A Bibliography on Semi-Markov Processes BIBLIOGRAPHY 004

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A bibliography on semi-Markov processes BIBLIOGRAPHY 004

Jozef L. Teugels (*)

INTRODUCTION

At the appearance of this bibliography we want to thank warmly all those who have helped compiling this edition by sending us titles of publications, preprints, reprints and other re- levant information. Especially Cheong C. Kong and Jos H.A. de Smit have contributed at an early stage. All publications by the same author have been arranged by the year of publication. This will be convenient if in the future we should decide to publish a supplement to this bibliography. The present version contains about 600 papers written by some 300 authors. We have indicated to the best of our kwowledge where a publication has been reviewed or summarized. We write ST for Statistical Theory and Method Abstracts, MR for Mathematical Reviews and Zbl for Zentralblatt fiir Mathematik und ihre Grenzgebiete. The first number refers to the volume and the second to the number of the page (for Zbl) or review/abstract (for ST and MR). Thus MR 27-1999 refers to review number" 1999 of volume 27 of Mathe- matical Reviews.. We follow MR in our abbreviations and transliterations for the names of journals. The reader's attention is drawn on translations made of journals published in Russian. The index volumes of MR should be consulted. New information can always be forwarded to the author.

BIBLIOGRAPHY

Akimov A.P. and Pogosjan I.A. Andronov A.M. and Gertsbakh I.G. On structural reservation systems with repair and cold reser- On properties of multidimensional functionals on semi-Mar- vation 1974 kov processes with finite state space. 1972a (Kussian). Kibernetika, 1974, 91-95. Zbl : 275-509. (Russian). Kybernetika, 1972, 118-122. MR : 47-1150, Zbl : 293-416. Aladzev B.M. Application of semi-Markov processes in estimating the re- Andronov A.M. and Rosenblit P. Ya. liability of separable duplicating systems. 1972a Statistics of semi-Markov birth and death processes and their {Russian). Avtomat. vy~islit. Tehn. Riga. Zbl : 245-400. application to the analysis of complex queueing systems. 1972a Aleksandrov Ju. A. and Jancevi~ A.A. (Kussian). Izvestija Akad. Nauk. SSSK, Tehn. Kibernet., 3, Some classes of stochastic processes with after effect.1970a 1972, 113-120. Zbl : 283-349. (Russian). Vestnik Har'kov. Gos. Univ., 53 , 139-157. MR : 44-1091. AniSimov V.V. Limit theorems for semi-Markov processes with a countable Anderson L.B. set of states. 1970a Filtered semi-Markov processes. 1967a Soviet Math. Dokl., 11,945-948. MR : 42-3851, Zbl : 228- M. So. Thesis. Northwestern University. 340. Limit distributions of functionals of a semi-Markov process Markov renewal theory on the whole line. 1971a given on a fixed set of states, up to the time of first exit. Ph.D. Thesis, Northwestern University, Evanston (Ill.), 1970b U.S.A. Soviet Math. Dokl., 11, 1002-1005, MR : 42-3852, Zbl : 228-340.

