A multi-agent network system of different computing nodes processing tasks of different priority levels is considered. Agents exchange information about their states in presence of noise in communication channels in the system with switching topology. Load balancing problem in the network for each priority level is formulated as differentiated consensuses achievement problem and solved via local voting protocol. The stochastic approximation type algorithm is used to adjust step-size of proposed protocol for each priority level. Simulation example demonstrating step-size adjustment is provided.