Abstract　 　　  

   Two timescales are usually invoked in the literature to estimate the intrinsic GRB central engine activity time $T_{\rm ce}$, one being the $\g$-ray duration $T_{90}$, and the other being a generalized burst duration $t_{\rm burst$ which encompasses both the $\g$-ray emission and (when present) an extended plateau or flaring period seen in the early X-ray light curve. Here, we define a more specific operational description  of $T_{\rm ce}$, and within the framework of the internal-external shock model, we develop a numerical code to study the relationship between $T_{90}$ and $T_{\rm ce}$, as well as between $t_{\rm burst}$ and $T_{\rm ce}$, for a range of different initial conditions. We find that when $T_{\rm ce}\lesssim 10^4$ s, late internal collisions or refreshed external collisions from early ejected shells result in values of $T_{\rm 90}$ and $t_{\rm burst}$ larger than $T_{\rm ce}$, usually by factors of $2-3$. For $T_{\rm ce}\gtrsim 10^4$ s cases, $t_{\rm burst}$ is always a good estimator for $T_{\rm ce}$, and $T_{90}$ might be much smaller than $T_{\rm ce}$ when the late central engine activity is moderate. We also find a clear bimodal distribution for $T_{\rm ce}$, based on the results of our simulations as well as the observational data for $T_{90}$ and $t_{\rm burst}$. We suggest that $t_{\rm burst}$ appears to be a reliable measure to define ``ultra-long" GRBs. Bursts with $T_{90}$ of order of $10^3$ s need not belong to a special population, while bursts with $t_{\rm burst} > 10^4$ s, where the late central engine activity is more moderate and shows up in X-rays might point towards a new population.