(*) J.L. Teugels, Katholieke Universiteit te Leuven, Celestijnenlaan 200 B, 3030 Heverlee, Belgium. Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 125 Anisimov V.V. Some theorems on limit distributions for sums of random On the asymptotic behaviour of a generalization of Markov variables connected into the homogeneous Markov Chain. renewal processes. 1972b 1970c Soc. Sci. Fenn. Comment. Phys.-Math., 42, i7-25. MR : 47- Dopovidi Akad. Nauk. Ukrain. RSR, Ser. A, 99-103. 1146, Zbl : 238-424. (English summary). MR : 44.3390, Zbl : 194-496. On the use of a fundamental identity in the theory of semi- Limit theorems for semi-Markov processes, I. 1970d Markov queues. 1972c (Russian). Teor. Verojatnost. i Mat. Statist., 2, 3-12. MR : Advances Appl. Probability, 4, 271-284. ST : 14-1651, MR : 43-5624, Zbl : 222-403. 49-4115, Zbl : 243-417. Limit theorems for semi-Markov processes, II. 1970e Arjas Elja and Speed Terrance P. (Russian). Teor. Verojatnost. i Mat. Statist., 2, 13-21. MR : An extension of Cramer's estimate for the absorption proba- 43-5624, Zbl : 222-403. bility of a random walk. 1973a Multidimensional limit theorems for semi-Markov processes proc. Camb. Philos. Soc. ST : 14-1652. with a countable set of states. 1970f Symmetric Wiener-Hopf factorizations in Markov additive pro- (Russian). Teor. Verojatnost. i Mat. Statist., 3, 3-15. MR : cesses. 1973b 45-2809, Zbl : 238-424. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 26, 105-118. Limit theorems for sums of random variables on Markov MR : 48-9848, Zbl : 244-413. chains, connected with the exit from a set, forming a class Topics in Markov additive processes. 1973c in the limit. 1971a Math. Scandinav., 32L, 171-192. MR : 49-6369, Zbl : 277-369. (Russian). Teor. Verojatnost. i Mat. Statist., 4, 3-17. MR : 44.7648, Zbl : 225-383. A stopping problem in Markov additive processes. 1973d Advances Appl. Probability, 5, 2-3. Limit theorems for sums of random variables, in series scheme, given on a subset of states of a Markov chain up to the Arseni~vili G.L. instant of exit. 1971b Some queries on semi-Markov processes of order r. 1970a (Russian). Teor. Verojamost. i Mat. Statist., 4, 18-26. MR : (Russian). Voprosy razrab, i vnedrenija, sredstv vy~isl, tehn. 44-7649, Zbl : 225-383. Thilisi, 128-132. On the summation of random variables on a Markov chain On a class of functionals for complex semi-Markov processes with a countable splitting set of states. 1972a with discrete intervention of chance. 1970b Doklady Akad. Nauk. SSSR, 203 , 735-737. Soviet Math. (Russian). Sakharth. SSR Mecn. Akad. Moambe, 58, 25-28 Dokl., 13,431-434, Zbl : 264-380. (English summary). MR : 43-4136, Zbl : 195-477. The limiting behaviour of a semi-Markovian process with a On a problem in the theory of mass service. 1971a decomposable state space. 1972b (Russian). Sakharth. SSR Mecn. Akad. Moambe, 59, 545-548 Doklady Akad. Nauk. SSSR., 206, 777-779. Soviet Math. (English summary). Zbl : 205-485. Dokl., 13, 1276-1279. MR : 47-2685, Zbl : 266-361. Certain limit theorems for semi-Markov processes with coun- Arseni~vili G.L. and E~ov LI. table state space in a scheme of series. 1972c The distribution of the sojourntime in a given region of a semi- (Russian). Teor. Verojatnost. i Mat. Statist., 6, 3-13. MR : Markov process of order r. 1969a 46-8296, Zbl : 284-383. RUSsian). Thbilis. Sahelmc. Univ. Gamogeneb. Math. I~sti. om., 2, 151-157. MR : 43-4135. Limit theorems for random processes with a splitting set of states. 1972d A certain limit tlaeorem for semi-Markov processes or order r. (Russian). Doldady Akad. Nauk. SSSR, 210, 1001-1003. 1969b MR : 50-3305. (Russian; Georgian and English summaries). Sakharth. SSR Mecn. Akad. Moambe, .53_, 25-28. ME : 40-6624, Zbl : 196- Asymptotic consolidation of the states of stochastic pro- 199. cesses. 1973a (Russian). Kibernetika, 1973, 109-118. MR : 49-6350, Zbl : A generalization of Markov chains with semi-Markov interven- 273-364. tion of chance. 1969c (Russian; Georgian and English summaries). Sakharth. SSR Limit theorems for sums of random variables defined on a Mecn. Akad. Moambe. 54, 285-288. MR : 41-1113, Zbl : countable subset of a Markov chain up to time of exit. 177-218. 1973b (Russian). Teor. Verojatnost. i Mat. Statist., 8, 3-13. Zbl : Arseni~vili G.L. and Prizva G.I. 274-375. On the distribution of the size of the first jump of a semi- Markov process of order r over a random level. 1972a Annaev T. (Russian. English summary I. Soohscenija Akad. Nauk, Gruzin. A certain problem in queueing theory with semi-Markov SSR. 68, 297-300, Zbl : 244.416, MR : 50-5968. servicing of demands. 1971a (Russian), Izv. Akad. Nauk. Turkmen. SSR. Ser. Fiz.-Tehn. Arseven Ersen and Kshirsagar Anant M. Him. Geol. Nauk., 3, 98-100. MR : 47-1152. Stationary state probabilities of a Markov renewal process and optimum scores associated with the states. 1974a Anselone Philip M. Commun. Statist., 3, 923-931. Zbl : 295-371. Ergodic theory for discrete semi-Markov chains. 1960a Duke Math. J., 27, 33-40. MR : 22-12567. Zbl : 104.370. Asakura T. and Osaki Shunji. Limit theorems for semi-Markov processes. Part L 1960b A two-unit standby redundant system with repair and preven- Amer. Math. Monthly, 67, 565-566. tive maintenance. 1970a J. Appl. Probability, 7, 541-648. Arias Elja On a fundamental identity in the theory of semi-Markov Bandura V.N. and E~ov I.L processes. 1972a The distribution of the first passage time of a given level for Advances Appl. probability, 4, 258~270, ST : 14.1650, a certain class of functions with steplike trajectories, I, IL MR : 49-4114, Zbl : 243-417. 1970a (Russian-English summary). Teor. Verojamost. i Mat. Statist., 1, 7-21 and 22-36. MR : 43-1258, Zbl : 259-395.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 126 Barlow Richard E. Borovkov A.A. A~lications of semi-Markov processes to counter and re- Certain problems for controlled stochastic processes. 1964a liability problems. 1962a Sibvisk. Mat. ~, 5., 996-1006. Ph. D. Thesis. Techn. Rep. 57, Appl. and Stat. Labs., Stan- ford University, Stanford. On convergence of weakly dependent processes to the Wiener process. 1968a Applications of semi-Markov processes to counter problems. Theor. Probability Appl., 12, 159-186. Zbl : 214-162. 1962b Studies in Appl. Probabs~ity and Management Sc. ed. Arrow, Borovkov A.A. and Rogosin B.A. garlin, Scarf. Stanford University Press, Stanford, Cal., 34-62. Boundary problems for certain two-dimensional random MR : 25.2641,Zbl : 116-105. variables. 1964a Theor. Probability Appl., 9, 401-430. Barlow Richard E. and Proschan Frank Mathematical theory of reliability. 1965a Boyse John W. grdey New York. MR : 33-3765, Zbl : 132-393. Determining near-optimal policies for Markov renewal decision processes. 1974a Barlow Richard and Marshall Albert W. and Proschan Frank. IEEE Trans. Systems Man Cybernetics SMC, 4, 215-217. ~operdes of probability distributions with monotone hasard Zbl : 301-377. rate. 1963a Ann. Math. Statistics,34. 375-389. Zbl : 249-363. Branson M.M. and Shah B. Reliability analysis of systems comprised of units with arbit- Basawa I.V. rary repair-time distributions. 1971a ]rarametric estimation based on Poisson sampling from a se- IEEE Journal Reliability, 20, 21%223. ST : 14-1749. mi-Markov process. 1974a Austral. J. Stat.. Brock Dwight B. Statistical inference for Markov renewal processes. 1971a Belenkil V.Z. Ph. Thesis. Southern Methodist Univ., Dept. Statist., Themis- A new algorithm for the search of optimal stationary con- contract. Technical report, nr. 103. trol in a semi-Markovian solution process. 1970a (Russian). Kibernetika, 1970, 102-107. Zbl : 256-547. Bayesian analysis for Markov renewal processes. 1973a Metron, 29, 185.198. Zbl : 298-422. Beljavskaja T.G. Finding the optimal policy on semi-Markov decision pro- Brock Dwight B. and Kshirsagar A.M. cesses. 1970a On X2 goodness of fit test for Markov renewal processes. (Russian}. primenen. Mat. Ekonom., 6, 123-138. MR : 48- 1973a Ann. Inst. Statist. Math. 5605. Brodi S.M. Berg Menachem Study of mass service systems by using semi-Markov proces- Optimal replacement policies for two-unit machines with ses. 1965a increasing running costs I. 1976a (Russian). Kibernetika, 1965, 55-58. MR : 35-2366, Zbl : Stochastic Processes AppL, 4, 89-106. 203-190.

