69 Throughput Bounds for Closed Queueing Networks with Queue-Dependent Service Rates J. George Shanthikumar School of Business Administration, University of California, Berkeley, CA 94720, U.S.A. David D. Yao * Division of Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A. Received September 1986 Revised May 1987 and November 1987 Consider a closed queueing network (CQN) with a set of stations; the service rate at each station can be any function of the queue length at that station. Upper and lower bounds are developed for the throughput of the CQN. The bounds make use of some results recently developed by the authors on likelihood ratio ordering and its preservation under convolution. As a special case, bounds for the throughput of CQN with multi-server stations are also considered. Keywords: Closed Queueing Network, Throughput Bound, Stochastic Monotonicity. I. Introduction Recently, several studies have been developing bounds for the throughput of the closed queueing network (CQN) of product-form type. For the throughput of single-class CQNs with fixed service rates, J.G. Shanthikumar is Professor of Management Science at the University of California, Berkeley. He holds a B.Sc. degree in Mechanical Engineering from the University of Sri Lanka in 1972 and an M.A.Sc. and Ph.D. in Industrial Engineering from the University of Toronto, in 1977 and 1979, respectively. He received the EVE Pereira Gold Medal for the outstanding student graduating from the College of Engineering, University of Sri Lanka, and the Canadian Commonwealth Scholarship from 1975-1979 for his M.A.Sc. and Ph.D. at the University of Toronto. His research interests are in production system modeling and analysis, queueing theory, reliability, scheduling, and simulation. He is an associate editor for the International Journal of Flexible Manufacturing Systems and Operations Research. David D. Yao is Associate Professor of Systems Engineering at Harvard University. From 1983 to 1986 he was Assistant Professor at Industrial Engineering and Operations Research at Columbia University. He holds M.A.Sc. and Ph.D. degrees in Industrial Engineering from the University of Toronto. His main research interests are in stochastic models, queueing networks, control and optimization of discrete event dynamic systems. * This author was partially supported by the National Science Foundation under Grants Nos. DMC-8503896 and ECS-8658157, and by ONR under Contract No. N00014-84-K-0465. North-Holland Performance Evaluation 9 (1988) 69-78 0166-5316/88/$3.50 © 1988, Elsevier Science Publishers B.V. (North-Holland)