j - AGH University of Science and Technology

12th GI/ITG CONFERENCE ON MEASURING, MODELLING AND 

EVALUATION OF COMPUTER AND COMMUNICATION SYSTEMS 

3rd POLISH-GERMAN TELETRAFFIC SYMPOSIUM 

AVAILABILITY ASSESSMENT OF RESILIENT NETWORKS 

Piotr Chołda*, Andrzej Jajszczyk** 

Department of Telecommunications, AGH University of Science and Technology, 

Al. Mickiewicza 30, 30-059 Kraków, Poland 

*E-mail: cholda@kt.agh.edu.pl 

**E-mail: jajszczyk@kt.agh.edu.pl 

Abstract 

In the paper we present approaches to calculate single connections availability. Approximate 

calculations for the most representative protection topologies as well as for a particular case of 

restoration in MultiProtocol Label Switching (MPLS) are presented and discussed. On this basis some 

simple conclusions concerning the way in which paths should be allocated are drawn. 

Keywords 

Availability, protection, restoration 

1. INTRODUCTION 

The problem of network reliability assurance has been present since the first 

network was built. We propose some methods for the calculation of one of the 

basic and most important reliability measures used by network engineers and 

planners, the availability. It can be used for many different purposes: in general 

network performance evaluation as well as an important factor during the path 

computation phase. In the latter case it could be incorporated in dynamic protocols, 

providing a new important dimension in path computation algorithms. Although it 

is relatively easy to calculate the availability for simple ring networks, exact 

analytical calculations in the case of mesh networks lead to serious difficulties: the 

changing environment caused by routing should be taken into account and the fact 

that the capacity is shared among different connections. These factors hinder the 

enumeration process of probabilistic events related to failures and recovery 

procedures. Therefore, the availability of selected paths and connections, and not of 

the whole network, is usually considered [1].

Piotr Chołda, Andrzej Jajszczyk 

To show how reliability measures are calculated and how to compare different 

recovery procedures, we chose only a few typical protection schemes. We were 

also paying attention to simplicity and transparency of the relevant formulas. We 

can note that there are also other reliability measures, e.g., the reliability 

polynomial for the whole network, down time ratio or average traffic loss. 

However, the availability is the most common measure and can be used both in 

very simple as well as very sophisticated (e.g., the most recent [2]) analyses. 

It is very important to note that many different types of availability are 

defined. Formally, the so called instantaneous availability is defined in terms of the 

ITU-T Recommendation [3] as the probability that an item is in an up state at a 

given instant of time. However, for our calculations we will use the concept of 

asymptotic (steady-state) availability, which means the limit, if such exists, of the 

instantaneous availability when the time tends to infinity. During calculations, it is 

assumed that the failures of the elements are statistically-independent. The 

availability defined in such a way could be understood as an average ratio of time 

in which an item or a connection works properly, to the whole time. 

2. AVAILABILITY OF THE CONNECTION WITHOUT 

PROTECTION 

An unprotected connection consists only of a working path. The recovery 

(alternative) path is not used. The connection is interrupted when any of its 

elements fails. Thus, its availability equals simply an availability of a path on 

which this connection is established. As a path we consider a set of #L links and #N 

nodes through which a signal from an input node (source) to an output node (sink) 

is transmitted. From the reliability standpoint, this is a serial structure, i.e., the 

structure remaining in the operation state only if all of its elements are in the up 

state. Therefore, the availability of a path ( A ) is determined as [4]: 

A 

= 

# L 

∏ 

ALi N j 

A 

P 

× 

# N 

∏ 

A 

P Li 

N j 

i= 

1 j= 

1 

where is the availability of link i; A is the availability of node j. 

3. DEDICATED PROTECTION 

The simplest protection scheme is called dedicated protection or 1+1 

protection. From the reliability point of view it is a parallel-serial structure with hot 

standby, because traffic is carried both through the working and the protection 

paths all the time. The parallel structure means that only if all N paths fail, the 

connection is down. Availability for the parallel structure is calculated according to 

the following formula [5]: 

(1)

Availability Assessment of Resilient Networks 

N 

∏ 

i= 1 

A(parallel item1, …, itemN) = 1 − P (itemi 

= unav) = 1 − ( 1 − A ) (2) 

where P(event) is the probability of an event; ‘unav’ means that an item is 

unavailable; Ai is the availability of item i. 

