The phrase "allotted period" refers to a specific amount of time that is given or assigned to complete a task or activity. It means the time period that has been set aside or allocated for a particular purpose. Full definition
The apps let you block access to certain websites for an allotted period of time. (canadianbusiness.com)
On the other hand, and in seeming contradiction to this position, Paul is quoted as having said that the search for God is of His appointment, and as declaring that God had made of one blood all nations of men and had allotted periods and the boundaries of their habitation, that they should seek Him in the hope of finding Him. (religion-online.org)
It's important to remember, though, naps are always shorter than night - time sleep, so after an allotted period of time — half hour, 45 minutes — take your child out of his room if he hasn't fallen asleep and try the method again at night. (thestir.cafemom.com)