Delta's obligations are outlined in the Contract of Carriage.

You can ask about be routed on another carrier but DL has no obligation to provide it. As for compensation, perhaps you will get a voucher ($100?) or some SkyMiles. From the C of C, Rule 240:

Delta may substitute alternate carriers or aircraft, delay or cancel flights, change seat assignments, and alter or omit stopping places shown on the ticket at any time. Schedules are subject to change without notice. Except as stated in this rule, Delta will have no liability for making connections, failing to operate any flight according to schedule, changing the schedule for any flight, changing seat assignments or aircraft types, or revising the routings by which Delta carries the passenger from the ticketed origin to destination.

If you can buy another ticket on a different carrier at a competitive price, do so - a 90 minute delay by DL means you can request a refund.