Berman Simeon M. Brodi S.M. and Pogosjan I.A. Note on extreme values, competing risks and semi-Markov On a queueing model with priorities. 1971a processes. 1963a (Russian). Kibernetika, 1971, 72-75. Zbl : 261-360. Ann. Math. Star., 34. 1104-1106. ST : 7-740, MR : 2% 1999, Zbl : 203-217. Imbedded stochastic processes in queueing theory. 1973a (Russian). Naukova Dumka, Kiev. MR : 49-11653, Zbl : Bhat U. Narayan 274-394. A study of the queueing systems M/G/1 and GIIM/1.1968a Lecture Notes in Operations Research and Mathematical Brodi S.M. and Koroljuk V.S. and Turbin A.F. Economics nr. 3, Springer-Verlag, Berlin. MR : 41-4686, Semi-Markov processes and their applications. 1974a Zbl : 167-171. (Russian).!togi Nauki Techn. Set. Teor. Verojatn., Mat. Sta- tist. teor. Kibemet., 11,47-97. Zbl : 298-422. Some problems in finite queues. 1974a Lecture Notes Economics Math. Syst., 98, 139-156, Zbl : Brodi S.M. and Spak V.D. 291-409. Application of associated semi-Markov processes to the reliability of systems, I. 1965a Bhat U. Narayan and Nance Richard E. (Russian). Kibernetika, 1965, 55-58. Zbl : 271-535. Busy period analysis of a time sharing system modeled as a semi-Markov process. 1971a Brown Mark and Ross Sheldon M. J. Assoc. Comput. Mach., 1_88, 221-238. MR : 43-8272, Asymptotic properties of cumultative processes. 1972a Zbl : 219-467. SIAM J. Appl. Math., 2_22, 93-105, Zbl : 283-346. Dynamic quantum allocation and swap-time variability in time-sharing operating systems. 1973a Burtin Yu D. and Pit-tel B.G. Southern Methodist University, Computer Science, Opera- Semi-Markov decisions in a problem of optimizing a check- tions Research. Technical Report, CP-73009. ing procedure for an unreliable queueing system. 1973a Theory Probability Appl., 17,472-493. MR : 47-1156, Bh_at U. Narayan and Nance Richard E. and Oaybrook Zbl : 269-362.

.Busy period analysis of a time sharing system : Transform Cane Violet R. reversion. 1972a Behaviour sequences as semi-Markov chains. 1959a J. Assoc. Comput. Mach., 19,453-463. J. Royal Statist. Soc. Ser. B, 21, 36-58. ST : 2-184 and 2-185, MR : 21-7867, Zbl : 87-344.

