Network-on-chip (NoC) is an effective interconnection solution of multicore chips. In recent years, wireless interfaces (WIs) are used in NoCs to reduce the delay and power consumption between long-distance cores. This new communication structure is called wireless network-on-chip (WiNoC). Compared to the wired links, demand to use the shared wireless links leads to congestion in WiNoCs. This problem increases the average packet latency as well as the network latency. However, using an efficient control mechanism will have a great impact on the efficiency and performance of the WiNoCs. In this paper, a mathematical modeling-based flow control mechanism in WiNoCs has been investigated. At first, the flow control problem has been modeled as a utility-based optimization problem with the wireless bandwidth capacity constraints and flow rate of processing cores. Next, the initial problem has been transformed into a dual problem without limitations and the best solution of the dual problem is obtained by the gradient projection method. Finally, an iterative algorithm is proposed in a WiNoC to control the flow rate of each core. The simulation results of synthetic traffic patterns show that the proposed algorithm can control and regulate the flow rate of each core with an acceptable convergence. Hence, the network throughput will be significantly improved.