On the Correlation Structure of Closed Queueing Networks

References

• Adan , I. and van der Wal , J. 1987 . Monotonicity of the Throughput of a Closed Erlang Queueing Network in the Number of Jobs. Technical report; Eindhoven University of Technology, Department of Mathematics and Computing Science: Eindhoven, The Netherlands.
   Google Scholar
• Adan , I. and van der Wal , J. 1987 . Monotonicity of the Throughput of a Closed Queueing Network in the Number of Jobs. Technical report; Eindhoven University of Technology, Department of Mathematics and Computing Science: Eindhoven, The Netherlands.
   Google Scholar
• Adan , I. and van der Wal , J. 1989 . Monotonicity of the throughput of a closed queueing network in the number of jobs . Oper. Res. , 37 : 953 – 957 .
   Web of Science ®Google Scholar
• Baccelli , F. and Bremaud , P. 1994 . Elements of Queueing Theory New York : Springer .
   Google Scholar
• Boxma , O.J. and Donk , P. 1982 . On the response time and cycle time distributions in a two-stage cyclic queue . Perform. Eval. , 2 : 181 – 194 . [CROSSREF]
   Web of Science ®Google Scholar
• Boxma , O.J. and Daduna , H. 1990 . “ Sojourn times in queueing networks ” . In Stochastic Analysis of Computer and Communication Systems Edited by: Takagi , H. 401 – 450 . Amsterdam : IFIP, North Holland .
   Google Scholar
• Boxma , O.J. , Kelly , F.P. and Konheim , A. -G. 1984 . The product form for sojourn time distributions in cyclic exponential queues . J. Assoc. Comput. Machinery , 31 : 128 – 133 .
   Web of Science ®Google Scholar
• Bremaud , P. , Kannurpatti , R. and Mazumdar , R. 1992 . Event and time averages: A review . Adv. Appli. Probab. , 24 : 377 – 411 .
   Web of Science ®Google Scholar
• Boxma , O.J. 1984 . “ Analysis of successive cycles in a cyclic queue ” . In Performance of Computer Communication Systems Edited by: Rudin , H. and Bux , W. 293 – 306 . Amsterdam : IFIP, Elsevier Science Publisher, North-Holland .
   Google Scholar
• Burke , P.J. 1969 . The dependence of sojourn times in tandem M/M/s queues . Oper. Res. , 17 : 754 – 755 .
   Web of Science ®Google Scholar
• Daduna , H. 1997 . “ Sojourn time distributions in non-product form queueing networks ” . In Frontiers in Queueing: Models and Applications in Science and Engineering, chapter 7 Edited by: Jewgeni Dshalalow . 197 – 224 . Boca Raton : CRC Press .
   Google Scholar
• Disney , R.R. and Kiessler , P.C. 1987 . Traffic Processes in Queueing Networks: A Markov Renewal Approach London : The Johns Hopkins University Press .
   Google Scholar
• Daduna , H. and Szekli , R. 1995 . Dependencies in Markovian networks . Adv. Appl. Probab. , 27 : 226 – 254 .
   Web of Science ®Google Scholar
• Daduna , H. and Szekli , R. 1996 . A queueing theoretical proof of increasing property of Polya frequency functions . Stat. Probab. Lett. , 26 : 233 – 242 . [CROSSREF]
   Web of Science ®Google Scholar
• Daduna , H. and Szekli , R. 2002 . Conditional job observer property for multitype closed queueing networks . J. Appl. Probab. , 39 : 865 – 881 . [CROSSREF]
   Web of Science ®Google Scholar
• Efron , B. 1965 . Increasing properties of polya frequency functions . Ann. Math. Stat. , 36 : 272 – 279 .
   Google Scholar
• Gordon , W.J. and Newell , G.F. 1967 . Closed queueing networks with exponential servers . Oper. Res. , 15 : 252 – 267 .
   Web of Science ®Google Scholar
• Jackson , J.R. 1963 . Jobshop-like queueing systems . Manage. Sci. , 10 : 131 – 142 .
