Multi-agent systems (i.e. systems comprising many agents) have been proposed for many Internet and distributed applications. The proposed systems have little or no consideration of the effects of this multi-agent approach on network resources. In this paper, we presented a simulation assessment of the effect of multi-agent systems on network resources. The routing scheme of the agents was formulated based on the travelling salesman problem. Lightweight agent (LWA) controller was modelled using a fuzzy logic toolbox in the MATLAB environment. The performance metrics of bandwidth usage, response time and throughput were used to compare the network resources usage by different groups of LWAs (10 LWAs, 40 LWAs, 100 LWAs, 150 LWAs) during their computational task on the network. Java programs were written for the implementation of lightweight agents in the simulation. The inputs to the system were realised by multiplicative pseudorandom number generation during the simulation. The simulation result analysis was carried out based on the performance metrics stated above for the four groups of agents. Increasing the number of LWAs in a simulated multi-agent system decreased the response time but increased the throughput and the bandwidth usage. All these performance measures should be considered for developing countries with bandwidth shortages, because having too many agents in a multi-agent system could result in bandwidth wastages.