A globally convergent algorithm for solving special utilization equations

摘要

Traffic and network equilibria, utilization of emergency vehicles and police patrol units can be determined by solving particular nonlinear equations. In most applications, these equations are equivalent to the fixed point problems of monotone operators. A general globally convergent algorithm is suggested for solving such equations. With the appropriate selection of the initial approximations, the smallest and largest solutions are obtained. The method can also be used as a practical check for solution uniqueness.