The human multi-drug resistance membrane transporter, P-glycoprotein, or P-gp, has been extensively studied due to its importance to human health and disease. Thus far, the kinetic analysis of P-gp transport has been limited to steady-state Michaelis-Menten approaches or to compartmental models, neither of which can prove molecular mechanisms. Determination of the elementary kinetic rate constants of transport will be essential to understanding how P-gp works. The experimental system we use is a confluent monolayer of MDCKII-hMDR1 cells that overexpress P-gp. It is a physiologically relevant model system, and transport is measured without biochemical manipulations of P-gp. The Michaelis-Menten mass action reaction is used to model P-gp transport. Without imposing the steady-state assumptions, this reaction depends upon several parameters that must be simultaneously fitted. An exhaustive fitting of transport data to find all possible parameter vectors that best fit the data was accomplished with a reasonable computation time using a hierarchical algorithm. For three P-gp substrates (amprenavir, loperamide, and quinidine), we have successfully fitted the elementary rate constants, i.e., drug association to P-gp from the apical membrane inner monolayer, drug dissociation back into the apical membrane inner monolayer, and drug efflux from P-gp into the apical chamber, as well as the density of efflux active P-gp. All three drugs had overlapping ranges for the efflux active P-gp, which was a benchmark for the validity of the fitting process. One novel finding was that the association to P-gp appears to be rate-limited solely by drug lateral diffusion within the inner monolayer of the plasma membrane for all three drugs. This would be expected if P-gp structure were open to the lipids of the apical membrane inner monolayer, as has been suggested by recent structural studies. The fitted kinetic parameters show how P-gp efflux of a wide range of xenobiotics has been maximized.