within the
In the Reliability analysis of Computer Networks network.Reliability here is gotten by summing the
(especially Ring Networks), the following assumptions are probabilities of disjoint success paths. The complexity of
made (depending on the number of components identifying all disjoint success paths is exponential and as
understudied): such determining K -terminal reliability for a network could
Components are either operative or failed at any be very time-consuming. Most existing researches on K–
given time. Component state is a random event, s, terminal reliability speed up calculations by reducing the
independent of the state of any other component computation efforts as much as possible.
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
C. K – Terminal Reliability of Ring Networks assume that the K stations of interest are sorted in token-
A ring can be defined by a network graph; G = (V, L), passing order and are renumbered with an additional index
whose vertices (V) and directed edges (L) are connected in a from 1 to K. We refer to the station pair (ij) in this
cycle(circuit). The vertices represent nodes and the directed renumbered K element subset as consecutive stations if j =
edges represent fiber path from one NAP (Network (i±𝟏 ) mod K. [24]
Attachment Port) transmitter to another NAP receiver.
Whenthe primary ring is operative, then the vertices and D. K – MEC in Dual Rings
edges comprising the subgraph of these elements are A dual ring has two sets of K-MEC.
traversed exactly once, forming an Eulerian circuit. If a link Set #1 consists a circuit which contains all the stations
or a station should fail on the primary link, it is eliminated and links in the operative primary ring.
from G and self-healing is invoked. Consequently a new Set #2 comprises other circuits that are formed by using
subgraph is formed which comprises operative stations on two consecutive stations of the K given stations;having the
both the primary and secondary links. This constitute the self-healed end stations. Since there are K end-station pairs,
needed Eulerian circuit. The derivedsubgraph provides there are K K-MEC in set #2, making the total number of
communication among operative stations and links in a ring K-MEC in a dual ring K+ 1.
network. It also provide communication among stations that Using the concept of case analysis (stated in
can communicate using the ring network protocol. [20] introduction); we effect graphical decomposition around a
For K stations, at least one component is not in any other single keystone. The keystone chosen here was the node at
K-MEC. Each of its K-MEC (minimal eulerian circuit) is ITS-InfoTech Studies center.
distinct in graph.Edges and vertices in G that are not in these
circuits are irrelevant and contribute nothing to K-terminal
reliability for this subset. The reliability of the ring network IV. COMPUTING THE K-TERMINAL RELIABILITY OF THE
having k nodes, 𝑅𝑘 (G), then becomes the probability that a NETWORK
set of K-MEC is operative. The sum of probabilities of this For K ordinary DAS and K =9
set, using inclusion-exclusion to evaluate the K-terminal Notation
reliability of a ring network containing the set of K-MEC, Ei, P Station Reliability
for i = 1. . . m, is given in equation 1 𝐷𝑙 Link/ Fiber path Reliability
𝐷𝑝 Port Reliability
pr 𝐴 = 𝑖 𝐴𝑖 −𝑖<𝑗 𝐴𝑖 ∩ 𝐴𝑗 + 𝑖<𝑗 <𝑘 𝐴𝑖 ∩ 𝐴𝑗 ∩ ⨁ Addition modulo K
𝐴𝑘 + ⋯ + −1 𝑚 −1 . 𝑃𝑟 𝐴𝑖 ∩ 𝐴𝑗 ∩ 𝐴𝑘 … 𝐴𝑚 𝑡𝑗 ( (𝑡. 𝑥)𝑗 , 0, *), j = 1... K; addresses of the K
(1) stations of interest in a dual ring (These addresses
are sorted in token-passing order on the fault-free
Where Ai is a MEC having i nodes and Aj has j number ring)
of nodes.
