Approaches such as increasing the number of intermediate stages are introduced to increase the reliability and throughput of Multistage Interconnection Networks (MINs). However, they mainly try to change the network architecture to achieve the goal of having more reliable network. When multiple sources in such a network try to send data, collision of packets and blocking problems are inevitable. Using existing networks, they cant be prevented completely and a multiple access protocol must be used to that end. Time division multiple access (TDMA) protocol can be used to overcome these problems. To improve the performance of this protocol, we propose an adaptive slot allocation approach using Monte Carlo random sampling method. This approach is applied to Shuffle-exchange network (SEN) and Shuffle-exchange network with one additional stage (SEN+). Results for 4000 simulation cycles using Network Simulator 2 (NS2) show that the new SENs perform better in terms of reliability and throughput compared to their regular types.