Dubai International Airport has been creeping up the aviation traffic rankings for years, fuelled largely by the rapid expansion of hometown champion Emirates and its younger sibling, low-cost carrier FlyDubai. Both airlines and the airport are owned by the emirate's government.
The most recent figures compiled by Airports Council International, covering the past 12 months through March 2014, show that Dubai "at least for now" has Heathrow beat for the crown of most international passenger traffic. It ended 2013 in second place behind the European hub.
Griffiths isn't shy about calling his facility, which handled 66.4 million passengers last year, the world's largest international airport. But the 56-year-old Briton was quick to hedge that claim during a recent interview with The Associated Press, saying he wants a bit more data, and to get through a major runway overhaul that's reduced flight numbers, to "proclaim that quite loudly."
"Once we've got through summer 2014 we'll have a look at the numbers and see if we can accurately claim that title, hopefully forever," he said.
The airport Griffiths oversees, with its mall-like duty free halls, tranquil Zen gardens and luxury car raffles, still has room to grow before it can boast being the world's busiest airport when all flights, foreign and domestic, are taken into account.
Griffiths thinks it's just a matter of time, likely before the decade is out.
His airport ended last year at No. 7, with Hartsfield-Jackson Atlanta International Airport in the top spot. But it's growing much faster than the competition. Dubai is the only airport in the top 10 posting double-digit percentage point gains.
Griffiths joined Dubai Airports in 2007 after a stint as managing director at London's Gatwick, Britain's second-biggest airport.He is a self-described "petrol-head" with a love for anything that moves and an avid organist, a passion that helps inform his job and its many moving parts.
"Running a multi-faceted organisation like an airport ... is very much like being part of an orchestra or playing the organ," he said. "You've got a lot of different strands that are moving independently of each other that you have to bring them in line so that they make perfect harmony together."
Below his office, not far from where arriving passengers wait to get their passports stamped, construction workers are noisily working to expand Dubai International once again.
A new concourse that will be connected to an existing terminal by automated train is due to open in the first three months of next year. It promises an eclectic mix of local and international restaurants ranging from Krispy Kreme up to an eatery boasting dishes by Wolfgang Puck.