How Long Might We Wait at Random?
arXiv:1906.07021
Abstract
In discrete time, customers arrive at random. Each waits until one of three servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. Algebraic expressions obtained for the two-server scenario do not appear feasible here. We also review well-known distributional results for maximum wait time associated with an M/M/1 queue and speculate about their generalization.
16 pages, 9 figures. arXiv admin note: substantial text overlap [in Section 1] with arXiv:1902.09272