Revisiting queueing output processes: a point process viewpoint |
| |
Authors: | D J Daley |
| |
Institution: | 1. Department of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia
|
| |
Abstract: | After some historical notes concerning queueing output processes N dep??, the paper discusses methods for establishing asymptotic linear relations for var??N dep??(0,t], whether in the crude form B 1 t or the more detailed form B 1 t+B 0+o(1) for t→∞. The crude form holds whenever the process N adm of customers admitted to service has a linear asymptote, and then (var??N dep??(0,t])/t and (var??N adm(0,t])/t share a common limit (that may be infinite) in stationary G/G/k/K systems. A standard integral formula for the variance of a stationary orderly point process shows that, if N dep?? is a renewal process whose generic lifetime X has finite second moment, then B 1=(var??X)/(E(X)]2), and the more detailed linear asymptote holds when E(X 3) is finite. Geometric ergodicity of the queue size process Q(?) in stationary M/M/k/K systems establishes that the more detailed linear asymptote is true for them. It is conjectured that var??N(0,t]~B 1 t for any stationary point process N possessing an embedded regenerative structure. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|