Blucher at Waterloo, the French at Inkerman, the Eagles at the Black Gate: nothing turns the tide quite so dramatically as the timely arrival of reinforcements. There are some battles (and, depending on the decisiveness of the battle, some wars) that would have went very differently if said reinforcements arrived later, or sooner, or not at all.
But reinforcements can pose a problem when it comes time to simulate those battles with cardboard squares and a paper map. If, for example, so-and-so arrived at such-and-such a time, which in game terms corresponds to Turn 6, then I know and you know that on Turn 6 so-and-so is going to arrive. What's more, we probably know where they are going to arrive, too. If I know that, as the friendly player I might take some risks in Turn 5 since I know my back-up is one Administrative Phase away. The enemy player knows not to push too far too near to the arrival hex, or conversely they know that they can block the entry hex. There's nothing quite like watching a huge chunk of the enemy army moving along an empty road that's nowhere near their actual military objectives to block the arrival of reinforcements. If only Napoleon had had the foresight to move his right wing toward hex 3838, all of European history could have been very different.
It feels kind of weird saying "perfect information, ugh", because I have no problem with knowing exactly where your stack is and who's in it, or knowing what your victory hexes are. I've never been one for the old "you are taking on the roles of the actual commanders" formulation, much preferring "the players are interested, informed historians playing with their paper time machine". So, perfect information, in general, doesn't bug me at all, and I generally prefer it, but perfect information with regards to reinforcements bugs me like crazy.
I think the reason why is that, while knowing what you're trying to do and what forces you have at your disposal to do it can lead to some "gaminess", it's usually limited, and doesn't result in actively aberrant behavior. Whereas a fixed schedule of reinforcements is practically a recipe for that kind of nonsense. Of course, I'm nowhere near the first person to say this. Gamers and designers alike have been grappling with this problem since the dawn of hobby history. So, let's look at a few different solutions, and also at a case where fixed reinforcements work like gangbusters.
Roll for Reinforcements
One of the simplest ways to introduce some suspense as to if and when the reinforcements will arrive is to roll for their arrival: so-and-so arrives when you roll a 5 or a 6. If you don't roll a 5 or a 6, roll again next turn.
Within this method, there's a lot of room for additional nuance to ensure that the game still operates within historical bounds. For example, if the cavalry came charging to the rescue around Turn 6, you can start rolling on Turn 4. On Turn 4, you need to roll a "6", on Turn 5 a "5" or a "6", on Turn 6 and every turn after, a three-plus. The result is that there's a slight chance they're going to arrive early, and a very good chance they'll arrive at the same time they did historically, or perhaps a little bit later.
In testing my upcoming-ish design Seven Pines; or Fair Oaks, I needed some way to represent Sedgwick's crossing of a bridge on the verge of collapse, and how that delayed his arrival. I wanted it to be very unlikely that he'd arrive early in the battle, but more likely that he'd arrive in the middle or late in the game. So, I used a rolling method: every turn, the Union Player rolls two dice, and if the total is equal to or less than the current game turn, he gets moving. The 2D6 bell curve being what it is, he's more likely to cross on Turns 6-8, finally arriving on the battlefield in the last few turns, and hopefully saving the day as he did historically.
Chit Pull Reinforcements
Another randomizing method is to have reinforcement chits in a cup. When the chit is pulled, the reinforcements arrive. This has its pluses and its minuses. It can be more random than the rolling method, in that it's not more likely, statistically speaking, for certain dudes to show up by a certain turn; there's generally going to be an equal chance of any of them showing up at any time. This increases the uncertainty and suspense for both players, which is great. But this can also lead to a heavier sense of historical distortion than some folks are comfortable with.
As such, it's a method that works best for games that cover either a very short or very long period of time. If a game represents a couple hours' worth of fighting, then it doesn't really matter if the Second Division arrives a half-hour early and the Third Division forty-five minutes late. If a game covers a period of some years, with each turn representing a month, of necessity it's going to be less granular, and therefore less concerned with exactly who arrived when and where. Anything in-between those two extremes, though, and you can end up with some very odd distortions.
VP for Reinforcements
Every time a reinforcement comes on, your opponent earns VP. This method turns the arrival of new guys into a decision. If you're turning your nose up at it because it's giving you too much control and predictability, think of it less as willing your relief force to appear on the horizon, and more as requesting or committing additional resources and assets from one area to another. It's a command decision.
