Dependence in Lag for Markov Chains on Partially Ordered State Spaces with Applications to Degradable Networks

REFERENCES

• Bäuerle , N. ; Rolski , T. A monotonicity result for the workload in Markov-modulated queues . Journal of Applied Probability 1998 , 35 , 741 – 747 .
   Web of Science ®Google Scholar
• Daduna , H. ; Kulik , R. ; Sauer , C. ; Szekli , R. Dependence ordering for queueing networks with breakdown and repair . Probab. Engrg. Inform. Sci. 2006 , 20 , 575 – 594 .
   Web of Science ®Google Scholar
• Daduna , H. ; Szekli , R. Dependence ordering for Markov processes on partially ordered spaces . Journal of Applied Probability 2006 , 43 , 793 – 814 .
   Web of Science ®Google Scholar
• Daley , D. J. The serial correlation coefficients of waiting times in a stationary single server queue . Journal of the Australian Mathematical Society 1968 , 8 , 683 – 699 .
   Google Scholar
• Daley , D. J. Stochastically monotone Markov chains . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1968 , 10 , 305 – 317 .
   Web of Science ®Google Scholar
• Hu , T. ; Joe , H. Monotonicity of positive dependence with time for stationary reversible Markov chains . Probab. Engrg. Inform. Sci. 1995 , 9 , 227 – 237 .
   Google Scholar
• Hu , T. ; Pan , X. Comparisons of dependence for stationary Markov processes . Probab. Engrg. Inform. Sci. 2000 , 14 , 299 – 315 .
   Web of Science ®Google Scholar
• Jackson , J.R. Networks of waiting lines . Operations Research 1957 , 5 , 518 – 521 .
   Web of Science ®Google Scholar
• Kulik , R. Monotonicity in lag for non-monotone Markov chains . Probab. Engrg. Inform. Sci. 2004 , 18 , 485 – 492 .
   Web of Science ®Google Scholar
• McNickle , D.C. Lagged queue-length correlations in two-node networks . Queueing Systems 1991 , 8 , 97 – 103 .
   Google Scholar
• Miyoshi , N. ; Rolski , T. Ross type conjectures on monotonicity of queues . Australian and New Zealand Journal of Statistics 2004 , 46 , 121 – 131 .
   Web of Science ®Google Scholar
• Müller A. ; Stoyan , D. Comparison Methods for Stochastic Models and Risks ; Wiley : New York , 2002 .
   Google Scholar
• Rolski , T. A note on the increasing directionally concave monotonicity in queues . Probab. Engrg. Inform. Sci. 2005 , 19 , 33 – 43 .
   Web of Science ®Google Scholar
• Sauer , C. Stochastic Product form Networks with Unreliable Nodes: Analysis of Performance and Availability ; Ph.D. thesis , Mathematics Department , Hamburg , 2006 .
   Google Scholar
• Sauer C. ; Daduna , H. Availability formulas and performance measures for separable degradable networks . Economic Quality Control 2003 , 18 , 165 – 194 .
   Google Scholar