Purple bacteria have developed an efficient apparatus to harvest sunlight. The apparatus consists of up to four types of pigment-protein complexes: (i) the photosynthetic reaction center surrounded by (ii) the light-harvesting complex LH1, (iii) antenna complexes LH2, which are replaced under low-light conditions by (iv) antenna complexes LH3 with a higher absorption maximum. Following absorption of light anywhere in the apparatus, electronic excitation is transferred between the pigment-protein complexes until it is used for the primary photoreaction in the reaction center. We calculate, using Forster theory, all rates for the inter-complex excitation transfer processes on the basis of the atomic level structures of the pigment-protein complexes and of an effective Hamiltonian, established previously, for intracomplex excitations. The kinetics of excitation migration in the photosynthetic apparatus is described through a master equation which connects the calculated transfer rates to the overall architecture of the apparatus. For two exemplary architectures the efficiency, distribution of dissipation, and time evolution of excitation migration are determined. Pigment-protein complexes are found to form an excitation reservoir, in which excitation is spread over many chromophores rather than forming an excitation funnel in which excitation is transferred without detours from the periphery to the RC. This feature permits a high quantum yield of 83% to 89%, but also protects the apparatus from overheating by spreading dissipation over all complexes. Substitution of LH2 complexes by LH3 complexes or changing an architecture in which few LH2 (LH3) complexes are in contact with LH1 to an architecture in which all LH2 (LH3) complexes are in contact with LH1 increases the quantum yield up to 94% and decreases the degree to which dissipation is evenly distributed.