What's great about this method is that it can introduce a lovely tension in the game. Can I achieve my goals without calling in the reinforcements? If I do call in the reinforcements, will I be able to make up the lost VP in time? In some games, there's a timing element involved as well: bring in these guys on Turn 2, and you're looking at a 5 VP deficit, but bring 'em in on Turn 5, and it's only costing you 1. This adds to that tension, because you're incentivized to bring them in as late as possible, but of course you don't want to bring them in too late.
I used a sort of variant of this method in Supply Lines of the American Revolution. The Crown Player can request additional troops and increased supplies at the beginning of a turn, but every time they do so, it's going to increase the number of Victory Cities they need to win the game. (Parliament's going to send you what you're asking for, sure, but if they do, they expect results!) There's also a sort of timing element here, but it's more situational: requesting troops will nudge the Patriot Support Marker further along its track, as the rebellious colonials are emboldened by your implicit admission of failure.
The Blocking Problem
What none of these methods address is "the blocking problem". I might not know when your guys are going to arrive, but if I have a pretty good idea of where they're going to show up, I can sit my guys on those hexes, blocking them indefinitely. (Of course this only works when relief forces are doing some kind of flanking maneuver; if your reinforcements only arrive on your map edge, and I've so thoroughly broken your line as to be in a position to block them, you probably have more serious problems.) There was one particular game I made the unfortunate decision to purchase in which one player started on the map, and the enemies entered from every direction along eight or nine different roads. But on Turn 1, that first player could move all his units to block the enemy units from entering, thus ensuring he'd win the game. Now, that's not something that I would do - I'm here to push cardboard and count hexes, not to congratulate myself on how clever I think I am - but it's still a problem. Why do I think this is a problem, while I didn't think "stack everything on Mount Doom" is such a big deal? I think stuff like that is more about goofballs exploiting edge cases, whereas blocking reinforcements is obvious enough and prevalent enough to not really be an edge case.
One solution is "units belonging to X side can't come within so many hexes of this hex until reinforcements arrive", but I'm not really crazy about that myself. It just feels too fiddly and restricting, especially as there might be legitimate reasons in the game why you'd need to move toward those hexes, and so now you need exceptions for that, and now someone on BGG is asking about this other exception you didn't think of, and it's all a lot of work to stop someone from blocking an entry hex. I used this one myself early in my career, but I didn't really dig it then and I don't really dig it now.
A better solution is "if entry hex A is blocked, units use entry hex B or C", but then you have the edge case of "what if A, B, and C are all blocked?" It doesn't really discourage jerks from being jerks so much as it encourages them to be jerkier.
My preferred solution is "if entry hex A is blocked by an enemy, reinforcements enter from any hex within a given range". So long as that range is reasonable, your units are still going to behave in a roughly historical fashion, at least arriving from the right direction if not the right road. And when the range isn't reasonable, you've just introduced the possibility of your enemy being flanked from any direction, which should be suitably terrifying to act as a deterrent against "ha-ha, I'm in this one hex and so now half your army can't come to help you".
When Scheduled Reinforcements Work
Now, there are games where fixed schedule reinforcements work. Usually it's going to be when there is a steady stream of units trickling in. Chadwick's Beda Fomm is a good example of this, as you have a constant stream of Italian reinforcements coming in on practically every turn for a good eighteen turns or so. It makes sense for that specific situation as well, as the whole thing for the Italians is to get guys from point A to point B, and the whole thing for the British is to stop those guys.
One feature of Beda Fomm that I like a lot is that at the start of the game, the Italian Player has to create nine "convoy groups" consisting of two transport and one personnel battalions. As these battalions have different factors and capabilities - the machine guns, for example, can only defend and cannot attack - the Italian Player has some latitude here and can sketch out a strategy. (Whether that plan will survive contact with the enemy or not is another story.) I'd actually like to see this kind of thing more often, personally, and in a more robust, extended form - both players secretly committing their reinforcements in ad-hoc groups, including turns of arrival, at the start of the game. Of course, the historical situation would need to warrant that approach.
Really, though, that's true across the board. Whatever the solution to these problems, and even whether or not it even is a problem, is going to depend on the situation being simulated, and also on how the designer is choosing to simulate it - what features they want to emphasize and what they want to abstract away.