This paper investigates a queueing system consisting 

of two-parallel queues and two servers. The service 

policy is a hysteretic control one such that a set of 

two forward thresholds $(F_{1}, F_{2})$ and a set of 

two reverse thresholds $(R_{1},R_{2})$ are set up 

in one of two queues, say, the second queue, and 

at each epoch of service completion, the server 

decides which queue is to be served next according to 

the control level the number of customers in the second 

queue reaches. The arrival process for each queue is Poisson, 

and the service times are exponentially distributed with 

different means. We derive the generating functions of 

the stationary joint queue-length distribution, and then 

obtain the mean queue length and the mean waiting time 

for each queue.