New bounds for optimum traffic assignment in satellite communication

The use of satellites to exchange information between distant places on the earth is a well assessed technique, but each satellite has high cost, so it is important to utilize it efficiently. A satellite receives requests of transmission between pairs of earth stations, which can be represented by a traffic matrix. One of the methods used for managing these communications is the satellite switched time-division-multiple-access system which requires to partition the traffic matrix in submatrices and transmits the information of each submatrix in a single time slot. Therefore a crucial decision for an efficient use of the satellite is how to partition the given traffic matrix so that the total time required to transmit the information is minimized. In the literature this problem has been addressed mainly in the special case in which the number of possible contemporary transmissions is equal to the number of rows and columns in the traffic matrix. In this paper we consider the general case in which the size of the matrix is larger than the number of contemporary transmissions. Our scope is to provide effective heuristic algorithms for finding good approximating solutions and to give tight lower bounds on the optimal solution value, in order to evaluate the quality of the heuristics. In this paper we assume that a satellite has l receiving and transmitting antennas, and we are given a traffic matrix D to be transmitted by interconnecting pairs of receiving–transmitting antennas, through an on board switch. We also assume that l is strictly smaller than the number of rows and columns of D, that no preemption of the communications is allowed, and that changing the configuration of the switch requires a negligible time. We ask for a set of switch configurations that minimizes the total time occurring for transmitting the entire traffic matrix. We present some new lower bounds on the optimum solution value and a new technique to combine bounds which obtains a dominating value. We then present five heuristics: the first two are obtained modifying algorithms from the literature; two others are obtained with standard techniques; the last algorithm is an implementation of a new and promising tabu search method which is called exploring tabu search. Extensive computational experiments compare the performances of the heuristics and that of the lower bound, on randomly generated instances.