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It is certainly likely that this activity will result in a brief outage. Use of a Multi-AZ deployment for RDS helps mitigate that for most activities since AWS will first perform maintenance on the standby instance, promote that to primary, then perform maintenance on the "old primary/new standby". Emphasis is on "most" because some major changes, like modifying the database engine, may require updating both primary and standby at the same time. Multi-AZ also gives you increased availability in the case of an Availability Zone going offline. Keep in mind that Multi-AZ deployments come with additional cost. You will need to find the balance between desired availability and total monthly spend.
Web Hosting
What are my options for hosting a web site in AWS?
While we can help you setup almost any type of web site in AWS, you best bet may be to start with the CIT Custom Web Development team, which brokers a varierty of web site hosting options. See Hosting Comparison Chart for options. In short the options are:
Basic
Static Web Hosting
Content Management Systems
CampusPress (WordPress)
Pantheon (WordPress and Drupal)
Acquia (Drupal)
Highly Customizable
Media3 (ColdFusion, LAMP)
Amazon Web Services (AWS) (CIT Cloud Services)
Managed Server