Computational grids may include many machines located in a number of sites. For efficient use of the grid we need to have an ability to estimate the time it takes to communicate data between the machines. For dynamic distributed grids it is unrealistic to know exact parameters of the communication hardware and the current communication traffic and we should rely on a model of the network performance to estimate the message delivery time. Our approach to a construction of such a model is based on observation of the messages delivery time with various message sizes and time scales. We record these observations in a database and use them to build a model of the message delivery time. Our experiments show presence of multiple bands in the logarithm of the message delivery times. These multiple bands represent multiple paths messages travel between the grid machines and are incorporated in our multiband model.