In this paper, we propose a Bernoulli-Threshold service 
schedule for a queueing system consisting of two-parallel queues and a single 
server.  A threshold $N (0<N)$ is set up in one of the two queues, say, the 
second queue. When the queue length of the second queue is less than or equal 
to the threshold $N$, the server serves two queues with a Bernoulli service 
schedule, otherwise only customers of the second queue are served until its 
queue length is back to the threshold $N$. The sever takes switching times in 
its transition from one queue to the other. For the queueing model, we carry 
out the performance analysis and derive the generating functions of the joint 
stationary queue-length distributions at service completion instants. We also 
determine the Laplace-Stieltjes transforms of waiting time distributions for 
both queues, and obtain their mean waiting times.