From the analysis, a K-graph is derived. A K-graph is a
𝑠𝑗 (( 𝑡. 𝑥)𝑗 ⨁1 - ( 𝑡. 𝑥)𝑗 ⨁𝑘 ).mod N-station-separation
circuit formation containing one or more K-MECand is a distance.
subgraph of G. A particular K-graph can correspond to
several different circuit formations which might have many In order to determine the probability that stations 𝑡𝑗 , j =
repeated terms. Some of these have a positive coefficient 1. . . K, can communicate with each other in a dual ring, the
(−1)𝑘−1 corresponding to an odd number k of K-MEC and noncanceled K-graphs are derived and Pr {Ki} is computed.
some have a negative coefficient (−1)𝑘−1 corresponding to
an even number k of K-MEC in the formation. Statedcircuit
formations are odd or even formations respectively. The A. Case l
combination of these positive and negative coefficients on K-graph 𝐻1 results from circuit formation 𝐹1 and
repeated terms cancels out some of the terms in the final contains all DAS and links on the primary ring. This occurs
expression. The net number of noncanceled terms which is for all K in the noncanceled graphs at k=0 in the derived k-
also the net number of noncanceled K-graphs of type Hi, viz, MEC.
the net number of noncanceled circuit formations is
termedthe domination value 𝑑𝐻𝑖 . To reduce the number of 𝑅𝐷𝑅1 = 𝑝𝑁 . 𝐷𝑙𝑁 . 𝐷𝑝2𝑁 (3)
repeated terms in the final expression we introduce the
denomination value as given in (2). B. Case 2
Pr 𝐴𝑖 = 𝑛
𝑖=1 𝑑𝐻𝑖 . 𝑃𝑟 𝑘𝑖 (2) K-graph 𝐻𝑗 results from circuit formation 𝐹𝑗 , j = 2... K,
and contains all DAS and links connecting the K specific
Where Ki is the K-MEC derived at i stations in both primary and secondary ring segments with
Computational complexity of the decomposition is self-healed end stations 𝑡𝑗 ⨁𝑘 𝑎𝑛𝑑 𝑡𝑗 ⨁1 . This is formed from
dependent on the number of K-graphs in the network. the nodes under consideration in the network.
In order to apply this to the Ethernet ring network
topology deployed in the Campus (FUT MINNA), the 2(𝑁−𝑆𝑗 ) 2(𝑁−𝑆𝑗 +1)
𝑅𝐷𝑅𝑗 = 𝑝𝑁−𝑆𝑗 +1 . 𝐷𝑙 . 𝐷𝑝 (4)
number of K-MEC in each topology is first determined. We
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
C. Case 3
K-graph 𝐻𝑗 +𝑘 results from circuit formation𝐹1𝑗 , j = 2... From [21] [22],
K, and contains: FIT (/109 hours) = 958; hence FR = 958/ 109 = 0.958
−6
x10
all DAS and links connecting the K specific stations
in both primary and secondary ring segments with −6 ×20×365 ×24
self-healed stations 𝑡𝑗 ⨁𝑘 𝑎𝑛𝑑 𝑡𝑗 ⨁1 𝐷𝑡 = 1 − 𝑒 −𝜆𝑡 = 1 − 𝑒 −0.958 x10 =
0.1545123
all DAS and primary ring
2𝑁−𝑆𝑗 𝐷𝑟 = 1 − 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1 − 𝑒 −𝜆𝑡
𝑅𝐷𝑅1𝑗 = 𝑝𝑁 . 𝐷𝑙 . 𝐷𝑝2𝑁 (5)
From [21] [22],
