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Glucose transport in plasma membranes is the prototypic example of facilitated diffusion through biological membranes, and transport in erythrocytes is the most widely studied. One of the oldest and simplest models describing the kinetics of the transport reaction is that of alternating conformers, schematized in a cycle of four partial reactions where glucose binds and dissociates at two opposite steps, and the transporter undergoes transconformations at the other two opposite steps. The transport kinetics is entirely defined by the forward and backward rate constants of the partial reactions and the glucose and transporter concentrations at each side of the membrane, related by the law of mass action. We studied, in silico, the effect of modifications of the variables on the transient kinetics of the transport reaction. The simulations took into account thermodynamic constraints and provided results regarding initial velocities of transport, maximal velocities in different conditions, apparent influx and efflux affinities, and the turnover number of the transporter. The results are in the range of those experimentally reported. Maximal initial velocities are obtained when the affinities of the ligand for the transporter are the same at the extra- and intracellular binding sites and when the equilibrium constants of the transconformation steps are equal among them and equal to 1, independently of the obvious effect of the increase of the rate constant values. The results are well adjusted to Michaelis-Menten kinetics. A larger initial velocity for efflux than for uptake described in human erythrocytes is demonstrated in a model with the same dissociation constants at the outer and inner sites of the membrane. The larger velocities observed for uptake and efflux when transport occurs towards a glucose-containing trans side can also be reproduced with the alternating conformer model, depending on how transport velocities are measured.