It is said that neutrophils, a kind of leukocytes, can be retained in pulmonary alveolar capillary bed, even in normal lungs, resulting in higher concentration than in systemic circulation due to their relatively low deformability, and the concentrated neutrophils help the lung to effectively eliminate the enemies invading from outer air. The authors have developed a model to simulate the flow of neutrophils through an alveolar capillary network, considering the cells' low deformability as the dominant factor for the retention. Flow of a suspension of neutrophils in plasma through a simplified lattice alveolar capillary network model was numerically simulated to investigate the effect of the retention on the increase in the concentration ratio of the cells between in the network and in the suspension. The numerical result showed that the ratio was lower than the experimentally obtained value. Other possible factors to influence the cell's retention time are friction and adhesion of the cell on the endothelium. In the last study, effect of the retention time of the cells in individual capillary segments on the increase in the concentration ratio was investigated to suggest the ratio may have an upper limit no matter how long the retention time is extended. In this paper, the authors investigated the contribution of various parameters which affect transit time of a neutrophil through a single capillary segment to the relationships between the retention time and the concentration ratio. Finally, it was shown that the number of cells in the network increased to approach a finite value as the increase in the coefficient, independent of the cell property, concentration of the cells in the suspension or the capillary shape. Transition of the relationship was changed with the parameters.