A multi-agent network system of different computing nodes processing tasks of different priority levels is considered. Agents balance their loads for each priority level by achieving consensus of their load values. Agents operate by local voting protocol and exchange information about their states in presence of noise in communication channels in the system with switching topology. The network usage for task exchange is limited by the constraints on average cost of utilized links. A way to meet the constraints by randomization of link usage is considered. Simulation illustrating the considered approach is provided.