Optimality of the Symmetric Workload Allocation in a Single-Server Flow Line System
证明了制造流水线系统中对称工作量分配性质（SAP），即最优解中存在对称分配，通过凸性和线可逆性给出证明，并放宽了服务时间分布和缓冲区容量的假设条件。
This paper provides a proof of the symmetrical allocation property (SAP), conjectured in an earlier work on the workload allocation problem for a manufacturing flow line system. The system consists of N single-Erlang servers in series having a common interstation buffer capacity. SAP says a symmetric workload allocation exists among the optimal solutions. We first show the reciprocal of the throughput is increasing and jointly convex, not component-wisely, in workloads. Then we apply the line reversibility property to obtain an alternative optimal allocation symmetric for any optimal workload allocation that is asymmetric. A sufficient condition for SAP to hold is also given, which relaxes the hypothesizing assumptions on the service-time distribution and interstation buffer capacities.