To draw an instance activity diagram using swimlanes format for this use case, follow these steps:

Define the swimlanes: In this case, you have two swimlanes $-$ User $($Traveler$)$ and System.

Start with the initial state: This is when the traveler decides to book a flight on the system.

User Swimlane: The first action in the User swimlane is to input the desired departure and arrival locations, and the preferred dates of travel.

System Swimlane: The system will then search its database for available flights that match the traveler's input. This is the next action in the System swimlane.

User Swimlane: The system will display the results to the traveler, who will then choose a suitable flight. This is the next action in the User swimlane.

System Swimlane: Once the traveler has selected a flight, the system will prompt him to input his personal information and other important information. The system will then calculate the cost and display it to the traveler. These are the next actions in the System swimlane.

User Swimlane: The traveler will then pay for the flight. This is the final action in the User swimlane.

System Swimlane: The system will confirm the booking if the payment is successful. This is the final action in the System swimlane.

End with the final state: This is when the flight is booked or not booked.

Remember to connect all these actions with arrows indicating the flow of the process. Also, use a diamond shape to represent decision points, such as the traveler choosing a flight or the system confirming the payment. $//$ Draw this swimlanes diagram immediatly