Int. J. Production Economics 58 (1999) 1—15 Manufacturing systems with machine vacations, arbitrary topology and finite buffers Ayse Kavusturucu, Surendra M. Gupta*  IBM, Burlington, Mail Drop 964-A, 1000 River Road, Essex Junction, VT 05402, USA  Laboratory for Responsible Manufacturing, 334 SN, Department of MIME, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA Received 28 October 1996; accepted 1 August 1997 Abstract We consider a manufacturing system with finite buffer and arbitrary topology where a machine takes a vacation (i.e. is unavailable for processing due to the processing of secondary jobs or maintenance of machines) of random duration every time the machine becomes idle. To this end, we develop an approximation (analytical) methodology to calculate the throughput of the system using queueing networks together with decomposition, isolation and expansion methodologies. The methodology was tested rigorously covering a large experimental region. We used orthogonal arrays to design the experiments in order to keep the number of experiments manageable. The results obtained using the approximation methodology were compared to simulation results. The t-tests carried out to investigate the differences between the two results showed that the proposed methodology is very accurate as well as robust.  1999 Elsevier Science B.V. All rights reserved. Keywords: Manufacturing systems; Expansion methodology; Machine vacations; Split-merge topology; Finite buffers 1. Introduction Analysis of a manufacturing system becomes complicated as the structure of the manufacturing system grows more complex. A manufacturing sys- tem can be described as a collection of various service areas where jobs arrive at different rates and demand services with unequal processing times. Due to this nondeterministic behavior, researchers develop stochastic models (using queueing net- * Corresponding author. Tel.: #1 617 373 4846; fax: # 1 617 373 2921; e-mail: gupta@neu.edu. works) to analyze such systems. Queueing net- works are efficient tools for modelling large systems of nondeterministic nature. For less complicated networks they provide product form solutions. However, when the system becomes more complic- ated, a queueing network can no longer provide product form solution. In this case, the approxima- tion approach is the best alternative to model the system. A complication arises when a limit is imposed on the number of jobs that can wait in the queue in front of a service area. This complication is quite serious, since many real life situations impose even greater restrictions on the system. In this paper we 0925-5273/99/$ — see front matter  1999 Elsevier Science B.V. All rights reserved PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 0 9 - 6