An investigation has been launched into an air-traffic control outage at Sydney Airport that caused major disruptions for thousands of passengers after more than 340 flights were delayed or cancelled.

The system went into meltdown shortly after 5am on Monday at Australia's largest airport, just as passengers began arriving to catch flights for the start of school holidays.

Chaotic scenes played out throughout the morning as passengers on all airlines at the domestic and international terminals were told they would not be able to depart due to the outage.

It took Airservices, the agency managing the country's airspace, about two hours to resolve the software fault but most of the rest of the day to clear the massive backlog of flights from the incident, which caused a knock-on effect throughout the network.