Air carrier Captain reported communication difficulties and congestion in the ramp area at AUS. Pilot reported a ground conflict with an aircraft being pushed back. Reportedly; the area is uncontrolled; does not have a common frequency for pilots and lacks guidance markings for aircraft.

Narrative

Two days in a row I arrived at AUS with no gate. Ramp is uncontrolled; large; with parking spots for overnight aircraft on western end of ramp. Ground clears to ramp; noting uncontrolled; park where you want to; contact Company. First day was ok; went to west end; made something up and shut down an engine. Not too busy; plenty of room. However------ there are no lines; it was daylight; and ENTIRE ramp is lined with carts; equipment; stands; and light poles. I was very nervous about blowing equipment behind the aircraft when taxing out (you have to be close to edge to keep only taxi line clear). Second day; showed up; and Ground said same but they are really behind- suggest you park next to Company at East end of ramp (where customs is). Customs gates are few; and overwhelmed. I again made something up; pulled up next to Company and set brake. Not bad actually; but to do so safely with no guidance uses up at least two park spots (there are no lines; even more of above obstacles). it becomes clear that Company had lost total control of gate/customs issue. Other aircraft is desperate for parking too. We are told it is an unknown delay. Operations is either clueless or helpless or both. They tell us to call Name on a freq. Turns out some aircraft are on that frequency and some are not. Name is clueless and offers no help. Back to Operations - they defy multiple attempts to contact. Finally they answer and defy all attempts for assistance in rectifying situation. After over an hour ramp delay (we had showed up early); aircraft started clearing off customs gates; but total chaos ensued with no coordination. Not necessarily because ramp is uncontrolled; but because there is no common frequency. Our Company Aircraft Y goes to his gate. We are assigned one with a heavy on it. Aircraft Z; Aircraft A; Aircraft B; Aircraft C; and Aircraft D must make their way out. It is very tight; and we are not sitting on lines. Aircraft D pull up nose to my wing also not on lines. In the middle of this an Aircraft E under tow pushes from behind the terminal and then proceeds to push backwards at high speed across the ramp; through this chaos and right in between the nosed in Aircraft D next to me and my wing- no wing walkers at high speed. From my vantage point it appears that aircraft will impact nose of Aircraft D and be very close to my wing tip. I attempted multiple calls on frequency and ground screaming at them to stop- to no avail. Apparently either no one in cockpit or not listening. I literally thought I was witnessing an aircraft accident (apparently nothing hit). We finally have a gate and Name comes over to us and 'orders' us in. I decline over radio as there is equipment (a lot of it) was in middle of my spot Operations will not answer. Name goes over in his truck and literally laughs at us over radio; stating it is our Company equipment. About 20 minutes later he gets it cleared out. We had been there an hour and absolutely no effort by Company ground personnel!!! Embarrassing. I taxied in finally; with same concerns/caution from day before for all the equipment around edges. I talk to Manager at gate- says this happens every Monday; and today was a good day! He had no interest in the safety considerations and blamed it all on City of Austin (except a lot of it is our equipment). I noted to FO (First Officer) I would not be comfortable with this at night; and the time will change soon.Total lack of direction by City of Austin and Company leaves a very large; busy ramp uncontrolled with no common frequency or process for pilots to talk on and no guidance lines on ramps for staging waiting aircraft that must taxi in/out. Ramp edges are lined with equipment and are a possible hazard for getting blown when aircraft must engine park there.Have City publish a common frequency for ramp for pilots to self announce on. Paint lines to waiting spots that are easy to taxi in and out of; and remove spare equipment from areas that could get blown.over. Get Company Ground to be quick on repositioning equipment when widebodies leave. Get City to better manage customs gates with scheduling; or provide stands and buses to customs. Not sure if hiring a Ramp Tower is necessary; but that's always an option too.