Dynamically assign Business Hours

1. Click Your Name | Setup | Company Profile | Business Hours
2. Click New Business Hours and create the business hours setting 
3. Remember to Click Active to allow users to associate the business hours with cases and escalation rules. [Click Active again to deactivate the business hours. You cannot delete business hours.] 
4. Optionally, click Use these business hours as the default to set the business hours as the default business hours on all new cases.

Lightning
 

1. Click the gear button on the upper right of the page.
2. Select "Setup".
3. On the Quick Find box, search for Business Hours.
4. Select "Business Hours" (Under Company Settings).
5. Click "New Business Hours" Button.
6. Set the business hours name (Step 1)
7. Click Active. (You can click "Use these business hours as the default" to set this as default)
8. Set the Timezone. (Step 2)
9. Uncheck "24 hours" checkbox to set Business Hours. (Step 3)
10. Click Save.

Default business hours on cases can be automatically updated with other customized business hours on escalation rules: if the cases match escalation rule criteria and the rule is set to override business hours.

1. Choose Your Name | Setup | Customize | Cases | Escalation Rules
2. Choose New, and give the rule a name. Specify whether you want this to be the active escalation rule [only one escalation rule can be active per time]. Click Save. 
3. To create the rule entries, click New. Each rule can have a maximum of 3000 entries. Each entry defines a condition that determines how cases are processed. 
4. Specifies conditions that the case must match for it to be escalated [in your issue: Choose criteria are met and set a case filter to case: priority equal to ...] 
5. Specifies how business hours apply to an escalated case (click on Set business hours and search for the business hour you created)

1. Click the gear button on the upper right of the page.
2. Select "Setup".
3. On the Quick Find box, search for Escalation Rules
4. Select Escalation Rules (Under Service in Feature Settings).
5. Click New.
6. Set the Rule Name (You can make this Active but NOTE that only one active escalation rule per time)
7. Click Save.
8. Click The Rule Name.
9. Click New button in Rule Entries.
10. Set Sort Order. (Number)
11. Specify criteria for escalation. (Step 2)
12. Specify Business Hours. (Step 3)
13. Specify escalation times. (Step 4)
14. Click Save or "Save & Next" button to create more entries.