In this paper, a threshold policy is considered for the Markovian queueing system with server vacations. The threshold policy considered in this paper has the following form: "when the number of customers present in the system increases to N, the server is turned on and serves customers until the system becomes empty". In this paper, we show how the finite capacity or finite population queueing system under a threshold policy can be modeled by the stochastic Petri net. The performance evaluation of the model is carried out using the software called "SPNP". Some examples are also presented in which it is shown that how the optimal threshold policies can be obtained under a linear cost structure.