Your scenario is not per the ITIL framework. In ITIL parlance:
A Request is a request for service (e.g. I need an email account or a mobile phone). Requests have nothing to do with Problems.
An Incident is an unplanned outage or degradation in a service (e.g. A web page is not loading or an application transaction which normally takes 2 seconds now takes 45 seconds to complete). The goal of Incident Management is to restore the service back to operation (or as close to operational parameters as possible) as quickly as possible. If the restoration is achieved quickly by simply restarting a service or device then, in may cases, that is all you do (other than documenting the Incident and resolution).
Problems are raised following a major Incident or repeating Incidents impacting the same service. The goal of Problem Management is to do a deep dive analysis of the Incident(s), determine the root cause(s), and make recommendations to management regarding how this could be addressed in the future. The report to management should include an estimate of the cost of the Incident(s) and the costs of each possible solution in the recommendations.
So a Problem may have many related Incidents but an Incident would be (typically) related to a single Problem. Service Desk is built with that in mind.