Full-Service Probability for Regular Arrangements

Abstract

A regular arrangement is a multiple correspondence between a set of elements supplying a service, called stations, and a set of elements requiring service, called installations. There are n installations and 2 n stations. The regular arrangement is such that stations a j and a n + j are able to supply service to installations b j and b j +1 . Each station therefore can service either of two installations and each installation is associated with four stations. It is supposed that after this arrangement has been made a random event removes some stations. The remaining stations are used in the best possible way to supply service to the installations, a station being able to serve only one of its associated installations. The present paper obtains the probability that after the random event it is possible for all installations to receive service.