تجزیه و تحلیل عملکرد برای سیستم های تولید مدار بسته با ماشین های غیرقابل اطمینان و زمان پردازش تصادفی

In this study, we propose some simple but effective throughput-approximation methods for finite-buffered closed-loop production systems with unreliable machines and exponentially distributed processing times. The proposed approximation methods are based on decomposition and aggregation principles. According to the method representing the decomposed systems, three different approximation methods are developed, along with a simple upper bounding method for throughputs. Extensive computational experiments are performed to show the effectiveness of the approximation and upper bounding methods.

Finite-buffered closed-loop queuing networks with machine failure (FCQNs-F) have been major tools for evaluating the performances of production systems (Frein et al., 1996 and Gershwin and Berman, 1981). Two major characteristics of FCQNs-F are the blocking and machine failure phenomenon. The queuing networks with this type of characteristics are basically unsolved except for some special cases (Dallery and Frein, 1993 and Frein et al., 1996). Therefore, exact solutions can be obtained by means of numerical techniques requiring time and space consumption, and the numerical technique can be used only for small networks. As a result, a considerable amount of effort has been devoted to the development of approximation methods (Choong and Gershwin, 1987 and Dallery and Frein, 1989). Only a few studies have been dedicated to the analysis of FCQNs-F. But even these studies are confined to the FCQNs-F with deterministic processing times (Frein et al., 1996) or the open-loop queuing networks (Gershwin & Berman, 1981). To our knowledge, there is no study dealing with FCQNs-F with random processing times. In this study, we propose some simple but effective throughput-approximation methods for FCQNs-F with random (specifically, exponential) processing times, along with an upper bounding method for the throughput. This paper is organized as follows. The FCQNs-F model is introduced in Section 2. Section 3 contains a detailed description of the approximation methods, and Section 4 presents a simple throughput bounding method. Some numerical results are discussed in Section 5. Conclusions are drawn in Section 6.

We proposed some simple but effective throughput-approximation methods for FCQNs-F with unreliable servers and exponentially distributed processing times. The proposed approximate methods are based on the decomposition and aggregation principles. According to the technique representing the decomposed systems, three different approximation methods were developed. We also discussed how throughput upper bound could be obtained for FCQNs-F. The extensive computational experiments show that the proposed throughput approximation and upper bounding methods are very effective.