Date: 201503
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: Large Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Reporter organization: Air Carrier
Reporter function: First Officer; Pilot Not Flying
Second reporter function: Pilot Flying; Captain
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence; Inflight Event / Encounter Fuel Issue
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Executed Go Around / Missed Approach
Contributing factors: Weather; Airport; Procedure
Primary problem: Procedure

Narrative: On our first approach; we conducted the visual approach to runway XX; while we are on the base portion about to turn final; Tower told us to turn left and enter a 4 mile final; and we queried to make sure that they wanted us to turn left. They confirmed. We were hearing tower talk to a truck (ops) on the runway asking them how long it was going to take to remove the debris from the runway. We then heard them tell two aircraft in front of us to go around. We turned final and then talked about expecting a go around. When we were approximately 800 feet we were told to go around. We executed a go around and noticed we had 6;000 lbs of fuel on board. Captain and I agreed that we were minimum fuel and I told approach. We then got a few vectors around and then vectored for the visual approach again. As we were vectoring towards ZZZ; I messaged Dispatch and told them we went around and are trying again; 6;000 lbs of fuel on board and where did they want us to go if it didn't work out a second time. Dispatch replied back with ZZZ1 1;200 lb burn or ZZZ2 1;400 lb burn. The Captain and I agreed that ZZZ1 will be the better choice due to the winds and less Burn. We decided ahead of time that if we go around again; we will be at [low] fuel to make it to ZZZ1 and probably have to land under 3;000 lbs by the time we got to ZZZ1. I did a quick call to the Flight Attendant (FA) and told them we were still going to [intended destination]. We conducted another full visual approach; and as we were turning final approach; tower told us to go back out and join a 4 mile final. We decided that we were unable to do that safely because we were almost on final course and it would have caused us to do a big 360 at a thousand feet in that tight area. So we said unable.  After I said 'unable'; tower said 'roger'; and cleared an aircraft to take off.  I then saw an aircraft rolling down the runway; then when we were about 700 ft; Tower cleared Aircraft X to takeoff and they began pulling onto the runway. This is when we got frustrated because if they had just let us land the Aircraft X could have taken off right after we pulled off the runway. For some reason it was more important to get them to take off than it was for us to land in a min fuel situation; after a go around. I asked the tower 'are you really going to clear someone to take off right now?' and tower then cancelled the Aircraft X's takeoff roll and told us to go around. As we were going around I said roger we are now [low] fuel. After we climbed to 2;000 feet; I said we are [low] fuel; then tower started vectoring other aircraft around and clearing someone to take off. I felt that our point was not getting through to the tower; so we decided to get their attention and say what the First Officer Monitoring (FOM) ([low] fuel) communication of mayday mayday mayday; aircraft X is [low] fuel and we need to land at ZZZ1 or ZZZ immediately. (Thinking that we may have to go to ZZZ1. ) Then we got priority handling and were told they were going to get us on the ground immediately in ZZZ. We decided that that would work; and they gave us a immediate downwind visual to Runway XX. We landed and taxied to the gate. As soon as the main cabin door opened up; we got a visit from two management pilots to talk about what happened.


Second narrative: Enroute ATIS showed very strong winds. We asked Dispatch if we could expect delay vectors and/or holding and he said it was possible. We evaluated our fuel and decided that ZZZ provided the closest opportunity and its Runway 31 aligned with the strong winds. After contacting Approach we were vectored with minor delays and felt that a divert wasn't likely. We planned and briefed the Visual landing with all considerations.During the first approach ATC requested that we turn east bound prior to final in an attempt to extend final for a vehicle on the runway. We complied. At approximately 500 Feet AGL on final ATC directed a go around. During the go-around I instructed my First Officer (FO) to declare [low] fuel and ask when we could expect that the runway would open. Tower stated that he wasn't sure and we told him we would be diverting and would get back with him momentarily with a divert airport. Tower shortly came back to us informing us that the runway was open. My FO pointed out a small aircraft at the midway point of the runway and stated that Takeoff should be ok. We both then realized that Aircraft X was taking the runway and we would most likely have to go around. At approximately 500 feet AGL Tower cancelled takeoff clearance for Aircraft X and directed us to go around.During the go around I directed my FO to request immediate vectors to ZZZ. He did so and received no response. He made the same request a second time with no response. He followed the lack of response with a 'Mayday' call and they finally responded. Tower stated that we could land on Runway XY if we wanted but we said we were unable due to winds. He then said he had the pattern clear and we could fly a visual pattern for landing [Runway XX]. I discussed the options of Runway XX with my FO and we both agreed that the winds during the previous attempts were acceptable and safe and we accepted a visual for Runway XX. Our third attempt was uneventful and we taxied to the gate.Our first approach was initiated with an FMC landing fuel estimate of approximately 6;500lbs. Our second attempt had an FMC landing fuel estimate of approximately 5;000lbs. We realized a second go around would have resulted in a landing at ZZZ of approximately 3;500lbs and the reason for the '[low] Fuel' declaration during the second go around.


Synopsis: Air Carrier flight crew and the Dispatcher involved report two go-arounds from the visual approach with the airport landing a single westbound runway due to strong gusty winds. Minimum fuel is declared after the first go-around due an airport vehicle on the runway clearing FOD and low fuel is declared after the second due to the Tower clearing Aircraft X to takeoff with insufficient spacing. A visual pattern is flown for the third attempt successfully.