Overworld Movement

Travel Time
A common metric regarding movement is the square. One could say that a Warlock moves one square every half hour. This is fine, because it's true. But over large distances this can get very inaccurate, because the length of the journey is not restricted to moving at right angles along the grid.

You can see this when you have two settlements next to you; one to the southeast, and one to the south. Because the world map is a grid of squares rotated 45 degrees, the settlement to the southeast shares an edge with your mountain's square, and the one to the south only shares a single vertex.

If you send raiding parties with the same speed to both, you'll see that the travel times differ; this because the southeast square is actually closer. After all, if we take a square of size 1, two points that share a line are exactly 1 apart, But two points that do not share a line are across the square, $$\sqrt{2}$$ away. So Dungeon Overlord doesn't move from square to square, it calculates the distance from point A to point B and travels in a straight line.

It should also be noted that it always takes one square worth of movement to exit the dungeon, regardless of direction.

Another factor is the travel speed bonus you receive from Swift Raiding Party and Swift Pillage Party. The research text indicates it will "Increases the travel speed by 10%". That's exactly what it does; it takes the speed (in distance per second) and adds 10% to it. This is not the same as reducing travel time by 10%, which would be better. If the speed is 1 square per 1800 seconds ($$1/1800$$), and increase the speed by 10% ($$(1/1800)*1.1$$), and calculate the travel time ($$1/((1/1800)*1.1) = 1800/1.1 = 1636.3636...$$), which is more than we'd get if we simply reduced travel time ($$1800*0.9 = 1620$$).

This gives us the following way to calculate travel time:

$${s(1+\sqrt{\Delta{x}^2+\Delta{y}^2})}\over{b}$$

Where s is the creature's base speed (30 minutes for a warlock), and b the bonus from research (1.1 from swift). Whether the 5% bonus from Forgotten Lore: Overlord Mastery is additive or multiplicative remains to be seen.

Travelling to Other Regions
Creatures can also move between regions on the continent map (After you research the Stonegating technology upgrade). Creatures travel from your dungeon to a nearby stonegate (always the closest one?), then from the stonegate across the continent map, then emerge from the stonegate in the destination region and move toward the target. You will see arrows on both the region map and the continent map when you are doing this kind of travel. The distance between regions does appear to affect travel time (Survey mission from Windward to Angel Vale takes over 12 hours). To choose targets in a different region, you need to first have the stonegating technology researched, then you need to go to the overworld map and click the "globe" in the right-hand menu bar. You will now be able to click on other regions and enter their maps. If you don't have the stonegating technology, you will be able to see the other regions, but they will not be clickable.

Note that you can also switch between continents by clicking the arrows at the top of the continent view. There is a high-end technology for traveling between continents.