Brownian models of closed queueing networks with homogeneous customer populations

References

• Azema , J. , Kaplan-Duflo , M. and Revuz , D. 1967 . Mesure invariante sur les classes recurrentes desprocessus de Markov . Z. Wahr, verw. Geb , 8 : 157 – 181 .
   Google Scholar
• Baskett , F. , Chandy , K. M. , Muntz , R. R. and Palacios , F. G. 1975 . Open, closed and mixed networks of queues with different classes of customers . J. of the ACM , 22 : 248 – 260 .
   Web of Science ®Google Scholar
• Billingsley , P. 1968 . Convergence of Probability Measures , New York : Wiley .
   Google Scholar
• Blumenthal , R. M. and Getoor , R. K. 1968 . Markov Processes and Potential Theory , New York : Academic Press .
   Google Scholar
• Burman , D. Y. 1986 . Performance analysis techniques for IC manufacturing lines . AT&T Tech. J. , 65 : 46 – 57 .
   Web of Science ®Google Scholar
• Chen , H. , Harrison , J. M. , Mandelbaum , A. , van Ackere , A. and Wein , L. M. 1988 . Empirical evaluation a queueing network model for semiconductor wafer fabrication . Operations Research , 36 : 202 – 215 .
   Web of Science ®Google Scholar
• Chen , H. and Mandelbaum , A. Stochastic discrete flow networks: . Diffusion approximations and bottlenecks , preprint
   Google Scholar
• Chen , H. and Mandelbaum , A. Leontief systems . RBV's and RBM's, , preprint
   Google Scholar
• Chow , W. , Macnair , E. A. and Sauer , C. H. 1985 . Analysis of manufacturing systems by the research queueing package . IBM J. Rsch. Dev , 29 : 330 – 342 .
   Google Scholar
• Qnlar , E. , Jacod , J. , Protter , P. and Sharpe , M. J. 1980 . Semimartingales and Markov processes . Z.Wahr. verw. Geb , 54 : 161 – 219 .
   Google Scholar
• Ethier , N. and Kurtz , T. G. 1986 . Markov Processes, Characterization and Convergence , New York : John Wiley and Sons .
   Google Scholar
• Fredericks , A. 1986 . Performance analysis modeling for manufacturing systems . AT&T Tech. J , 65 : 25 – 34 .
   Google Scholar
• Gordon , W. J. and Newell , G. F. 1967 . Closed queueing networks with exponential servers . Operations Research , 15 : 244 – 265 .
   Google Scholar
• Harrison , J. M. 1985 . Brownian Motion and Stochastic Flow Systems , New York : John Wiley and Sons .
   Google Scholar
• Harrison , J. M. 1988 . “ Brownian models of queueing networks with heterogeneous customer populations ” . In Stohastic Differential SystemsStochastic Control Theory and Applications, IMA , Edited by: Fleming , W. and Lions , P. L. Vol. 10 , 147 – 186 . New York : Springer-Verlag .
   Google Scholar
• Harrison , J. M. and Reiman , M. I. 1981 . Reflected Brownian motion on an orthant . Ann. Prob , 9 : 302 – 308 .
   Web of Science ®Google Scholar
• Harrison , J. M. and Williams , R. J. 1987 . Multidimensional reflected Brownian motions having exponential stationary distributions . Ann. Prob , 15 : 115 – 137 .
   Web of Science ®Google Scholar
• Harrison , J. M. and Williams , R. J. 1987 . Brownian models of open queueing networks with homogeneous customer populations . Stochastics , 22 : 77 – 115 .
   Google Scholar
• Jackson , J. R. 1963 . Jobshop-like queueing systems . Management Science , 10 : 131 – 142 .
   Web of Science ®Google Scholar
• Kelly , F. P. 1979 . Reversibility and Stochastic Networks , New York : John Wiley and Sons .
   Google Scholar
• Lazowska , E. D. , Zahorjan , J. , Graham , G. C. and Sevcik , K. C. 1984 . Quantitative System Performance , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Reiman , M. I. 1984 . Open queueing networks in heavy traffic . Math, of Ops. Rsch , 9 : 441 – 458 .
   Web of Science ®Google Scholar
• Reiman , M. I. and Williams , R. J. 1988 . A boundary property of semimartingale reflecting Brownian motions . Prob. Theor. Rel. Fields , 11 : 87 – 97 .
   Google Scholar
• Sauer , C. H. and Chandy , K. M. 1981 . Computer System Performance Modeling , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Solberg , J. J. 1977 . A mathematical model of computerized manufacturing systems . Paper presented at the 4th International Conference on Production Research , : 22 – 30 .
   Google Scholar
• Solberg , J. J. 1983 . “ Mathematical design tools for integrated production systems ” . In Efficiency of Manufacturing Systems , Edited by: Wilson , B. New York : Plenum Press .
   Google Scholar
• Thompson , C. J. 1972 . Mathematical Statistical Mechanics , New York : Macmillan .
   Google Scholar
• Weiss , A. 1981 . Invariant Measures of Diffusion Processes on Domains with Boundaries , New York University . Ph.D. diss.
   Google Scholar
• Whitt , W. 1983 . “The queueing network analyzer and Performance of the queueing network analyzer” . Bell Sys. Tech. J , 62 : 2779 – 2843 .
   Google Scholar
• Whitt , W. 1984 . Open and closed models for networks of queues . AT&T Tech. J. , 63 : 1911 – 1979 .
   Google Scholar
• Williams , R. J. 1987 . Reflected Brownian motion with skew symmetric data in a polyhedral domain . Prob. Theor. Rel. Fields , 75 : 459 – 485 .
   Google Scholar