If you want to know about the investment of Bronze Age cities I hope someone can come to your aid. But the question I'm afraid doesn't make sense for Troy. Setting aside the fact that the Trojan War is mythical and did not happen, in Homer--the origin of the ten-year war--Troy is not under siege. The city is never invested, and there is no attempt in the poem on the part of the Achaeans to surround it. The war is fought on the coastal plain in front of Troy in repeated set-piece battles. The Trojans are capable of communicating and trading with the interior of Anatolia, and as Homer's catalog of the Trojan allies shows perfectly well there are contingents from all over the place showing up to fight on their side. The Trojans are still calling on allies in the poem and in the rest of the Epic Cycle. In Book 10 (interpolation though it most likely is) a contingent from Thrace finally shows up. In the Aethiopis both Penthesilea and Memnon--an Amazon and Ethiopian, respectively--were supposed to have been summoned.

Xenophon has already answered that the Iliad doesn't say anything about full-time siegery, so I know this is kind of an unnessesary. So this is more of an exercise in self-indulgence, because I want to read a bit about Bronze Age warfare.

I'm not aware of any year-round military activity during the Late Bronze Age, and the location of Troy makes it even less likely. There's also a hypothesis that the Greek colonial expansion into the sphere of the Phrygians and Lydians (and the transition between the two kingdoms) caused a war that spawned the legend. That seems less likely to me because discounting the actual attestations of war in Wilusa in favor of just the possibility of war later seems unreasonable, but I'm partial to the Bronze Age over the Iron. I also know far less about it, so I'm going to stick to the LBA.

Siege in the LBA "While scholars often assume that those conducting a siege... had the upper hand over those being besieged, the preponderance of historical data from the pregunpowder era suggests that defenders had a better chance of thwarting a siege than historians and archaeologists often assume." (Burke 2009). I agree with Burke that the propaganda of ancient empires plays an outsize role in perceptions (certainly including mine; I love me some Assyrian siege descriptions), and defense is rarely sexy enough to be worth showing (the defeat of the Assyrian siege of Jerusalem comes to mind as an immediate counter example). Certainly, siege equipment has been long attested (Jericho is early, and 3rd millennium Ebla both mentions and depicts battering rams [Nadali 2009]). While I can't speak much to the particular techniques of a given time or place, siege was undoubtedly a proper part of Near Eastern war making.

The question is: did 'starve-them-out' sieges form a main component of LBA warfare. The answer: maybe? The tricky thing, as far as I can tell, is that only the end destruction is visible archaeologically, and records are generally after-the-fact summaries that want to emphasize how powerful a king is, rather than a play-by-play of a grueling campaign. In Old Babylonian-era Mari (c. 1800 BCE, and we do actually have play-by-play documentation) maneuver warfare and control of resources was the standard; the ability to deny a city/populace was enough to force a settlement, and there weren't too many instances of cities being fought to their last dying breath. When cities had to be fought, they were taken by storming them with overwhelming force. This principal seems to be at work in the Hittites' invasion of Syria under Hattusili I and Mursili I (1600-1500 BCE), where they sieged and sacked Alalah and Aleppo before returning across the mountains. In neither case did they spend more than a single season campaigning, The Annals are actually very clear on this, as they layout a year-by-year synopsis of royal activities. Beyond the difficulties and expenses of maintaining an army in hostile territory across a mountain pass, the next few years' campaigns give another reason not to spend a long time at siege: other frontiers had their own enemies, and the kings had to fight in the west. Though in some cases it may have not been so much a choice: Bryce says of 6-month siege of Urshu, which saw total failure to stop enemies entering and reinforcing the city that "it does, however, throw interesting light on one of the chronic deficiencies of the Hittite military machine—its ineffectiveness in siege warfare" (Bryce 2005). However, another half-year siege at Sanahuitta, after some raiding of the countryside, seems to have forced a surrender via starvation after having previously devastated the countryide (the line in the Annals' description of his first and fourth years is, in Beckman's translation, " I went to (the city of) Sanahhuitta, but I did not destroy it; I destroyed its countryside. I left forces in two places as garrisons, and I gave whatever sheepfolds there were (in that vicinity) to the garrison troops... In the [fourth] year I went in battle to Sanahhuitta, and I fought Sanahhuitta for five months. [Then] I destroyed [it] in the sixth month."). Thats about as much detail as I can find on any given Hittite siege, but again the various kings' Annals' talking about campaigning in the southeast one year and the west the next give an impression of a limited war season.

