This is a complicated question to answer, because there are a number of different elements here that we need to deal with. "Homer", the figure who in Antiquity was credited with having composed the Iliad, or at least whipping it into the shape that is familiar to us, is thought to have lived around 700 BC. But the text of the poem may not have reached its final form until the sixth century BC. For a more detailed discussion of how the Iliad (as well as the rest of the Epic Cycle, i.e. the poems about the Trojan War) came to be, refer to J.S. Burgess, The Tradition of the Trojan War in Homer and the Epic Cycle (2001).

A complicating factor is that the Iliad is the product of a long oral tradition, with elements that clearly date back to the Bronze Age, viz. the Mycenean era (ca. 1700 to 1100 BC, depending on how you date the Santorini eruption). These elements include part of the political geography: Mycenae was indeed a powerful centre during the heyday of Mycenaean civilization. But during the historic era, Mycenae was eclipsed by Argos (which itself was small during the Bronze Age), so the prominence of Diomedes, the king of Argos, in the Iliad is no doubt an element from later times.

Archaeologist Anthony Snodgrass is one of the scholars who argue that the different elements in the Iliad can no longer be untangled and that the epics are thus useless as sources of information for any period in particular. See his article, "An historical Homeric society?", Journal of Hellenic Studies 94 (1974), pp. 114–125. But other scholars were (and are) more optimistic than Snodgrass. Historian Moses Finley argued that we should look at the structure of Homeric society rather than try and determine which (material) elements are Mycenaean or Archaic; see his book The World of Odysseus (second edition, 1978) in particular.

While Finley insisted that we shouldn't be distracted, as it were, by our hunt to determine which objects described in the poem belong to what period, this hasn't stopped some from doing exactly that. Enlightening is archaeologist Jan Paul Crielaard's "Homer, history and archaeology: some remarks on the date of the Homeric world", in the volume he edited, Homeric Questions. Essays in Philology, Ancient History, and Archaeology (1995), pp. 201-288. For example, the boar's tusk helmet worn by Odysseus in Iliad book 10 is an object that was in use during the Mycenaean era; it may be a genuine element that stretches back to the Bronze Age, or perhaps Homer was familiar with an heirloom that had been passed down through the ages. The famous shield of Achilles, forged by Hephaestus, is described in detail by Homer, but this type of metalwork is mostly familiar from shields and other metal objects that date to the Archaic period (ca. 800–500 BC). See also, more recently, Susan Sherratt and John Bennett (eds), Archaeology and Homeric Epic (2017).

Historian Hans van Wees has argued pursuasively that the Homeric epics are internally consistent (as Finley and others have also argued) and can, indeed, be used as a source of historical information. He lays out the argument in his PhD thesis, published as Status Warriors. Violence and Society in Homer and History (1992). This book is the most detailed treatment of how the society described in the epics functioned, and the central place occupied in this society by violence (i.e. "status rivalry"). Van Wees has also expanded on elements of his original thesis in a large number of articles, but I'll focus on his book for now.

In his conclusion, Van Wees writes (p. 261):

Following the approach set out in Chapter One, we have found it possible to reconstruct a coherent image of all aspects of the heroic world that have been examined. Some of these images, though coherent, are fantastic, that is to sya, they do not reflect historical reality; instead, they appear to reflect certain ideals articulated in the epics.

Among these elements are the consistent use of bronze swords by the heroes. Some see this as a reflection of the conditions of the Bronze Age, when bronze instead of iron was used for swords (hence: Bronze Age). But Van Wees emphasizes that bronze was picked because it's a more beautiful metal than iron. Others have pointed out that there are inconsistencies in how Homer depicts bronze: it seems to be forged (rather than melted and poured into moulds!), the heroes are able to easily chop off arms and legs with these weapons, and so on.

Van Wees emphasized in the preface to his book that one can ill afford to ignore the Homeric epics as a source of historical enquiry. As he concludes (p. 263):

Ironically, the implications of the present reconstruction of Homeric society are somewhat similar to the effect of ignoring the epics as sources. Homer's image of the heroic age turn out to be so similar to what we know of the Archaic Age that many perceived contrasts between Homer/Dark Age and Archaic society are reduced to the point of vanishing.

It is very unlikely that there were sieges in Archaic – or even Bronze Age – Greece that lasted a full decade. Within the context of the epics, however, it makes perfect sense, since it needs to be "epic"! As far as we can figure out, wars were likely to be relatively short; there are, indeed, references to what we migth assume to have been normal engagements in the Iliad itself. At one point, Achilles boasts how he destroyed (alapazō) – i.e. captured and sacked – no less than twenty-three towns in the vicinity of Troy, twelve by sea and eleven by land (Il. 9.328–329). Admittedly, though, we don't have a lot of information on wars before the sixth century BC, but again, long sieges are unlikely.

If you're interested, chapter 7 of my PhD thesis (available in Open Access) deals with the Homeric epics in more detail, with references.

Does this answer your question? Feel free to post follow-up questions.