K –terminal Reliability of a dual ring network having N FIT (/109 hours) = 130; hence FR = 130 / 109 = 0.13
= 9 nodes and 1 ≤ 𝑆𝑗 ≤ 8 is obtained by summing the x10 −6
probabilities in cases 1, 2 and 3 after multiplying by the
−6 ×20×365 ×24
appropriate domination coefficient gives [24] 𝐷𝑟 = 1 − 𝑒 −𝜆𝑡 = 1 − 𝑒 − 0.13 x10 =
0.02251858
𝐾+1
𝑅𝐾 (𝐺)𝐷𝑅 = 𝑅𝐷𝑅1 + 𝑗 =2 (𝑅𝐷𝑅𝑗 − 𝑅𝐷𝑅1𝑗 ) (6)
𝐷𝑙 = 𝐷𝑡 . 𝐷𝑟 . 𝐷𝑓𝑙 = 0.99999×0.1545123×0.02251858 =
0.003479
V. RESULTS
From [23],
Applying the above stated equation to the K-graphs for
FIT (/2.92x106 hours) = 1;
the understudied network, we have
1
TABLE I. RESULTS FOR RELIABILITY INDEX COMPUTATION FROM K Hence, 𝐹𝑅 = 𝜆 = = 3.424658x10−7
2.92x10 6
= 1 TO K = 9
Skeleto
Given Rules
This gives the Reliability of the port as 𝐷𝑝 = 1 − 𝑒 −𝜆𝑡
n over a time frame of 20 years as
𝑅1 (𝐺)𝐷𝑅 𝑝9 . 𝐷𝑙9 . 𝐷𝑝18 −7
1 − 𝑒 −𝜆𝑡 = 1 - 𝑒 −3.424658 x10 ×20×365 ×24 = 0.0582354
𝑝9 . 𝐷𝑙9 . 𝐷𝑝18 + 𝑝7 . 𝐷𝑙6 . 𝐷𝑝14
1 − 𝑝2 . 𝐷𝑙1 . 𝐷𝑝4 + 𝑝4 . 𝐷𝑙3 . 𝐷𝑝8 (1
𝑅2 𝐺 𝐷𝑅
− 𝑝 . 𝐷𝑙4 . 𝐷𝑝10 )
5
Readings taken from the campus shows an average of
𝑝 . 𝐷𝑙 . 𝐷𝑝 + 𝑝 . 𝐷𝑙 . 𝐷𝑝14 1 − 𝑝2 . 𝐷𝑙1 . 𝐷𝑝4
9 9 18 7 6
128 failures in 1month; (30×24) hours on the nodes. High
𝑅3 (𝐺)𝐷𝑅 + 𝑝7 . 𝐷𝑙6 . 𝐷𝑝14 1 − 𝑝2 . 𝐷𝑙1 . 𝐷𝑝4 rate of failure here is due primarily to the erratic power
+ 𝑝7 . 𝐷𝑙7 . 𝐷𝑝14 (1 − 𝑝2 𝐷𝑙1 𝐷𝑝4 )
supply in the campus and the absence of working standby
𝑅4 (𝐺)𝐷𝑅 𝑝9 . 𝐷𝑙9 . 𝐷𝑝18 + 2 𝑝7 . 𝐷𝑙6 . 𝐷𝑝14 1 − 𝑝2 𝐷𝑙1 . 𝐷𝑝4 + 𝑝8 𝐷𝑙7 𝐷𝑝16 power banks.
𝑅5 (𝐺)𝐷𝑅 𝑝9 𝐷𝑙9 𝐷𝑝18 + 4{𝑝8 𝐷𝑙7 𝐷𝑝16 }
This gives 30 × 24hours = 128
𝑃𝑟𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 128/ (30 × 24)
𝑅6 (𝐺)𝐷𝑅 𝑝9 𝐷𝑙9 𝐷𝑝18 + 4{𝑝8 𝐷𝑙7 𝐷𝑝16 } P = 1 − 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1 - 128/ (30 × 24) = 0.82222
𝑅7 (𝐺)𝐷𝑅 𝑝9 𝐷𝑙9 𝐷𝑝18 + 2{𝑝8 𝐷𝑙7 𝐷𝑝16 } 1 − 𝑅𝑓𝑎𝑖𝑙𝑢𝑟 𝑒 = 1 − 𝑒 −𝜆𝑡 → 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 𝑒 −𝜆𝑡
𝑅8 𝐺 𝐷𝑅 𝑝9 𝐷𝑙9 𝐷𝑝18 + 𝑝8 𝐷𝑙7 𝐷𝑝16 1 – 0.82222 = 𝑒 −𝜆×20×365×24
𝑅9 (𝐺)𝐷𝑅 𝑝9 𝐷𝑙9 𝐷𝑝18 0.18888 = 𝑒 −𝜆×175200
λ = In 0.18888 ÷ -175200 = 9.512805×10−6
p, 𝐷𝑙 , 𝐷𝑝 are the operative probabilities (and hence,
reliability) of the nodes, links and ports respectively. SAS reliability = 𝐷𝑆𝐴𝑆 = p. 𝐷𝑝 = 0.82222×0.0582354 =
0.04788231
To calculate 𝑝, 𝐷𝑙 𝑎𝑛𝑑 𝐷𝑝 we use
DAS reliability = 𝐷𝐷𝐴𝑆 = p.𝐷𝑝2 = 0.82222×0.05823542 =
1 − 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1 − 𝑒 −𝜆𝑡 (7)
0.002788446
Where 𝜆 the failure rate of the component under Determining the Mean Time before Failure, MTBF,
discussion,𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 is the failure probability of component entails summing the mean time to fail (MTTF) and the mean
and t is the time frame used to understudy the component in time to detect and repair (MTTR) [24]
the link.