Therefore, the availability of the whole connection using the 1+1 protection 

( A1+ 

1 ) will be calculated as follows (see Fig. 1): 

ASo ASp 

( ( AP 

)( AP 

) ASw 

A 

1 2 Si 

1 1 1 

A1+ 1 = − − − 

(3) 

where , A are the availabilities of the source and sink node, respectively; 

ASo Si 

APi P2 

is the availability of the first path, and of the second path; , A are the 

availabilities of a splitter and switch, respectively. 

N 

∏ 

i= 

1 

A ASp Sw 

Using the example of a Unidirectional Path-Switched Ring (UPSR), a 

particular case of the 1+1 protection, we present how practically calculate the 

availability. The availability of connections established in some of ring topologies 

is relatively simple to calculate; some effort has already been made [6]. In UPSR 

each pair of nodes is connected by two separate paths. Traffic from the source node 

is transmitted simultaneously in both directions: clockwise on the working path and 

counterclockwise on the protection path. The working path is located on a fiber 

which is different from the fiber carrying the protection path. In the case of any 

working path element failure, the sink node starts to receive the signal from the 

protection path [7]. 

Figure 1. Dedicated protection: reliability block diagram 

If we assume that availabilities of all nodes are equal and each span is of an 

identical length (which means that also availabilities of all spans are equal) the 

availability of a connection between two nodes in UPSR ( A ) is given by the 

UPSR 

following formula (cf. the reliability block diagram shown in Fig. 2): 

A A 1− 

1− 

A 1− 

A A 

( ( )( ) ) = 

UPSR = N 

WP PP N 

k k −1 

n n−1 

⎛ ⎛ 

⎞⎛ 

⎞⎞ 

= ⎜ − ⎜1− 

∏ A S × ∏ AN 

⎟⎜1− 

∏ A × ∏ ⎟ 

⎜ 

S ⎟ 

⎟ 

= 

⎝ ⎝ i= 

1 i= 

1 ⎠⎝ 

i= 

k + 1 i= 

k + 1 ⎠⎠ 

2 A N 1 AN 

2 

= A 

k k −1 1− 

1− 

A A 

n−k 

n−k 

−1 

1− 

A A 

n−k 

n−k 

+ 1 k k + 1 

= A A + A A − A 

N 

n n 

( ( )( ) A 

S 

N 

S 

N 

S 

N 

S 

N 

S 

i 

N 

(4)


where A , , , A are the availabilities of a node, a span, the working and 

N 

AS AWP PP 

the protection path, respectively; k is the number of spans between source and sink 

nodes; n is the total number of spans in the ring. 

The availability function achieves its minimum in the case of the connection 

between the most distant nodes (the nodes which are present at the opposite sides 

of the ring). Fig. 3 illustrates the way the availability is changing depending on the 

length of the protection path ( A A = 99. 

95% 

, n = 16 ). The graph is 

N 

= S 

symmetric: the availabilities calculated for connections which can be characterized 

by span length k equal values calculated for connections with span length n − k . 

It also means that the connection from X to Y has the same availability as the 

connection from Y to X. 

Figure 2. Reliability block diagram for a connection established in UPSR 

Figure 3. A comparison of connection availabilities in UPSR 

4. SHARED PROTECTION 

Except for the 1:1 protection case, that from the reliability standpoint, has the 

same structure as the 1+1 protection, schemes describing shared protection form


non-series-parallel structures (an example: Fig. 4a). For exact calculations, 

methods based on enumeration of probabilistic events should be used. We employ 

a simplified model which reduces all switches to one (see Fig. 4b). Therefore, it 

will be possible to apply calculations for the r-out-of-s reliability structure (i.e., the 

whole system is up if r out of s items are in the operating state). We will calculate 

the availability of the 1:N protection scheme ( ), i.e., for N-out-of-(N+1) 

A 1: 

N 

reliability structure. In such a method one protection path is shared by N working 

paths. For clarity, we disregard unnecessary details such as the source/sink nodes 

availability (as is commonly practiced [8]). The following formula considers the 

only availability of the “parallel” part: 

N N 

N + 1 

N + 1 

⎛ ⎞ 

A ∏ ∑⎜( ) ∏ ⎟ 

1: 

N = Ai 

+ 

⎜ 

1 − Ai 

Aj 

⎟ 

= ∑∏ Aj 

− N∏ 

Ai 

(5) 

i = 1 i= 1 ⎝ 

j≠i 

⎠ i= 1 j ≠i 

i = 1 

where is the availability of path i ( A for the protection path). 

