A Review of Regenerative Processes

The authors present an expository review of the theory of regenerative processes starting with the more traditional notions and then moving on to some of the more recent and modern developments. Fi...

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[2]  H. Thorisson.  Construction of a stationary regenerative process , 1992 .

[3]  M. Yu. Svertchkov.  On wide-sense regeneration , 1993 .

[4]  J. Kiefer,et al.  On the theory of queues with many servers , 1955 .

[5]  P. Glynn,et al.  Simulation output analysis for general state space Markov chains , 1982 .

[6]  E. Nummelin.  General irreducible Markov chains and non-negative operators: Preface , 1984 .

[7]  S. G. Foss,et al.  Regeneration and renovation in queues , 1991, Queueing Syst. Theory Appl..

[8]  E. Nummelin,et al.  A splitting technique for Harris recurrent Markov chains , 1978 .

[9]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[10]  T. Lindvall,et al.  W. Doeblin, 1915-1940 , 1991 .

[11]  F. Chariot,et al.  Irréductibilité et récurrence au sens de Harris des «Temps d'attente→ des files GI/G/q , 1978 .

[12]  S. Orey.  Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities , 1971 .

[13]  Ronald W. Wolff,et al.  Upper bounds on work in system for multichannel queues , 1987, Journal of Applied Probability.

[14]  Walter L. Smith,et al.  Regenerative stochastic processes , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  W. Whitt.  Embedded renewal processes in the GI/G/s queue , 1972, Journal of Applied Probability.

[16]  P. Glasserman.  Regenerative derivatives of regenerative sequences , 1993, Advances in Applied Probability.

[17]  S. Asmussen.  On Coupling and Weak Convergence to Stationarity , 1992 .

[18]  Ronald W. Wolff,et al.  A note on the existence of regeneration times , 1994, Journal of Applied Probability.

[19]  Peter W. Glynn,et al.  Stationarity detection in the initial transient problem , 1992, TOMC.

[20]  H. Thorisson.  The coupling of regenerative processes , 1983, Advances in Applied Probability.

[21]  K. Athreya,et al.  A New Approach to the Limit Theory of Recurrent Markov Chains , 1978 .

[22]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[23]  Sلأren Asmussen,et al.  Applied Probability and Queues , 1989 .

[24]  Karl Sigman,et al.  One-Dependent Regenerative Processes and Queues in Continuous Time , 1990, Math. Oper. Res..

[25]  Walter L. Smith.  Renewal Theory and its Ramifications , 1958 .

[26]  Kai Lai Chung,et al.  Markov Chains with Stationary Transition Probabilities , 1961 .

[27]  A. A. Borovkov,et al.  Asymptotic Methods in Queueing Theory. , 1986 .

[28]  M. Loève,et al.  Probability Theory II (4th ed.). , 1979 .

[29]  K. Sigman.  The stability of open queueing networks , 1990 .

[30]  K. Sigman.  Regeneration in tandem queues with multiserver stations , 1988, Journal of Applied Probability.

[31]  Douglas R. Miller.  Existence of Limits in Regenerative Processes , 1972 .

[32]  Tomasz Rolski,et al.  Stationary Random Processes Associated with Point Processes , 1981 .