  Convex combinations of the completely positive (CP) as well as CP-divisible,
continuous time dynamical maps arising from collision models are investigated.
While the individual maps are both CP and Markovian we find that convex
combinations remain CP but not necessarily Markovian. Examples of such
combinations for qubit dynamical maps arising from collisional models are
worked out and the invertibility, CP-divisibility, P-divisibility as well as
Markovian properties of such maps are explored.
