In the process of hunting down and confronting a swarm of drones, due to the large number of targets and their high mobility, it is often difficult to completely prevent the escape of sub-targets in the swarm. For the engineering background of multiple armed drones hunting swarm targets, there is an optimization design problem of the deployment quantity of defensive drones and the interception probability of the encirclement. The process of penetrating the encirclement by the swarm is modeled as an MX/M/1 queuing model with an impatient customer. Based on the constructed model, a numerical solution method based on binary search is proposed for the queuing model. This method adjusts the numerical solution of the system to approximate the analytical solution through the sum of state probabilities in the model. In this way, the problem of nested infinite summation when using analytical methods can be avoided, and the accuracy requirements are met at the same time. Finally, simulation tests verify the effectiveness of the proposed algorithm.