5 types of Speed dimensions:
1- Perceptual Speed. Quickness of eye to see openings and to discourage the opponent, confusing him and slowing him down.
2- Mental Speed. Quickness of mind to select the right move to frustrate and counter the opponent.
3- Initiation Speed. Economical starting from the right posture and with the correct mental attitude.
4- Performance Speed. Quickness of movement in carrying the chosen move into effect. Involves actual muscle contraction speed.
5-Alteration Speed. The ability to change direction midstream. Involves control of balance and inertia.
There is some principles that you need to focus when you are working on your speed. Mobility, elasticity, stamina, alertness, anticipation.Remember that tension act as brakes, reducing speed and dissipating energy.
I think that Shadow Boxing and Sparring would be good exercices to increase the “Speed” you need. Make sure that you had preliminary warm up, a suitable stance and a proper attention focus.