Waiting time computation for blood collection sites

As blood donations are provided on a voluntary non-remunerated basis, blood donors should be treated as user-friendly as possible. Delays and waiting times within blood collection sites (donor centers) should thus be kept at acceptable levels. Waiting times are not incorporated directly other than by practical experience. A more rigorous approach is required. An analytic waiting time computation is therefore investigated to compute waiting times as a function of production. An analytic so-called product form solution for joint queue lengths is concluded. This product form leads to: • an exact expression for the marginal waiting time percentiles at each separate phase • a more formal justification for approximate computation of the total mean waiting time for the non- exponential case. A computational algorithm is provided to numerically approximate the total delay time distribution, an algorithm that has not been presented before. The results are tested for and applied to a real life test case of a Dutch representative blood collection site. These results illustrate the practical usefulness for Sanquin, but also the applicability of the models in general.