Jagatjyot, I tried the following and it seemed worked well for me...
1. make sure there are two status transitions for the ticket type: resolved->reopen and resolved_>closed. In my case, it is for call request status transitions
2. from administrator web interface, go to Administration->Service Desk->application data->codes->auto closure setting
and create a new record with number of business hours for request set to 1
From this point on, whenever a call request goes to Resolved status, the auto closure event triggered and within one hour if the status does not change to reopen then the ticket will be closed 1 hour after status Resolved is set.
You may try the same to see if it works for you. Thanks _Chi