Ai N + 1 

While calculating Eq. (5) we take into account N+1 probabilistic events: one in 

which all of N working paths are in the up state, and N similar events in which one 

(in each event different) of the working paths fails, but all remaining paths 

(including the protection one) are up. The availability calculated according to the 

presented method concerns the probability that the whole protected traffic will be 

carried properly. We have to remember, however, that even if some working paths 

and the protection path fail, the rest of the traffic (i.e., that on working paths in the 

up state) will be transmitted. Therefore, we consider the best case. 

Figure 4. 1:N shared protection: a) exact view of the structure, b) simplified structure


As a numerical example, we compare three different protection topologies: 

three working connections with the same availabilities are to be protected. The 

following schemes are compared: the 1:3 protection; the topology in which each 

working path has its own protection path, it is in fact the 1+1 protection applied 

three times (six paths in total); and the 3:3 protection (three protection paths shared 

by three working paths). The analytical formula for the last case is rather complex, 

so we do not present it here. It is based on the 3-out-of-6 structure. The relevant 

formulas and comprehensive information how to calculate them can be found in 

[9]. The results are presented in Fig 5. We can see that the 1:3 protection results in 

a large increase of the availability in relation to unprotected connections. The gain 

is especially visible in the case when availabilities of the working paths are small 

(even if availabilities of protection paths are relatively low). It is the least reliable 

but the most cost efficient scheme of the three compared. Moreover, from the 

reliability point of view, the most favorable is the 3:3 protection, even better than 

applying the 1+1 protection for each working path separately. The reason is that in 

the case of 3:3 protection the scheme is more flexible. When one of the working 

paths fails, the traffic is rerouted on the protection path. And again, when this path 

fails, the traffic can be rerouted again. It is impossible in the case of the 1+1 

protection. However, we have to remember that the gain is minimal and practically 

such a solution could not be advantageous: it is, after all, necessary to use 

additional switching elements. Some analyses [10] indicate that the influence of 

switching nodes cost on the total expenditure can be quite large. It seems that this 

fact is often neglected and optimization based only on the link cost could be 

insufficient. 

5. RESTORATION 

Unlike in the case of a protection, where an alternative path is established 

before a failure, in the case of the restoration such a path is sought after the fault 

notification. It makes the calculation of the availability more difficult. For example, 

the availability is calculated not for connections, but for carried traffic. Therefore, 

it is called the availability of a load ( A ). The authors of [4] propose the 

following formula for calculating it in a restoration scheme: 

M ⎛ CRec 

⎞ 1 

A = − ∑ ( ) × ⎜ ⎟ 

Load 1 P Sceni 

⎜ 

1− 

⎟ 

(6) 

i= 1 ⎝ CT 

⎠ 

where P ( Sceni 

) is the probability of failure scenario i (out of M scenarios); C T is 

the total capacity of traffic (sum of all working capacities); is the total 

capacity of the connections recovered upon failure scenario number i (this capacity 

includes also capacities of connections unaffected by a failure). 

Load 

C Rec 

i


Eq. (6) is very useful. Firstly, it enables us to calculate the availability of a 

load when no restoration procedures are applied. Consider the following example: 

we have three physical links: how to allocate three connections on them to reach 

the highest availability? There are no protection schemes, so in the case when link i 

(this link has capacity C ) fails, the recovery capacity which can be used by 

traffic carried by link i is: 

Wj 

= ∑ 

j≠ 

i 

C C . P ( Scen ) is the probability that a link 

Reci 

will fail, so it is equal to the unavailability of link i: ( i ) i 

Wj 

i 

P Scen = 1− 

A . The 

availability of a load is an average of path availabilities weighted by capacities. 

The calculation results are presented in Table 1. The connection which carries the 

greatest load brings the largest contribution. If one pays attention to rows printed in 

bold, will be able to notice that it is better to increase the availability of such a 

connection (with capacity of 25 units) than to even more significantly increase the 

availability of a connection carrying much less capacity (10 units). 