-- i Journal of Computational and Applied Mathematics, volume 2, no .2, 1976. 127 Chen Shun-Zer Cin!ar Erhan Contributions to the theory of queues with semi-Markovian Stream balking from the queueing system SM/M/1. features. 1969a undated b Ph.D. Thesis, Purdue University, Dept. of Statistics. Technological Institute, Northwestern University, preprint. Analysis of systems of queues in parallel. 1965a Chen Shun-Zer and Neuts Marcel F. Ph.D. Thesis. Univ. of Michigan, Ann Arbor, 159 pp., 6 The infinite server queue with semi-Markovian arrivals and fig., in 4 ° . negative exponential services. 1972a J. Appl. Probability, 9, 178-184. ST : 14-819, MR : 45- Decomposition of a s0mi-Markov process under aMarkovian 1290, Zbl : 239-413. rule. 1966a Austral. J. Stat., 8, 163-170. ST : 8-1019, MR : 34-8482, The infinite server queue with Poisson arrivals and semi- Zbl : 146-384. Markovian services. 1972b Operations Res., 20, 425-433. Zbl : 267-395. Decomposition of a semi-Markov process under a state dependent rule. 1967a .Cheong Choong Kong SIAM J. Appl. Math. 15, 252-263. MR : 35-6219, Zbl : 152- Geometric convergence of semi-Markov transition probabili- 165. ties. 1967a Time dependence of queues with semi-Markovian services. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 7, 122- 1967b 130. ST : 9-482, MR : 35-1083, Zbl : 146-384. J. Appl. Probability, 4, 356-364. ST : 9-483, MR : 35-5008, Solidarity and ergodic properties of semi-Markov-transition Zbl : 153-199. probabilities. 1968a Queues with semi-Markovian arrivals. 1967c Ph.D. Thesis. Australian National University, Canberra, pp. J. Appl. Probability, 4, 365-379. ST : 9-484, MR : 35-5009, 123. Zbl : 153-200. Ergodic and ratio limit theorems for ¢X-recurrent semi-Markov On the superposition of m-dimensional point processes.1968a processes. 1968b J. Appl. Probability, 5, 169-176. ST : 10-1025, MR : 37- Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 9, 270- 963, Zbl : 284-369. 286. ST : 10-261, MR: 37-5949, Zbl : 162-490. Some joint distributions for Markov-renewal processes.1968b Quasi-stationary distributions in semi-Markov processes. Austral. J. Stat., 10, 8-20. ST : 12-935, MR : 38-1754, Zbl : 1970a 162-487. Correction. Journal of Applied Probability, 7, 388-399, Cor- rect. : 788. ST: 12-612 and 1255, MR : 42-3853 and 43- On semi-Markov process on arbitrary spaces. 1969a 5625, Zbl : 206-485 and 214-170. Proc. Cambridge Philos. Soc., 66,381-392. ST : 13-1499, MR : 41-4631, Zbl : 211-484. Cheong Choong Kong and Teugels, Jozef L. Markov renewal theory. 1969h General solidarity theorems for semi-Markov processes.1972a Advances in Appl. Probability, 1, 123-187. ST : 13-1071, J. Appl. Probability, 9, 789-802. ST : 14-1667, MR : 49- MR : 42-3872, Zbl : 212-496. 11650, Zbl : 246-417. On dams with continuous semi-Markovian inputs. 1971a On a semi-Markov generalization of the random walk.1973a J. Math. Anal. Appl., 35,434-448. Zbl : 229-424. Stochastic Processes Appl., 1, 53-66. ST : 14-1200, Zbl : 252-407. Markov additive processes I. 1972a Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24, 85-93. Cheong Choong Kong and De Smit Jos and Teugels Jozef L. ST : 14-1669, MR : 48-7389, Zbl : 236-403. Bibliography. Notes on semi-Markov theory, part II. 1973a CORE Discussuon Papernr. 7310, revised and enlarged edi- Markov additive processes II. 1972b tion. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24, 95- 121. ST : 14-1670, MR : 48-7389, Zbl : 236-403. Cheong Choong Kong and De Smit Jos and Janssen Jacques Markov renewal processes : preliminaries. 1972c ind Lambotte Jean-Pierre and Teugels Jozef L. and Vande- Stanford Univ. Dept. Operations Res. Technical report nr.22. wiele Georges Definitions, classification and limit theorems. Notes on se- Markov renewal processes ; regeneration property and the mi-Markov theory, part I. 1971a • classification of states. 1972d CORE Discussion paper, hr. 7118. Stanford Univ. Dept. Operations Res. Technical report nr.23. Markov renewal processes : approach to infinity. 1972e .Cherry W. Peter and Disney Ralph L. Stanford Univ., Dept. Operations Research, Technical report Some topics in queueing network theory. 1974a hr. 24. Lecture Notes Economics Math. Syst., 98, 23-44. Zbl : 291- 410. Theory of continuous storage with Markov additive inputs and a general release rule. 1973a Chitgopekar S.S. J. Math. Anal. Appl., 43, 207-231. MR : 47-5989, Zbl : Continuous time Markovian sequential control processes. 265-392. 1969a Periodicity in Markov renewal theory. 1974a SIAM J. Control, 7, 367-389. MR : 41-9631. Advances Appl. Probability, 6, 61-78. Zbl : 281-383. MR : 50-11511. Chistyakov V.P. and Sevastyanov B.A. Comparison of multistage repairs and moments of branching L~vy systems of Markov additive processes. 1975a of processes. 1969a Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31, 175-185. Reports of the Soviet-Japanese Symposium on probability Entrance-exit distributions for semi-regenerative proces- theory, Novosibirsk. ses. 1975b The Center for Math. Studies in Economics and Manag. Cinlar Erhan Science, Northwestern Univ.. Discussion paper hr. 146. Queueing system SM/M/1 with Balking. undated a Introduction to stochastic processes.. 1975c Technological Institute, Northwestern University, preprint. Prentice-Hall, New York.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 128 ~tu Disney Ralph and Hall William K. re of semi-Markov processes. 1975d [~inite queues in parallel under a generalized channel selec- Advances Appl. Probability, 7, 230. tion rule. 1971a J. Appl. Probability, 8, 413-416. MR : 44-4826, Zbl : 223- han and Disney Ralph L. 430. ~ f overflows from a finite queue. 1967a Operations Res., 15, 131-134. MR : 34-5176, Zbl : 158-168. Disney Ralph L. and Vlach T.L. The departure process from the GI/G/1 queue. 1969a Cinlar Ethan and Pinsky Mark A. J. Appl. Probability, 6, 704-707. ST : 11-1072, MR : 41- ~ochastic integral in storage theory. 