Journal of Applied Mathematics and Decision Sciences
Volume 7 (2003), Issue 1, Pages 11-28
Minimal waiting times in static traffic control
Department of Mathematics, University of Hagen, Hagen D–58084, Germany
Copyright © 2003 O. Moeschlin and C. Poppinga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The paper discusses the question of the optimal control of an unsymmetric bottleneck system with Poisson arrival processes having the minimization of the mean individual waiting time as objective. The setup allows the straightforward generalization to more complicated forms of traffic organization. The notion of the mean individual waiting time is based on a theorem of the Little type, which is derived by a strong law of large numbers. The proof makes use of McNeil's formula, which connects the expected total waiting time with the expected queue length.