In mammalian fat and muscle cells, insulin stimulates the translocation of the glucose transporter GLUT4 from intracellular storage compartments to the plasma membrane in adipocytes and muscle cells, significantly increasing glucose uptake. In unstimulated (basal) cells, GLUT4 is sequestered in non-cycling/very slowly cycling compartments. Insulin mobilizes GLUT4 by releasing it from sequestration, enabling its exocytosis and continuous cycling between the plasma membrane and endosomes. Upon insulin withdrawal, GLUT4 is rapidly internalized and re-sequestered internally for future activation. Dynamic studies using tagged GLUT4 have revealed that this trafficking mechanism is regulated post-translationally, with GLUT4 undergoing repeated cycles of mobilization and sequestration in response to fluctuating insulin levels. The trafficking of GLUT4 under basal and maximal insulin concentrations can be modeled as a single cycling pool, with different amounts of GLUT4 in the actively cycling pool. In this model, insulin regulates both the rate constant of exocytosis, k_ex, and the distribution of GLUT4 between the cycling and a non-cycling pool. Here, we present modeling of the kinetics of GLUT4 trafficking in 3T3-L1 adipocytes over a range of insulin concentrations, under steady state, and in transition after adding insulin or after adding an inhibitor of exocytosis. Given the observed characteristics of the experimental data, parsimonious explanatory models incorporating different hypotheses of the insulin-dependence of the GLUT4 recycling system are optimized to the data sets to identify dominant processes acting in the dynamics. The steady-state data is best fit with a model that includes a dose-dependent increase in the size of the cycling pool at submaximal insulin concentrations (quantal release). Simultaneous fits of the transition and steady-state data indicate that insulin regulates a second kinetics rate constant, in addition to increasing k_ex and the cycling pool size.