1971a 2803, Zbl : 187-181. Wahrscheinlichkeitstheorie und Verw. Gebiete, 17,227- 240, ST : 12-1326, gbl : 195-475. D~ney Ralph L. see Mso Che~yW.P.,~nlarE., De Morais R.P. Claybrook BiUG. ~eBhatU..N. Dobridjen V.A. Optimal observation of semi-Markov processes. 1971a Clifford Peter and Sudbury Aidan (Russian). Engrg. Cybernetics, 4, 47-50. linear cell-size-dependent branching process. 1972a j. Appl. Probability, 9, 687-696. Zbl : 271-379. Ee Soo Mei Some problems relating to semi-Markov theory. 1971a Cox D.R. and Lewis P.A.W. M. Sc. Thesis, University of Malaya, Kuala-Lumper. A'~ultivariate point processes 1972a Proc. 6th Berkeley Symp. Math. Statist. Prob., Univ. CaliL, Ekholm Anders 1970, p3,401-448. Zbl : 267-379. A pseudo-Markov model for stationary series of events.1971a Commentationes phys.-math., soc. Sci. Fennica, 41, 73-121. Crabill Th. B. MR : 43-8197, Zbl : 217-505. gufficient conditions for positive recurrence and recurrence of specially structured Markov chains. 1968a A generalization of the two-state interval semi-Markov mo- Operations Res. 16, 858-867. Zbl : 165-197. del. 1972a Stochastic point processes, Ed. Lewis Peter, Wiley, 272-284. Deb R, and Serfozo Richard F. Zbl : 259-406. 6primal control of batch service queues. 1973a Adv. Appl. Probability, 5,340-361. MR : 49-6403.Zbl : 264- Emrich O. 387. Bestimmung optimaler Stoppmengen bei bin/iren Markoffschen Erneuerungsprozessen mit Hilfe yon Verfahren der Politikitera- De Cani J.S- tion. 1972a dynamic programming algorithm for embedded Markov Operations ges. Verf., 12, 116-129. Zbl : 252-560. chains when the planning horizon is at infinity. 1964a Management Sci., 10, 716-733. Eshel nan De MoraLs Paulo Kenato and Disney Ralph L. Evolution processes with continuity of types. 1972a Some properties of departure processes from MIGlllN Adv. Appl. Prob., 4, 475-507. ST : 14-1680. queues. 1971a Instituto Tecnolbgico de Aeron~lutica, Brasil. Preprint. F~ov I.I. Ergodic theorems for Markov processes with discrete inter- De Morals Paulo Renato and Disndy Ralph L. and Fanell vention of chance. 1966a .Robert L. (Ukranian, Russian and English summaries). Dopovidi Akad. A characterization of M/G/1 queues w~th renewal departure Nauk, Ukrain. RSK Ser. A., 579-582. MR : 35-4989, Zbl : processes. 1973a 161-151. Management ScL, Theory, 19, 1222-1228. MR : 49-6398, The time of attaining a given region in the case of a Markov Zbl : 272-395. chain with discrete intervention of chance. 1966b (Ukranian, Russian and English summaries). Dopovidi Akad. Denardo Eric V. and Fox Benneth L. Nauk, Ukrain. RSK Ser. A., 851-854. MR : 35-2342, Zbl : Multichain Markov renewal programs. 1968a 156-185. SIAM J. Appl. Math., 16,468-487. MR : 38-3037, Zbl : Markov chains with discrete interference of an event forming 201-193. a semi-Markov process. 1966c (Kussian). Ukrain Mat. Z., 18, 48-65. MR : 34-857, Zbl : Denardo Eric V. 183-234. Markov renewal programs with small interest rates. 1971a Ann. Math. Statist.,42,477-496. MR : 44-7963, Zbl : 234- An ergodic theorem for Markov processes, which describe 384. a general queue. 1966d (Russian) Kibernetika, 1966, 79-82. MR : 36-2221, Zbl : Derman ~rrus 183-233. R.emark concerning two-state semi-Markov processes. 1961a Ergodic theorems for stochastic processes with semi-Markovi- Ann. Math. Statist., 32,615-616. Zbl : 115-137. an transition probabilities. 1968a (Russian) Ukrain Mat. ~, 20,384-388. Zbl : 249-376. De Smit Jos H.A. see Cheong C.K. On the distribution of the size of a jump of given level for a sequence of maxima of random variables controlled by a Dikarev V.E. and gi~'onok N.A. Markov chain. 1969a Reliability analysis for operating a complex of complex (Kussian) Ukrain Math. J., 21,694-698. Zbl : 199-527. systems. 1971a Markov chains that are homogeneous in the second com- (Russian). Kibernetika, 1971, 108-115. Zbl : 248-~98. ponent and their applications to the problem of the time Disney Ralph L. of first crossing of a given level. 1969b {Russian). Proc. Sixth Math. Summer School : Probability Analytic studies of stochastic networks, using methods of Theory and Math. Statist. (Kaciveli, 1968), 295-311. Akad. network decomposition. 1967a Nauk. Ukrain. SSK, Kiev. MR : 43-1269, Zbl : 254-366. Industrial Eng., 18, 140-145.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 129 E~ov I.I. Fabens Augustus J. The distribution of the time of the first jump over a given The maximum sojourn time for a semi-Markov process.1968a level for a certain class of random sequences. I, IL 1970a Canadian Oper. Res. Soc. J., 6, 171-175. Zbl : 169-493. (Russian, English summary). Teor. Verojatnost. i Mat. Statis- ti., 2, 55-75 and 76-97. MR : 44.1108, Zbl : 257-357. Fabens Augustus J. and Karlin Samuel A generalization of renewal processes. 1972a Generalized renewal functions and stationary inventory mo- Selected Transl. Math. Statist. and Prob., 10, 246-250. dels. 1962a Zbl : 278-401. J. Math. Anal. AppL 5, 461-487. MR : 26-828, Zbl : 203-221. A stationary Inventory Model with Markovian Demand.1962b E[ov I.L and Koroliuk V.S. Mathematical Methods in the Social Science, Ed. Arrow, Kar- Semi-Markovian processes and their applications. 1967a lin, Suppes. Stanford University Press, Stanford, 159-175. (Russian). Kibernetika, 1967, 58-65. Cybernetics, 3, 50056. MR : 44-1124, Zbl : 183-234. Fabens Augustus J. and Neuts Marcel F. The limiting distribution of the maximum term in a sequence E~.ov LI. and Prizva G.I. of random variables defined on a Markov chain. 1970a A generalization of Markov chains with continuous para- J. Appl. Probability, 7, 754-760. ST : 12-621, MR : 43- meter. 1966a 6966, Zbl : 204-507. (Ukranian, Russian and English summaries/. Visnik Ki'~v Univ., 8, 145-152. MR : 35-6210. Fabens Augustus J. and Perera A.G.A.D. Some limit theorems for functionals of sums of random A correction to the "Solution of queueing and inventory variables controlled by a Markov chain. 1969a models by semi-Markov processes". 1962a (Russian) Kibernetika, 1969, 63-67. Cybernetics, 5, 1969, J. Roy Statist. Soc., Set. B, 25, 455-456. ST : 5.729, MR : 313-318. MR : 46-936, Zbl : 209-494. 29-5309, Zbl : 203-182.

