The research on online optimization can be distinguished into online problems where multiple decisions are made sequentially based on a piece-by-piece input and those where a decision is made only once.
In general, the output of an online algorithm is compared to the solution of a corresponding offline algorithm which is necessarily always optimal and knows the entire input in advance (competitive analysis).
In many situations, present decisions (for example, resources allocation) must be made with incomplete knowledge of the future or distributional assumptions on the future are not reliable.
For this method of analysis, the offline algorithm knows in advance which edges will fail and the goal is to minimize the ratio between the online and offline algorithms' performance.
There are many formal problems that offer more than one online algorithm as solution: This computer science article is a stub.