We consider cyclic flow line models, which repetitively produces multiple items in a cyclic order. We investigate performance analysis and balancing problems of cyclic flow lines. We first examine performance of a cyclic flow line model that has finite buffers and exponential processing times. While such a cyclic flow line model can be modeled by a finite continuous-time Markov chain, the number of states tends to explode and the chain becomes computationally intractable as the number of stations and the buffer capacities increase. Therefore, we present a computationally tractable approximate performance computing method. To do this, the cyclic flow line with multiple stations is decomposed into a number of two-station submodels. Each two-station submodel is modeled by a continuous time Markov process and the steady state performance measures are computed by an iterative method. In order to approximate the full line model from the performances of the two-station submodels, the two-station submodels are parameterized by the starvation propagation and blocking propagation methods so that the performances of each two-station submodel are close to those of the two stations in the original full line model. We develop approximate algorithms for computing the cycle time, the queue length distributions, and the blocking probabilities. We also report the experimental results of the proposed algorithms.
Second, we consider a two-station cyclic flow shop model where the first station has exponentially distributed processing times and the second station has general processing time distributions. When we regard the first station as an arrival generator, the model can be considered as a single-server queue similar to an M/G/1 queue that has cyclic arrival of customers. The different types customers arrive in a cyclic order with inter-arrival times that are independent exponentially distributed but have different mean times depending on the customer type. Each customer type ...