E[ov I. I. and Skorohod A.V. Fal' A.M. Markov processes with homogeneous second component L The simplest Markov random walk. 1973a 1969a (Russian). Dokl. Akad. Nauk SSSR, 211, 5400542. MR : 48- Theor. Prob. Appl., 14, 1-13. ST : 13-1083, MR : 40-929, 5187. Zbl : 213-200. Farrdl Robert L. Markov processes with homogeneous second component II. see D e MoraLs P.R. 1969b Theor. Prob. Appl., 14 , 652-667. ST : 13-1083, MR : 42- Feinleib M. and Zelen Marvin 2542, Zbl • 196-200. On the theory of screening for chronic deseases. 1969a Biometrika, 56, 601-604, ST : 11-1431, MR : 41-2871, E~ov I. I. and Wang-An Zbl : 184-237. Limit theorems for a class of random variables connected in a Markov chain. 1967a Feller William Dopovidi Akad. Nauk. Ukrain. RSR, Ser. A., 577-579. On semi-Markov processes. 1964a MR : 37-5922, Zbl : 154.429. Proc. Nat. Acad. Sci. USA, Sect. A, 51, 653-659. Zbl : 119- A limit theorem for a sequence of series of random varia- 346. bles linked in a homogeneous Markov chain. 1969a Dopovidi Akad. Nauk. Ukla~n. , RSR Ser. A., 108-110. Se- Finkbeiner B. and Runggaldier W. lected Transl. Math. Statist. and Prob., 10, 1971, 45-48. A value iteration algorithm for Markov renewal program- MR : 39-3567, Zbl : 164-476. ming. 1969a "Computing Methods in Optimazation problems IF', Acade- F~ov I. I. and Gahrovski 1.7_, and Zaharin A.M. mic Press, N.Y. MR : 41-6566, Zbl : 221-580. On a generalization of semi-Markov processes. 1973a Teor. Verojatnost. i Mat. Statist., 9, 47-60. Zbl : 303-375. Flaspohler David C. Quasi-stationary distributions. 1971a F_~ov I. I. and Gergely T. and Tsukanow L N. Ph. D. Dissertation, Rutgers University. ~atrkov chains governed by complicated renewal processes. 1970a Flaspohler David C~ and Holmes Paul T. Advances Appl. Probability, 2, 287-322. ST : 12-627, MR: Additional quasi-stationary distributions for semi-Markov 42-1229, Zbl : 205-443. processes. 1972a J. Appl. Probability, 9, 671-676. ST : 14-1219, MR : 49- F~ov I. I. and Koroljuk V. S. and Statland E. S. 11652, Zbl : 241-407. The maximum distribution of processes with independent increments which are governed by a Markov chain. 1969a Fong Seh-Ching (Humphrey) (Ukranian, English and Russian summaries). Dopovidi Akad. Contributions to the ergodic theory of semi-Markovian opera- Nauk. Ukra'~n RSR, Ser. A, 115-118. Selected Transl. Math. tors. 1969a Statist. and Prob., 10, 1971, 49-53. MR : 40-937, Zbl : Ph. D. Thesis. Ohio State University. 164-403. Fox Bennett L. see also Arseni~vili G.L., Bandura V.N. Markov renewal programming by linear fractional programming. 1966a Fabens Augustus J. SIAM J. Appl. Math. 14, 1418-1432. MR : 35-4023, Zbl : The solution of queueing and inventory models by semi- 154-450. Markov processes. 1959a Ph. D. Thesis. Tech. Rep. N ° 20. ONR Contract NONR 225, Semi-Markov processes : a primer. 1967a Stanford University, Stanford. Rand corporation Report P-3577-1.

