Performance evaluation of a production line operated under an echelon buffer policy

We consider a production line consisting of several machines in series separated by intermediate finite-capacity buffers. The line operates under an Echelon Buffer (EB) policy according to which each machine can store the parts that it produces in any of its downstream buffers if the next machine is occupied. If the capacities of all but the last buffer are zero, the EB policy is equivalent to constant work in process (CONWIP). To evaluate the performance of the line under the EB policy, we model it as a queueing network and we develop a method that is based on decomposing this network into as many nested segments as there are buffers and approximating each segment with a two-machine subsystem that can be analyzed in isolation. For the case where the machines have geometrically distributed processing times, we model each subsystem as a two-dimensional Markov chain that can be solved numerically. The parameters of the subsystems are determined by relationships among the flows of parts through the echelon buffers in the original system. An iterative algorithm is developed to solve these relationships. We use this method to evaluate the performance of several instances of five- and 10-machine lines including cases where the EB policy is equivalent to CONWIP. Our numerical results show that this method is highly accurate and computationally efficient. We also compare the performance of the EB policy against the performance of the traditional “installation buffer” policy according to which each machine can store the parts that it produces only in its immediate downstream buffer if the next machine is occupied.