Significant traffic variations occur in telecommunication networks. This paper focuses on hour-to-hour traffic variations during 24 hours and investigates the possibility of using idle periods effectively by introducing non-realtime service at a discount rate. In order to provide non-realtime service, memory is placed at each telecom center. When immediate service is not available, messages of non-realtime calls are stored in the memory and served later when network resources are available. Realtime calls are served with preference. A basic model and a method of dimensioning the memory capacity are presented. The basic model is extended to the network model, and methods of designing a minimum cost network and pricing and profit issues are presented. The results for a basic model are verified by traffic simulation. Numerical examples are given to show the effectiveness of non-realtime service.