Now, can this apply to our LBA Trojan war scenario nearly a half millennium years later? I think so. The political landscape hasn't changed much, and there have not been any earth-shattering innovations in battlefield warfare (the chariot-centric Battle of Kadesh is maybe 100 years earlier). In general, the LBA was a stable time, and new developments would be rather important (the rise of Assyria and the fall of Mitanni is a notable one, but doesn't seem to have been due to great technological difference; the difference between Egyptian and Hittite chariots is another factor much discussed), so I trust our absence of evidence as being evidence of absence. I think the Kadesh campaign is actually very instructive: the multi-year build-up to it, of Egyptian expansion into Hittite-dominated Syria, was seasonal campaigns conquering/converting cities, waiting to test the armies of the Great Kings against each other. Even though control of the land required urban palatial centers to be controlled, this seems a secondary consideration. Battlefield success and the potential to ravage the countryside seem to have been the standard way to win cities, with sieges only a secondary measure to be used for the most stubborn of cities. In fact, despite Ramses' battlefield (barely) success, he abandoned the siege shortly after the battle. The cities he did conquer were rebellious vassals in the Levant, and he conquered those quickly, not in prolonged sieges; Ramses' later successful incursions north were all single-season affairs that involved capturing cities. So, as of c. 1250 BCE, assaulting cities or simply intimidating them is still the main method of taking a city.

Finally, the archaeology of western Anatolia is in general spotty. I don't think I would trust any conclusions about the broader landscape. I have in mind a 'few fortified centers' versus '3-tiered hierarchy' versus 'numerous unfortified towns with few military centers' as the main models of comparison with other places and times in the Ancient Near East, but I don't think we can be certain right now about the broader setting of our LBA Trojan war. If only a few fortified centers exist without much population in the hinterland, then they will probably be hard to crack and starvation is necessary. If there is a parallel with 8th-century polities in Syro-Anatolia, then a defense in depth is to be beaten by assaulting the smaller forts and sieging the heavier-walled political capitals after cutting them off from their supplying regions (the settlement-hierarchy model is also attested for the Middle Bronze Levant about 1000 years before the Assyrian wars [Burke 2010] so its certainly not only an Iron Age thing, but Anatolia's urban landscape isn't well known). Finally, if you have a strong urban center that relies on an undefended area, raiding this until the enemy gives up or faces you in the field may seem the best strategy (I'm think Peloponnesian War, but if I'm wrong in that then I'm going way back to Umma-Lagash). In pretty much all of these scenarios, raiding coupled with intenisive assault--not protracted siege--is the standard, as seen in the Kadesh campaigns of both the Egyptians and the Hittites

Supply Lines Unless you buy the idea that the Mycenaeans dominated the land of western Anatolia and not just a couple particular trading centers, the supply lines of the main combatants would have been fairly difficult to maintain, the Mycenaeans having to sail frequently during winter and Hittites/vassal kings having to trek across the Anatolian plateau during its harsh winter. I don't buy the idea of a large territorial Mycenaean state on the mainland, because the Hittites seem to have no long-term problems with Ahhiyawa directly, only through sphere of influence vassal disputes--even if Ahhiyawa sends troops, its not their own land they're defending. More Venice/Athens than Rome. (I'm becoming more and more skeptical of territoriality pre-Rome anyway, but that's a long digression). Even if we do think that Ahhiyawa has substantial holdings in future Ionia, the texts seem pretty clear in centering them around Miletus and the south, not the north. Sure, client states could help with some of the logistics, but a full-blown confrontation of the Great Kings can't be fully outsourced.

tl;dr--I'm picking LBA because the Iron Age isn't as fun; sieges weren't typically year-round; and even if this one was Troy is too far from the powers involved to pull that off; and even if they could we don't know if that would have been an optimal solution.