The solution of queueing and inventory models by semi- Existence of stationary optimal policies for some Markov Markov processes. 1961a renewal programs. 19671) J. Roy. Statist. Sot., Set. B, 23, 113-127, ST :3-269,Zbl : SIAM Rev., 9, 573-576. Zbl : 158-386. 201-503.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 130 Fox Bennett L. age replacement. 1967c road with a two-lane road. 1964a Tech. Rep. nr. 11, University of Washington, Department j. Math. Analysis AppL, 1_88, 365-376. Zbl : 244-553. of Mathematics. (g,w)-optimal in Markov renewal programs. 1968a Management ScL, 15, 210.212. Gihman L.I. Semi-Markov decision chains. 1974a Fox Bennett L. and Rolph John E. (Rupiah). Kibernetika, 1974, 107-112. MR : 50-9405. A-"d~tive policies for Markov renewal programs. 1973a Ann. Statist., 1, 334-341. MR : 50-3918, Zbl : 259-533. Gihman L.I. & Skorohod A.V. Theory of Stochastic Processes II, 1973a Fox Bennett L~ (Russian). Nauka, Moskow. MR : 49-6288, Zbl : 298-412. se"e also Denardo E.V. Ginsberg Ralph B. Franken Peter Semi-Markov processes and mobility. 1971a ~rmeln ftir semimarkowschen Eingang. 1968a J. Math. Sociology, 1, 233-262. MR : 50-9376. Elektron. Informationsverarbeit. Kybernetik., 4_, 197-204. Critique of probabilistic models : application of the semi- Markov model to migration. 1972a Fukushima M. and Hitsuda M. J. Math. Sociology, 2, 63-82. Zbl : 242-523. (~n a class of Markov processes taking values on lines and the central limit theorem. 1968a Incorporating causal structure and exogenous information Nagoya Math. J., 30, 47-56. Zbl : 178-206. with probabilistic models; with special reference to choise, gravity, migration and Markov chains. 1972b Fursova T.I. J. Math. Socio!ogy, 2, 83-103. Zbl : 242-524. Study of an inventory system using a semi-Markov process. 1970a Gnedenko B.V. and Kovalenko LN. (Russian). Kibernetika, 1970, 93-97. Zbl : 231-520. Introduction to queuein$ theory, 1968a Israel Program for Scientific Translations, Jerusalem. Zbl : Gabrovsky I.A. 186-245. see E]ov I.I. Einflihrun$ in die Bedienun&stheorie, 1971a Translation from Russian by Jurgls Szlaza. Keedited by Hans- Gaede K.W. Joachim Kossberg. Appendix on the robustness properties Sensitivit£tsanalyse fiir einen semi-Markov prozess. 1974a of service systems by D. K~nig, K. Matthes and K. Nawrotz- Z. Operations Kes. Set. A-B, 18, A197-204. MR : 50-11515. ki. Mathematische Lehrbficher und Monographien, 16, Aka- demie-Verlag. Zbl : 228-341. Gaver Donald P. Jr Imbedded Markov chain analysis of a waitingline process Goyal T.L. in continuous time. 1959a The statistical analysis of semi-Markov processes with appli- Ann. Math. Statist. 30,698-720. ST : 1-121, MR : 21-6635, cations to queueing problems. 1970a Zbl : 87-336. Ph. D. Thesis, The George Washington Univ., Washington A comparison of queue disciplines when service orientation D.C., U.S.A. times occur. 1963a Goyal T.L. and Harris C.M. Nay. Keg L6gist. Quart. 10, 219-235. MR : 34-3990, Zbl : 124-324. Maximum likelihood estimates for queues with state dependent service. 1972a Sankhy~, A, 34, 65-80. ST : 14-777, MR : 49-1614. Gaver Donald P. Jr and Shedler Gerald S. Multiprogramming system performance via diffusion approximation. 1971a Grigelionis B. IBM Research, K.J., 938. On weak convergence of the sums of multi-dimensional stochastic point processes. 1972a Control variable methods in the simulation of a model of (Russian, English summary) Litov Math. Sbornik, 12, 53-59. a multiprogrammed computer system. 1971b MR : 47-7825, Zbl : 246-404. Nay. Res. Loglst. Quart., 18,435-450. On weak convergence of the sums of multivariate stochastic Gebhardt D. point processes. Die Ermittlung yon Kenngr/Sssen fiir das Wartesystem M/G/1 Stochastic point processes : statistical mudysis, theory and mit beschr/inkten Warteraum. 1973a application~ P.A.W. Lewis ed. Wiley, New York, 616-625. 7. Operat. Res., A. 17, 207-216. Zbl : 269-361. Zbh 268-399. Gross Donald and Harris Carl M. On one-for-one ordering inventory policies with state depen- see Ezov I.I. dent leadtimes. 1971a Operations Res., 19,735-760. Zbl : 226-423. _~rtsbakh I.G. Optimal control by a semi-Markov process when restrictions Gross Donald and Harris Carl M. and Lechner J. on the state probabilities are present. 1970a Stochastic inventory models with bulk demand and state (Russian). Kiberuetika, 1970, 56-61. Zbl : 256-547. dependent leadtimes. 1971a see also Andronov A.M. J. Appl. Probability, 8_, 521-534. ST : 13-660, MR : 46- 6511, Zbl : 222-532. Gheor~e Adrian V. Reliability prediction of systems with semi-Markov structure. Gubenko L.G. 1973a Optimal control of a monotone Markov process. 1974a Stanford University, Department of Engineering-economic (Russian). Kibernetica, 1974, 104-106. Zbl : 278-579. Ws~ems. EES Internat. Memorandum. Gubenko L.G. and Statland E.S. Gideon Kudy and Pyke Ronald Controllable semi-Markov processes. 1972a A Poisson traffic model for the intersection of a single-lane (Russian). Kibernetica, 1972, 26-29. MR : 48-1779, Zbl : 295-371.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 131 Gupta S.K. A queueing system with multiple service time distributions. Queues with hyper-Poisson input and exponential service 1967c time distributions with state dependent arrival and service Naval Res. Logist. Quart., 14 , 231-239. MR : 36-992, Zbl : rates. 1967a 156-185. Operations Res., 15, 847-856. Zbl : 178-208. Some results for bulk-arrival queues with state-dependent On bulk queues with state dependent parameters. 1967b service times. 1970a J. Operations Res. Soc. Japan, 9, 69-79. Zbl : 183-234. Management Sci. 16,313-326. Zbl : 191-505. Some statistical results for inventory models with state-de- Gupta Y.P. pendent leadtimes. 1973a Markov renewal processes. 1970a CoIL Math. Soc. J~nos Bolyai, 7, 105-120. Zbl :275-437. Ph.D. Thesis, University of Delhi, Delhi 7, India. Some results for zero order Markov renewal processes. see also Goyal T.L, Gross D. 1970b J. Indian Statist. Assoc., 8, nr 1,2. Harrison J.M. Countable state discounted Markov decision processes with Joint distributions and asymptotic values of the moments unbounded reward. 1970a for Markov renewal processes in space. 1972a Department Operations ges., Stanford Univ., Technical J. Indian Statist. Assoc., 10. Report, hr. 17. Gupta Y.P. and Kshirsagar A.M. Discrete dynamic programming with unbounded rewards. Asymptotic values of the first two moments in a Markov 1972a renewal process. 1967a Annals. Math. Statistics, 43, 636-646. ST : 14-11, Zbl : Biometrika, 54, 597-604. ST : 10-282, MR : 36-4657, 262-528. Zbl : 166-140. Hiir tler G. Mean and variance of the number of renewals in certain Experience with factorial experiments in reliability-of-com- Markov renewal processes. 1968a ponents problems. 1974a J. Indian Statist. Assoc., 6, 75-80. MR : 49-11651. Coll. Math. Soc. J~nos Bolyai, 9, 309-313, Zbl : 299-433. Some results in Markov renewal processes. 1969a Calcutta Statist. Assoc. Bull., 18, 61-72. MR : 41-6326, Hatori Hirohisa Zbl : 212-496. Some theorems in an extended renewal theory 1966a V. TRU Math., 2, 31-34. MR : 37-2332, Zbl : 158-354. Distribution of the number of Markovian renewals in an arbitrary interval. 1970a On Markov chains with rewards. 1966b Austral. J. Statist., 12, 58. ST : 12-656, Zbl : 193-453. Kodai Math. Sere. Rep., 18, 184-192. MR : 34-5155, Zbl : 139-345. A note on the matrix renewal function. 1972a J. Australian Math. Soc., 13, 417-422. Zbl : 242-393, On continuous-time Markov processes with rewards 1.1966c MR : 47-1147. Kodai Math. Sem. Rep., 18, 212-218. MR : 34-5156, Zbl : 147-164. Gusak D.V. and Koroljuk V.S. A limit theorem on (J,X)-processes. 1966d Asymptotic behaviour of semi-Markov processes with a Kodai Math. Sem. Rep., 18, 317-321. MR. 34.5158A, Zbl : split set of states. 1971a 168-162. (Russian-English summary). Teor. Verojatnost. i Mat. Sta- tist., 5, 43-50. MR : 44-6057, Zbl : 234-383. Hatori Hirohisa and Mori Toshio An improvement of a limit theorem on (J,X) processes. Gutjahr Allen Leo 1966a Sequential hypothesis tests for semi-Markov processes.1969a Kodai Math. Sem. gep., 18,347.352. MR : 34.5158B, Zbl : Ph.D. Thesis, Rutgers University. 168-162. Hall William K. On continuous-time Markov processes with rewards II. 1966b see Disney R.L. Kodai Math. Sere. Rep., 18, 353-356. MR : 34-5157, Zbl : 168-164. Harlamov B.P. A renewal type theorem on continuous time (J,X)-proces- On a random process with first entrance waitinglines. 1971a ses. 1967a Dokd. Akad. Nauk. SSSR, 196, 312-315. Kodai Math. Sem. Rep., 19,404-409. MR : 3%2333, Zbl : Random time changes and semi-Markov processes. 1972a 155-241. (Russian). Zapiski naucn. Sem. Leningrad. Otd. mat. inst. Steklov, 29, 30-37. MR : 50-11512. Hatori Hirohisa and Mori Toshio and Oodaira Hiroshi A renewal theorem on (J,X) -processes. 1967a Random processes with semi-Markov chains of hitting times. 1974a Kodai Math. Sem. Rep., 1__9_9,15%164. MR : 35.7429a, (Russian) Problems in the theory of probability distribu- Zbl : 178-198. tions, 12, 139-164, Izdat. "Nauka" Leningrad. Otdel., 1974. A remark concerning a renewal theorem on (J,X)-proces- Harris C.M. ses. 1967b Queues with state-dependent stochastic service rates. 1966a Kodai Math. Sem. Rep., 19, 189-192. MR : 35.7429b, Zbl: Ph.D. Thesis, Polytechnic Institute of Brooklyn. 178-198. Queues with state-dependent stochastic service rates. 1967a Operations ges., 15, 117-130. MR : 34-6879, Zbl : 157-253. Haussmann U.G. On the optimal long-run control of Markov renewal pro- Queues with stochastic service rates. 1967b cesses. 1971a Naval Res. Logist. Quart., 14,219-230, MR : 36-991, Zbl : 154.433. J. Math. Anal. AppL 36, 123-140. MR : 43-7243.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 132 Hawkes A;G. losifescu Marius A. and Tautu P. Bunching in a semi-Markov process. 1970a Stochastic Processes and applications in biology and medi- J. AppL Probability, 7, 175-182. ST : 12-254, MR : 41-4662, cine. Vol. I, Theory, Vol, IL Models.. 1973a Zbl : 227-355. Springer Verlag, Berlin. MR : 39-1006, Zbl : 262-538.