Figure 5. A comparison of three protection schemes 

The restoration will be considered only for a very simple case: we will model 

some procedures related to MultiProtocol Label Switching. Each Label Switched 

Path (LSP) i between two Label Switching Router (LSR) nodes is characterized by 

the three parameters: its availability (Ai), capacity of LSP in the up state (CWi) and 

capacity reserved for restoration on the link traversed by the path (CPi). In the case


of restoration the data from an affected LSP should be divided into some recovery 

sub-paths, i.e., we deal with the bifurcated recovery paths. When a path fails, 

restoration is based on the allocation of all available capacity reserved on all other 

paths. In some cases less capacity than that used by working LSP before failure 

will be allocated to recovery sub-LSPs. We take into account not only single 

failures but also double failures. In the latter case (when physical paths i and j fail) 

P Scen = 1− 

A 1− 

A . 

the probability of such a scenario equals ( ) ( )( ) 

Table 1. Comparison of availabilities of a load 

Capacity 10 15 25 Availability of a load 

99,95% 99,90% 99,85% 99,89% 

99,90% 99,95% 99,85% 99,89% 

99,95% 99,85% 99,90% 99,90% 

Availability 

of a path 

99,85% 99,95% 99,90% 99,91% 

99,99% 99,85% 99,91% 99,91% 

99,90% 99,85% 99,95% 99,91% 

99,85% 99,90% 99,95% 99,92% 

We considered the problem how to allocate three different LSPs on three 

physical links (cf. Table 2 for data concerning the example; total capacity reserved 

for restoration equals total working capacity, i.e., 6 units). We checked all possible 

situations of allocating LSPs and reserved capacity on different physical links (Eq. 

(6) was applied again). Some typical examples are presented in Table 3. We can 

see that the most favorable solution is to allocate paths in such a way that the path 

carrying the largest working capacity is allocated on the physical link with the 

largest availability, and simultaneously to allocate the reserved capacity on the link 

which has the second-largest availability (cf. the last row of Table 3). On the other 

hand, the use of the worst link (from the reliability standpoint) is not 

recommended, unless one is forced to do it (e.g., all capacity on “better” links is 

already used). Moreover, it would be reasonable to allocate the reserved capacity 

(instead of the working capacity) on the worst link (characterized by the lowest 

value of availability). We can also note that if it is not necessary it would be 

favorable not to balance utilization of paths (e.g., not to allocate paths in the 

following way: LSP 1 — link 1, LSP 2 — link 2, etc.), but allocate it in an “unjust” 

way (e.g., no capacity on link1; LSP 2 and LSP 3 on link 3, and the rest of capacity 

on link 2). Finally, we notice that the capacity reserved for restoration should be 

allocated on links different from those carrying the working capacity. Generally, 

the larger amount of working capacity is carried by a link, the smaller reserved 

capacity should be carried on it. 

ij 

i 

j


Table 2. Restoration example: used values 

LSP 1 LSP 2 LSP 3 

Capacity 1 unit 2 units 3 units 

Physical link 1 Physical link 2 Physical link 3 

Availability 99,85% 99,90% 99,95% 

Table 3. Example allocations of capacities and calculated availabilities 

A1 Cw1 Cp1 A2 Cw2 Cp2 A3 Cw3 Cp3 

Availability of a load 

without restoration 

Availability of a load 

with restoration 

99,85% 5 6 99,90% 1 0 99,95% 0 0 99,86% 99,87473% 

99,85% 5 6 99,90% 0 0 99,95% 1 0 99,87% 99,87473% 

99,85% 5 5 99,90% 1 0 99,95% 0 1 99,86% 99,89975% 

99,85% 0 0 99,90% 2 6 99,95% 4 0 99,93% 99,96657% 

99,85% 5 2 99,90% 1 0 99,95% 0 4 99,86% 99,97483% 

99,85% 3 0 99,90% 2 2 99,95% 1 4 99,88% 99,99990% 

99,85% 0 2 99,90% 3 2 99,95% 3 2 99,93% 99,99992% 

99,85% 0 2 99,90% 3 3 99,95% 3 1 99,93% 99,99992% 

99,85% 0 0 99,90% 3 3 99,95% 3 3 99,93% 99,99995% 

99,85% 0 0 99,90% 2 4 99,95% 4 2 99,93% 99,99995% 

99,85% 0 0 99,90% 1 5 99,95% 5 1 99,94% 99,99995% 

6. CONCLUSION 

Our intention was to show how simple models of protection schemes enable 

fairly useful evaluation of the basic reliability measure, i.e., the availability. 

Although the models are approximate, they can show us some necessary hints 

concerning network design. It is of a great importance to note that we focus only on 

availability problems and neglect other issues, for example cost-effectiveness. We 

can note that some solutions are characterized by a high availability, but they are 

not economical. The problem of balancing reliability parameters and cost requires 

introduction of some more complex mathematical models. 

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