A Queueing Theory, Bayesian Model for the Circulation of Books in a Library

The use of library materials is analogous to a queueing process where an arrival is “serviced” when he finds a book on the shelf and borrows it; when service is busy the arrival is lost to the system. Circulation, rate of output of the service channel, can be measured for each book; the circulation distributions for a number of classes of related books (homogeneous collections) have been determined. Circulation rate can be changed by changing circulation rules whereas the total rate of arrival for a book, whether “serviced” or not, is less affected by changes in rules. Although this total arrival rate (called demand rate) for a book cannot be measured directly, its expected value may be calculated, using Bayes' theorem. From this is developed a self-consistent model of book circulation with inter-related probability distributions, from which one can predict the effect on circulation of a change in loan rules or of the purchase of duplicate copies of the more popular books, and can also measure the decline in demand for a book with time. Results check available data on six collections in two libraries.