In the light-harvesting antenna of the Synechocystis PCC 6803 phycobilisome (PB), the core consists of three cylinders, each composed of four disks, whereas each of the six rods consists of up to three hexamers (Arteni et al., Biochim Biophys Acta 1787(4):272-279, 2009). The rods and core contain phycocyanin and allophycocyanin pigments, respectively. Together these pigments absorb light between 400 and 650 nm. Time-resolved difference absorption spectra from wild-type PB and rod mutants have been measured in different quenching and annihilation conditions. Based upon a global analysis of these data and of published time-resolved emission spectra, a functional compartmental model of the phycobilisome is proposed. The model describes all experiments with a common set of parameters. Three annihilation time constants are estimated, 3, 25, and 147 ps, which represent, respectively, intradisk, interdisk/intracylinder, and intercylinder annihilation. The species-associated difference absorption and emission spectra of two phycocyanin and two allophycocyanin pigments are consistently estimated, as well as all the excitation energy transfer rates. Thus, the wild-type PB containing 396 pigments can be described by a functional compartmental model of 22 compartments. When the interhexamer equilibration within a rod is not taken into account, this can be further simplified to ten compartments, which is the minimal model. In this model, the slowest excitation energy transfer rates are between the core cylinders (time constants 115-145 ps), and between the rods and the core (time constants 68-115 ps).