   Web of Science ®Google Scholar
• Joag-Dev , K. and Proschan , F. 1983 . Negative association of random variables with applications . Ann. Stat. , 11 : 286 – 295 .
   Web of Science ®Google Scholar
• Kelly , F.P. 1979 . Reversibility and Stochastic Networks Chichester, New York–Brisbane–Toronto : John Wiley and Sons .
   Google Scholar
• Koenigsberg , E. 1982 . Twenty five years of cyclic queues and closed queue networks: A review . J. Oper. Res. Soc. , 33 : 605 – 619 .
   Web of Science ®Google Scholar
• Kook , K.H. and Serfozo , R.F. 1993 . Travel and sojourn times in stochastic networks . Ann. Appl. Probab. , 3 : 228 – 252 .
   Google Scholar
• Liggett , T.M. 1985 . Interacting Particle Systems Berlin : Springer . Volume 276 of Grundlehren der mathematischen Wissenschaften
   Google Scholar
• Lavenberg , S.S. and Reiser , M. 1980 . Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers . J. Appl. Probab. , 17 : 1048 – 1061 .
   Web of Science ®Google Scholar
• Schassberger , R. and Daduna , H. 1987 . Sojourn times in queueing networks with multiserver nodes . J. Appl. Probab. , 24 : 511 – 521 . [CSA]
   Web of Science ®Google Scholar
• Sevcik , K.C. and Mitrani , I. 1981 . The distribution of queueing network states at input and output instants . J. Assoc. Comput. Machinery , 28 : 358 – 371 . [CSA]
   Web of Science ®Google Scholar
• Spieksma , F.M. Geometrically Ergodic Markov Chains and the Optimal Control of Queues. PhD thesis, Faculteit der Wiskunde en Natuurwetenschappen, Rijksuniversiteit te Leiden, 1990
   Google Scholar
• Spieksma , F.M. 1991 . Geometric ergodicity of the ALOHA-system and a coupled processors model . Probab. Eng. Informational Sci. , 5 : 15 – 42 . [CSA]
   Google Scholar
• Shanthikumar , J.G. and Yao , D.D. 1986 . The effect of increasing service rates in a closed queueing network . J. Appl. Probab. , 23 : 474 – 483 . [CSA]
   Web of Science ®Google Scholar
• Shanthikumar , J.G. and Yao , D.D. 1987 . Stochastic monotonicity of the queue lengths in closed queueing networks . Oper. Res. , 35 : 583 – 588 .
   Web of Science ®Google Scholar
• Shanthikumar , J.G. and Yao , D.D. 1988 . Second-order properties of the throughput of a closed queueing network . Math. Oper. Res. , 13 : 524 – 534 . [CSA]
   Web of Science ®Google Scholar
• Shanthikumar , J.G. and Yao , D.D. 1989 . Stochastic monotonicity in general queueing networks . J. Appl. Probab. , 26 : 413 – 417 .
   Web of Science ®Google Scholar
• Shanthikumar , J.G. and Yao , D.D. 1994 . “ Stochastic comparisons in closed Jackson networks ” . In Stochastic Orders and Their Applications , Probability and Mathematical Statistics, chapter 14 Edited by: Shaked , M. and Shanthikumar , J.G. 433 – 460 . Boston : Academic Press .
   Google Scholar
• van der Wal , J. 1985 . Monotonicity of the Throughput of a Closed Exponential Queueing Network in the Number of Jobs. Technical report; Eindhoven University of Technology, Department of Mathematics and Computing Science: Eindhoven, The Netherlands
   Google Scholar
• van der Wal , J. 1989 . Monotonicity of the throughput of a closed exponential queueing network in the number of jobs . ORSpektrum , 11 : 97 – 100 .
   Google Scholar
• Walrand , J. 1988 . An Introduction to Queueing Networks Englewood Cliffs : Prentice-Hall International Editions .
   Google Scholar
• Whitt , W. 1992 . Counterexamples for comparisons of queues with finite waiting rooms . Queue. Syst. Appl. , 10 : 271 – 278 .
   Google Scholar