A Time-Dependent Queueing-Network Model to Describe the Life-Cycle Dynamics of Private-Line Telecommunication Services

Abstract

We propose a model to help a service provider manage a family of private-line telecommunication services. The model is a time-dependent network of infinite-server queues. The queueing network is used to model switching from one service to another. The relevant time scale is quite long: service lifetimes are measured in years, while service life cycles are measured in decades. To capture changing technology and customer preferences over this extended period, the model includes time-dependent new-connection rates, time-dependent switching rates and general time-dependent service-lifetime distributions for the different services. Because of the long service lifetimes, there is typically a significant time lag between the peak arrival rate and the peak expected number of customers receiving service. Thus sales and revenue do not move together; instead sales is a leading indicator of revenue in a service life cycle. The network structure reveals how the life cycles of different services are related. We show that it is possible to reasonably fit a version of this relatively complex model to data and then analyze the model to obtain useful descriptions of system dynamics.