Levels?
Anyway, assuming the levels were equal and 100, the maximum possible speeds are, assuming beneficial nature, max IV's, and max EV's to the speed stat:
Dugtrio: 372
Tyranitar: 243
Thus, after one DD, that max tyranitar reaches 364 speed.
Of course, one IV corresponds exactly to one speed point at lv. 100, so if dugtrio has 22 speed IV's, its speed will also be 364 and tyranitar will have a 50% chance of going first against it. If it has a speed IV of 21 or less, it is guaranteed to move second.
And, of course, that's assuming that your speed EV's have been maxed as well.