The accepted probability for fiber failures in the MTBF = MTTF + MTTR (8)
distribution part of the new ITU-T G.657 proposal document
(in Annex I) is around 1/100000 over 20 years per fiber per
For the equipment in this research (RAD SWITCHES),
network element.
the repair time (actually, negligible since there have been no
This gives 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1/100000=0.00001 faults since their provisioning) is quite small compared to the
𝐷𝑓𝑙 = 1- 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1- 0.00001= 0.99999 MTBF, so this work approximates the MTBF to be equal to
𝐷𝑡 = 1 − 𝑅𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 1 − 𝑒 −𝜆𝑡 the MTTF.
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With the afore-stated and considering the Time frame for
data collection, we assume the average time between power
outages to be the MTBF of the RAD Switches.
MTBF = 1 ÷ (128/ (30×24)) hours
= 1 ÷ 0.178 = 5.625 hours
The average time taken to restore power supply to the
Station via alternate sources is around 15 minutes and supply
by the Generator set lasts about 4 hours.
MTTR = 15 minutes = 15/60 = 0.25hours
Unavailability of the Network, q = MTTR/MTBF = Figure 2. Reliability plot at P negligible
0.25/5.625 =0.0444444
MTBF ≈ MTTF= 5.625 hours
Availability and unavailability are often expressed as
probabilities. For the equipment understudied (RAD
Switches and Fiber Links), all of the failure rates were based
on field data or assumptions that devices of comparable
complexity and exposure should have similar failure nodes.
𝐴 = 𝑀𝑇𝐵𝐹/(𝑀𝑇𝐵𝐹 + 𝑀𝑇𝑇𝑅)= 5.625 / (5.625 + 0.25)
= 0.95744681
For the Optic Fiber Link, cuts/failures are usually due to
excavation or construction works on fiber path and attacks
by rodent. Data gotten from the ITS shows there have been Figure 3. Reliability plot at p, 𝑎𝑛𝑑 𝐷𝑙 negligible
no fiber cut/failure since the provisioning of the facility, and
considering the layout and terrain of the campus, there is
likely to be none for the next 2years.
The RAD Switches employed in the Network design
have not failed since provisioning too. Inoperability of the
devices is due primarily to challenges of erratic power
supply to the Station.
The average time taken to restore power supply to the
Station via alternate sources is around 15 minutes and supply
by the Generator set lasts about 4 hours.
MTTR = 15 minutes = 15/60 = 0.25hours
Figure 4. Reliability plot at 𝐷𝑙 𝑎𝑛𝑑 𝐷𝑝 negligible
Figure 1. Reliability plot at P, 𝐷𝑙 , 𝐷𝑝 Figure 5. Reliability plot at 𝐷𝑝 negligible
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
considered, it will take two nodes of priority for optimal
reliability (Fig 4).
