Balanced job bound analysis of queueing networks

References I. Bard, Y. A model of shared DASD and multipathing. Comm. ACM 23,10 (Oct. 1980), 564-572. 2. Bard, Y. Some extensions to multiclass queueing network analysis. In Performance of Computer Systems. Arato, M., Butrimenko, A., and Gelenbe, E. (Eds.), North Holland, Amsterdam, 1979. 3. Bard, Y. The VM/370 performance predictor. Comput. Surv. 10,8 (Sept. 1978), 333-342. 4. Brown, R.M., Browne, J.C., and Chandy, K.M. Memory management and response time. Comm. ACM 20,3 (March 1977), 153-165. 5. Buzen, J.P., and Denning, P.J. Measuring and calculating queue length distributions. Computer 13,4 (April 1980), 33--46. 6. Chandy, K.M., Herzog, U., and Woo, L. Approximate analysis of general queueing networks. IBM J. Res. Develop. 19,1 (Jan. 1975), 43-49. 7. Comput. Surv. 10,3 (Sept. 78), Special Issue on Queueing Network Models of Computer System Performance. 8. Lavenberg, S.S., and Reiser, M. Stationary state probabilities of arrival instants for closed queueing networks with multiple types of customers. Res. Rep. RC 7592, IBM Corp., April 1979. IBM Thomas J. Watson Research Center, Yorktown Heights, NY. 9. Little, J.D.C. A proof of the queueing formula L = ~ W. Oper. Res. 9 (1961), 383-387. 10. Reiser, M., and Lavenberg, S.S. Mean-value analysis of closed multichain queueing networks..L ACM 27,2 (April 1980), 313-322. II. Sauer, C.H., and Chandy, K.M. Computer System Performance Modeling: A Primer. Prentice-Hall, Englewood Cliffs, N J, 1980. 12. Schweitzer, P. Approximate analysis of multiclass closed networks of queues. Presented at the Int. Conf. Stochastic Control and Optimization, Amsterdam, 1979. 13. Sevcik, K.C., and Mitrani, I. The distribution of queueing network states at input and output instants. J. A CM 28,2 (April 1981), 358-371. 14. Zahorjan, J. The approximate solution of large queueing network models. Ph.D. Thesis, Univ. Toronto, Toronto, Ont., Canada, 1980; also Tech. Rep. CSRG-122, Univ. Toronto, Toronto, Ont., Canada August 1980. Applications of queueing network models to computer system performance prediction typically involve the computation of exact equilibrium solutions. This procedure can be quite expensive. In actual modeling studies, many alternative systems must be considered and a model of each developed. The expense of computing the exact solutions of these models may not be warranted by the accuracy required at the initial modeling stages. Instead, bounds on performance are often sufficient. We present a new technique for obtaining performance bounds with only a few arithmetic operations (whereas an exact solution of the model requires a number of arithmetic operations proportional to the product of the number of devices and number of customers). These bounds are often tighter than previously known bounds, although they require somewhat more restrictive assumptions to be applicable.