an useful source of articles for the question you asked is the Journal of Air Transport Management which you may consult through Science Direct. (Probably, a purchase fee may be requested unless you have a subscription)
I am confident you can find the Journal in the Library of your Institute.
I do not know such studies. Also how would you measure competition?
But intuitive approach gives ambiguous answer. On one hand, competition increases density of flights per airport and thus a flight may wait longer for landing. At the same time, competition gives an incentive to perform better for each company. However, delay is a sum of 3 factors: a) company's discipline, b) external shock (bad weather, etc), c) interaction between different companies in the airport (traffic density). Factor a) works to decrease delay, factor c) works to increase it, factor b) is independent on efforts and competition.
Paper: Congesting the commons: A test for strategic congestion externalities in the
airline industry∗
Alejandro Molnar†
Abstract
Access to scarce runway capacity at most airports in the United States is allocated by queuing, creating the scope for congestion externalities. Unlike a classic "tragedy of the commons", congestion externalities from airline decisions can be strategic. Airlines regularly schedule more departures than an airport’s runways can handle without delay, and delay to the average US passenger was 50 minutes in 2007.
Thank you for all your feedback!. Please find our paper on the issu on the following link: http://dx.doi.org/10.13140/RG.2.1.4162.1201 . Comments welcome!
This is really difficult as it will differ greatly by airport. Usually thou you will find arrival congestion (taxi times) to be less than departure congestion (taxi times). Perhaps look for taxi time research and slot controlled airports.