On the Asymptotic Behaviour of Queues
排队系统的渐近行为
SUMMARY The homogeneous process N(t) on the lattice of integers in continuous time is discussed. When the increment probability generating function ϵ(u) is analytic at u = 1, the transition functions γn(t) = p{N(t) = n | N(0) = 0} are Bessel-like functions with simple asymptotic properties. The asymptotic behaviour of a variety of M/G/1, G/M/1 and related queueing systems may be deduced from these properties. An appendix is devoted to a review of saddle point methods and…