This paper studies an $M/M/2/K$ queuing system with a threshold policy and asynchronous multiple vacations, where the service rates of two servers are not identical. At the completion instant of a service, the first server will take a vacation if there is no waiting customer, while the other server starts a vacation when the number of customers in the waiting line is less than the threshold value. The main purpose of this paper is to provide guidence for decision makers through detailed research on the performance of this system. Using the matrix analysis method, we obtain the stationary probability vectors and analytical expressions of the queue indexes. Finally, we establish a cost model which analyzes the influence of defferent parameters on the minimum cost and optimal threshold value of the system.