Retention time and dead time
The column is filled with the carrier (liquid or gas) before the sample is injected. Thus if there is no interaction between the sample and the column, then the fastest that the sample can get to the detector is the dead time denoted by $t_M$ in the diagram. If the sample does interact with the column, then it is retarded by a time $t_S$  shown in the diagram. Thus the total retention time from injection to detection is $t_M + t_S$.