I just upgraded to 4.9.3 from 4.9.2 and we are having some real problems with system resources being overused and crashing the site. Also, the Scheduler seems out of whack. Although the scheduled tasks caused no problem before, they now seem to be eating resources and taking too much time -- yet they aren't working. UsersOnline is scheduled to run every minute, but it shows as running (and only runs) about every four hours. The crashing of the system does not seem to take place consistently at the same time as the scheduled tasks, so I'm not convinced it's the scheduler.  Does anyone have a solution?

Thanks, Mitch! The Scheduler settings are:

Site Purge - 24 hours
Purge Schedule History - 24 hours
Active Modules Mail Connector - every 30 minutes
Active Forums Queue Schedule - 1 minute
DotNetNuke.Modules.Events.EventNotification         Every 1 Hour
BizModules.UltraPhotoGallery.Scheduling.AutoSyncScheduler,   Every 1 Hour   
Hyper.Modules.EventsCalendar.SendReminder, EventsCalendar    Every 2 Hours    Every 5 Minutes    5/14/2009 8:18:45 Hyper.Modules.EventsCalendar.SendReminder, EventsCalendar        Every 10 Minutes
Engage.Dnn.Events.Components.EmailScheduler    Every 5 Minutes    Every 60 Seconds   
Dataspring.DNN.Modules.OptInAdvanceEmail.SendNewsletters     Every 1 Hour
Dataspring.DNN.Modules.OptInAdvanceEmail.CheckBouncedEmails,Dataspring.DNN.Modules.OptInAdvanceEmail     Every 1 Hour

However, all of these task were running before on 4.9.2.  Performance is set as follows:

Page State Persistence - Page
Module Cacheing Memory - Memory
Performance - Heavy Caching
Authenticated Cacheability: Server and NoCache
Compression Setting GZip Compression
Use Whitespace Filter: Checked.

Any thoughts would be greatly appreciated!

This will not solve your issue - but switch off whitespace filter if you are using compression (no point in having this enabled).