Plot 5: When 𝐷𝑝 𝑎𝑛𝑑𝐷𝑙 is made negligible, the plot pikes
at K = 2 and K = 5 and 6. Optimal values is at K = 5 and 6
approximating one (1). Given that the links (fiber paths) and
ports on network devices (SAS and DAS) have not had any
fault since their commissioning, it is safe to assume their
overall effect on the network reliability is negligible. This
plot (fig 5) aptly describes FUT, MINNA; Gidan Kwanu
Campus Computer Backbone Network. As such it is
imperative to have priorities placed on five or six nodes out
of the nine nodes that comprise the backbone network.
Keeping priority on only one node (ITS), as it is presently,
makes the network very unreliable.
Figure 6. Reliabilit plot at 𝐷𝑙 negligible Plot 6: When 𝐷𝑝 is made negligible, reliability values
peaks at K = 2 (fig 6)
Plot 7: When p and𝐷𝑙 are made negligible, the lot peaks
at K = 4 (fig 7)
Where 𝐷𝑙 𝑎𝑛𝑑𝐷𝑝 are assumed to be 1, as in the case of
the FUT MINNA, GidanKwanu campus network (fig 5), it is
observed that 5 to 6 priority nodes are needed to have
optimal network reliability when the Network reliability is
dependent, primarily, on the station reliability ( as it is with
FUT MINNA, GidanKwanu campus computer backbone
network). . It is observed from all plots that at K = 1 the
network reliability is always minimal. Often in the range of
10−4 and in some cases 10−23 (fig 7).
The value of 𝐷𝑙 - composite link reliability, shows that it
is the weakest and most vulnerable of the parameters in the
understudied network. Hence, adequate protection measures
are needed to maintain its workability.
The value of reliability for DAS which comprises the
Figure 7. Reliability plot at p 𝑎𝑛𝑑 𝐷𝑝 negligible
backbone of the understudied network shows it is very low
and that the attached hosts (consisting of SAS) are more
reliable in the network. This is as a result of epileptic power
supply (𝑝. 𝐷𝑝2 ) and that the DAS are integral in the design of
VI. DISCUSSION OF RESULTS
the network.
Plot 1: The best value for reliability Index is at K = 2. The Mean Time before Failures (MTBF) value of
This plot shows the effect on Reliability Index when all the 5.645hours when compared to tens of hours for average
variables are considered (fig 1) enterprise networks is low.
When we make any parameter defining the node, port The average time taken to restore the network
and/or link to be one, we are assuming a perfect parameter, (0.25hours) is much given that current trend in
making its influence on the Reliability of the Network telecommunications is to limit the range to about 20ms.
negligible. In the computation for node reliability and overall The availability of the network is good, 0.95744681
reliability of the network, the events are independent and as (given it is an academic environment) even though it falls
such making any of the events to be one simply makes its short of the “five-nines” (99.999%) property needed of most
effect negligible. telecommunications networks.
Plot 2: When the effects of p is made negligible, best
values for reliability index is at K = 2. This implies that if the VII. CONCLUSION AND RECOMMENDATIONS
other parameters are considered only as variables,
considering the present network, it will be better to have FUT Minna campus computer backbone Network was
priorities placed on two nodes for optimal reliability values. analyzed and its reliability index was computed to be around
(Fig 2) 0.0007 using the K-Terminal Reliability measure.
Plot 3: When the effects of p and 𝐷𝑙 are made negligible The following outlined recommendations are given:
on the network, reliability values peaks at K = 3. This Future studies on the school’s network reliability
implies that if only the port reliability,𝐷𝑝 is considered, three analysis should go further to incorporate Capacity
nodes are needed to be given priority for optimal network related and travel time measures of reliability. This
reliability. (Fig 3) would answer questions of packet drops, effective
Plot 4: When the value of 𝐷𝑙 – link reliability, is made data throughput and transmission delays.
negligible, the plot peaks at K = 2 for optimal reliability. To improve the network, the station reliability has to
This implies that if only the station and port reliability are be upgraded. For optimal network reliability, priority
225
International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
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