This study deals with a push-pull queueing system attended by two machines, with homogeneous Poisson arrivals and general service times. In this system each job produced by machine 1 requires an operation a machine 2, while jobs produced by machine 2 move in the opposite direction.
We use the special assumption, so the P.G.F. of this system can be easily obtained. We also apply N policy to this system to minimize waiting times of each job with keeping throughput. Then we obtain explicit solution of a push-pull queueing system with N-policy. To do a cost analysis, a setup cost and a holding cost for machine 1 and 2 are considered. In the result we describe an optimal.
