# Fiber Cable Failure Impacts, Survivability Principles, and Measures of Survivability

• Print
This chapter is from the book

## 3.10 Restorability

A simple GOF-type measure that is widely used in design and characterization of transport networks is the restorability, also sometimes called the restoration ratio. Restorability is the most basic indication of survivability because it directly reflects the extent to which "single points of failure" have been removed as outage-causing circumstances. The biggest single step toward survivability is to eliminate single-span failures as a cause of service outage. This has a quantum effect on improving service availability as service outage can then only arise from much less frequent dual failures or node failures. As most commonly used the restorability is defined as the fraction of payload-bearing (i.e., "working") signal units that are subsequently restored, or that are topologically capable of being restored by replacement routes through the network. That is, for a specific failure scenario X,

Equation 3.4

where (most generally) wi,j is the number of service paths between nodes i,j that are failed in the failure scenario X. This way of stipulating a failure scenario is totally general; any number of span and/or node failures can be represented in terms of the set X of i,j node pairs that simultaneously have one or more failed paths in scenario X. Thus the denominator of Equation 3.4 can be thought of as a "total damage" sum in terms of the number of transport signal units that are severed in the failure scenario X. The numerator is the sum of what is restored (or can be restored) for each subset of failed signal units corresponding to a damaged span. ki,j represents the number of replacement (restoration) paths that can be provided for (i,j). The min(-) operator ensures that no credit is given for providing more restoration than is actually needed for any subgroup of failed working signals.

One set of failure scenarios that is of particular practical interest is the set of all single and complete span failures. That is the set of all X which just one (i,j). In this case the restorability for any one scenario m = (i,j) simplifies to:

Equation 3.5

and the network restorability is defined as the average restorability of all working paths that are failed under each single-span failure scenario. That is:

Equation 3.6

where S is the set of all spans in the network. Rn = 1 is often referred to as a "fully restorable" network. It is the mark of a network that can withstand any single-span failure without any service path outage. As a single figure of merit for network survivability Rn is of considerable practical interest because:

1. The likelihood of failure scenarios containing more than one (independent) span failure at a time is much lower than a single failure.

2. It is generally considered economically feasible (or at least necessary and reasonable) to design for Rn = 1 whereas it may be economically infeasible to protect against all possible multi-span or node failures by design.

3. Rn is a property of the network design, or current network state, that is independent of any knowledge or assumptions about actual failure frequencies or mechanisms.

4. Given the much higher failure rate of cables (outside plant structures in general) relative to node failures, achieving Rn = 1 by design is the most significant single step that can be taken in practice toward improvement of service availability.

A variety of purpose-specific variants from the basic definition of restorability are common. Examples are the "prompt restorability" which is the restorability level arising before a certain elapsed time from failure onset, or the "dual-failure restorability" which is as the name suggests and is considered further in Chapter 8. Other measures can include prioritized demand weightings Rn. These are all valid measures as long as their specifics are fully stipulated in terms of the specific set of failure scenarios being considered and the criteria being employed to define survivability against those failures.

Restorability, and GOF measures in general, are relatively simple to compute and to understand, because they reflect simple measures of recovery levels for a specific set of assumed failure scenarios. In contrast, ROF measures can be much more involved and/or require simulation. A grounding in reliability and availability theory is required for their appreciation. Let us therefore now cover the basic concepts of reliability and availability which underlie ROF measures, and are also highly relevant to work in network survivability in general.

• 🔖 Save To Your Account

### InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

## Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

## Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

### Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

### Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

### Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

### Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

### Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

### Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

## Other Collection and Use of Information

### Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

### Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

### Do Not Track

This site currently does not respond to Do Not Track signals.

## Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

## Children

This site is not directed to children under the age of 13.

## Marketing

Pearson may send or direct marketing communications to users, provided that

• Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
• Such marketing is consistent with applicable law and Pearson's legal obligations.
• Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
• Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

## Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

## Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

## Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

## Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

## Sharing and Disclosure

Pearson may disclose personal information, as follows:

• As required by law.
• With the consent of the individual (or their parent, if the individual is a minor)
• In response to a subpoena, court order or legal process, to the extent permitted or required by law
• To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
• In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
• To investigate or address actual or suspected fraud or other illegal activities
• To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
• To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
• To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.