대기네트웤에 있어서 대기자수와 대기시간사이의 관계

RELATIONSHIP BETWEEN QUEUE LENGTHS AND WAITING TIMES FOR QUEUEING NETWORK MODELS

For general open queueing network models, the relationship between weak limits of queue lengths and waiting times at stations is investigated under heavy traffic situations. It is shown that under suitable normalization, weak convergence of queue lengths and arrival processes is a sufficient condition for that of waiting times, and is also necessary condition when the network is of feedforward type. Moreover, these weak limits for queue lengths and waiting times are shown to be simply related.