Timing of DNA replication initiation as a function of the length of the cell cycle according to the Cooper and Helmstetter model. A: Plots of the values of X, Y and number of active processes (termed in the main text) in each region of the graph, for different values of the cell doubling time. The purple shading reflects the number of active processes in each region, with lighter shades denoting a greater number of active processes. Towards τ = 80 mins, the lines t = X and t = Y are shown curving off, showing that this is outside the regime 20 mins ≤ τ ≤ 60 mins where the C and D periods can be considered constant. Above the graph in panel A are diagrams of the state of the chromosome for critical time values, for each of the values of n (the number of overlapping replication rounds). B: Illustration of overlapping replication rounds, in the case of a complete replication round of n = 2 overlapping rounds, and 3 generations.