I know the historicity of the Trojan War is widely debated, and the common view seems to be that if Troy indeed fell to an invading force from mainland Greece, it was most likely on a much smaller scale and in shorter time than attested in the Illiad, and Homer probably merged tales about multiple different military operations into one big event. However, I am wondering how much of this story could have been possible.
My question is: With what we know about the civilizations of the Aegean Sea during the time in question, the logistics of warfare, and the political landscape, would it be possible for such an event to happen; that is for a ruler from mainland Greece (or multiple) to gather allies and/or vassals, invade Anatolia, and lay siege to a city for ten years, with that city also drawing on multiple allies from far away regions to aid in its defense? Where are the limitations to this idea?
Physically and logistically possible? Probably yes. What we know of how the Hittite empire worked, for example, suggests that they exerted force on outlying regions of their rule by sending a centralised army to trouble spots. In the case of Wilusa (the Hittite name for Troy, apparently). We don't know anything about the political organisation of the Greek world in the Late Bronze Age above the level of the individual palace, so we can only speculate whether it would have been politically possible to create a large-scale military alliance, but purely in logistical terms it doesn't seem like there's anything to rule it out.
We're entirely ignorant of Greek politics at the time, as I said. We do know something about international politics, though, and the international situation makes it very difficult indeed to imagine a war.
We have written testimony that the king of a place called Ahhiyawa (the name generally equated with Greek 'Achaia', but the boundaries and scope of Ahhiyawa are entirely unknown) and the Hittite king had some kind of dispute at one point, about Wilusa, probably around 1300 BCE or a little later. That doesn't tell us there was a Trojan War -- we don't know what kind of dispute it was, and it was a dispute relating to Wilusa, caused by the Hittites, not a Greek dispute against Wilusa -- but it does tell us that the Hittite king took an active interest in his western possessions.
In other words, if there had been a war between the Greek world and Wilusa, the Hittites would most definitely have got involved. 'Greece' would have found itself fighting not just Wilusa -- not just an Assuwan league in the Troad -- not just the Arzawa region in western Anatolia -- but the whole might of the Hittite empire. It seems to me extremely implausible that any Greek alliance would have tried something like that. Any attempts that Greeks did make on Anatolian territory, like Miletos/Millawanda, seem to have been opportunistic, made possible by the activity of disruptive forces and warlords from within Hittite territory.
Anyway, for the record, we know for certain that Wilusa did not fall to an invading Greek force. The material culture of LBA Wilusa is consistently Anatolian, and remained continuously Anatolian after the end of the Bronze Age, with continuous inhabitation until ca. 950 BCE. There are signs of immigration after the end of the Bronze Age, but from Thrace rather than Greece. The first Greek presence there dates to the Aeolian colonisation in the 700s BCE, which is when the civic cult of Athena was introduced (depicted in Iliad 6).