Is there a relation between the size of the list and the length of wait?

Abstract

Many investigators have hypothesised that an increase in admissions is associated with a decrease in Size.The Size of a waiting list must increase by any excess of additions to the list over deductions from the list. A real change in enrolments (relative to admissions) must therefore correlate directly with any change in the Size of the list while a real change in admissions (relative to enrolments) must correlate indirectly with any change in the Size of the list.But some of the results seem to provide support for an alternative in which an increase in admissions is associated with an increase in Size. When there is a problem, the first hypothesis calls for more resources, and the second for more restraint.We may define the length of wait prospectively, using the distribution of completed waits of those enrolled, or we may define it retrospectively, using the completed waits of those admitted. But our choice has consequences. The relationship between changes in the Length of the subsequent wait and changes in the Size of the list must be direct because changes in Size are directly correlated with a real change in enrolments. Similarly, the relationship between changes in the Length of the prior wait and changes in Size must be indirect because changes in Size are indirectly correlated with a real change in admissions.In this light, the second relationship appears to be an artefact and the second hypothesis a failure of reasoning.