Heffes H. and Hohzman J.M. Iosifescu-Manu~ Adela Peakedness of traffic carried by a finite trunkgroup with Nonhomogenous semi-Markov processes. 1972a renewal input. 1973a Studii Circ. Mat. 24, 529-533. (Rumanian-English summary~. Bell System Techn. J., 52, 1617-1642. MR : 49-9984. ST : 14-892, Zbl :245.368.

Hinomoto Hirohide 5--~quential control of homogeneous activities linear pro ~acobs P.A. gramming of semi-Markov decision. 1971a The motion of a distinguished particle in an infinite particle Operations Res., 19, 1664-1674. Zbl : 225-533. system. 1973a Dept. Operations Research, Stanford, Technical Report n ° 31. Hitsuda M. ~ima M. Jacod Jean Hobbs R.J. Un th~or~me de renouvellement pour les thames semi-Mar- Optimal maintenance policiesfor multi-statesystems ex- koviennes. 1970a periencingsemi-Markovian deterioration. 1972a C.R. Acad. Sci. Paris, S~r. A-B 270, A255-A258. MR : 41- Ph. D. Dissertation,Stanford University. 6311, Zbl : 191-470. Chafnes semi-Markoviennes transientes et rtcurrentes, chafnes Holmes Paul T. positives. 1970b see Flaspohler D.C. C.R. Acad. Sci. Paris, S~r. A-B 270, A776-A779. MR : 41- 6312, Zbl : 191-474. Holtzman J.M.. Th~or~me de renouvellement et classification pour les chafnes see Heffes H. semi-Markoviermes. 197 la Ann. Inst. H. Poincar~, Sect. B., 7, 83-129. MR : 46-4626, Howard Ronald A. Zbl : 217-505. Semi:Markov control systems. 1963a Tech. Rep. 3, O.R. Center, M.LT., Cambridge, Mass., pre- Gtn~rateurs infmit~simaux des processus i accroissements print. semi-Markoviens. 197 lb Ann. Inst. H. Poincar~, Sect. B., 7_., 219-233. MR : 46-958, Stochastic process models of consumer behaviour. 1963b Zbl : 224-422. J. Advertising Res., 3, 35.42. Semi-groupes et mesures invariantes pour les processus semi- Semi-Markovian decision processes. 1963c Markoviens ~ espace d'ttat quelconque. 1973a Bull. Inst. Internat. Statist., 4_.0, 625.652. ST : 6-1035, Ann. Inst. H. Poincar~. Sect. B., 9, 77-112, MR : 49-6384, MR : 30-3758, Zbl : 128-128. Zbl : 254-376. Research in semi-Markov decision structures. 1964a Syst~mes r~g~n~ratifs et processus semi-Markovien, 1974a J. Operations Res. Soc. Japan, 6, 163-199. ST : 7-626, MR: Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31, 1-23. 30-2918. Zbl : 282°347. Systems analysis of semi-Markov processes. 1964b Correction et compl~ments ~ "Thtor~me de renouvellement IEEE Trans. Military Electronics 8, 114-124. et classification pour les thames semi-Markoviennes". 1974b Dynamic probabflistic systems. VoL. I : Markov models; Ann, Inst. H. Poincar~, Sect. B., 10, 201-209. MR : 50-5969. VoL H : semi.Markov and decision processes. 1971a Series in Decision and Control, John Wiley and Sons, New Jancevi~ A.A. York. Zbl : 227-541. see Aleksandrov Ju.A.

Hunter Jeffrey J. Janssen Jacques On the renewal density matrix of a semi-Markov process. Processus de renouvellements Markoviens et processus semi- 1968a Markoviens, 1964a Ph.D. Thesis, University of North-Carolina at Chapel Hill, Cahiers Centre Etudes Recherche Op~r.,6,81-105. ST : 7- U.S.A. Institute of Statistics, Mimeo series, N ° 570. 399, MR : 31-797. On the moments of Markov renewal processes. 1969a Processus de renouvellements Markoviens et processus semi- Advances AppL Probability, 1 188-210. ST : 11-1017, M arkoviens, 2e pattie, Stationnarit~ et Application ~ un pro- MR : 40-8143, Zbl : 184-213. blame d'invalidit~. 1965a On the renewal density matrix of a semi-Markov process. Cahiers Centre Etudes Recherche Op&., 7, 126-141. ST : 1969b 7-400, MR : 34-8484, Zbl : 235-405. 8ankhy~, A, 31, 281-308. ST : 11-1019, MR : 46-10088, Application des processus semi-Markoviens ~ un probl~me Zbl : 186-511. d'invalidit~. 1966a Bulletin de I'A.R.A.B. 6_33, 35-52. H ursch Carolyn ~. and Yang Mark C.K. Les processus (J-X). 1969a The use of semi-Markov model for describing sleep pat- Cahiers Centre Etudes Recherche Op~r., 11, 181-214. MR : terns. 1971a 42-8558, Zbl : 211o209. Univ. Florida, Dept. Statist. and Psychiatry, Gainesville, F1.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 133 Janssen Jacques A note on the first two moments of times in transient states Sur une g~n~ralisation du concept de promenade al~atoire in a semi-Markov process. 1974a sur la droite r~eUe. 1970a J. Appl. Probability, 1_!, 193-198. MR : 50-5970, Zbl : 276- Ann. Inst. Poincar~, Sect. B, 6, 249-269. MR : 45-2803, 387. Zbl : 261-358. On the use of semi-Markov models in risk theory. 1967a Karlin Samuel Univ. Libre de Bruxelles, Technical Report. Stochastic models and optimal policy for selling an asset. see also Cheong C.K. 1973a Studies in Appl. Prob. and Management Sc., ed. Arrow, Jastrebeneckii M.A. Karlin, Scarf. Stanford University Press, Stanford, Cal. 148- The convergence of sums of Markov renewal processes to 158, Zbl : 142-178. a branching Poisson process. 1972a (Russian-English summary). Kybernetica, Kiev, 1, 95-98. see also Fabens A.J. MR : 46-970, Zbl : 233-356.. Karr Alan F. On a rarefied Markov-renewal process connected with some Weak convergence of a sequence of Markov chains. 1975a reliability problems. 1972b Z. Wahrscheinlichkeitstheorie verw. Gebiete, 3_33, 41-48. (Russian). Izv. Akad. Nauk SSSR, Tehn. Kibernet., 1972 , Zbl : 297-372. 9%107. MR • 48-7410. Keilson Julian Jastrebeneckii M.A. and Rykov V.V. Some comments on single-server queueing methods and so- On regenerative phenomena with regeneration points of me new results. 1964a several types. 1971a proc. Cambridge Philos. Soc., 60, 237-251. ST : 10-1037, (Russian). Kibernetika, 1971, 82-86. MR : 48-1337, Zbl : Zbl : 203-185. 265-394. The rule of Green's functions in congestion theory. 1965a Jewell Williams S. Proc. Symposium on Congestion Theory, Univ. of North Caro- Markov renewal programming. 1962a l/na, ed. W.L. Smith, W. E. Wilkinson, 43-71. Zbl : 203-i85. ORC 62-37 Operations Research Center. Univ. of California, A limit theorem for passage times in ergodic regenerative Berkeley. processes. 1966a Ann. Math. Statist., 3_Z, 866-870. Zbl : 143.191. Markov renewal programming I : Formulation, finite return models. 1963a The ergodic queue lenght distribution for queueing systems Operations Res., 1_!, 938-948. MR : 29-677, Zbl : 126.159. with finite capacity. 1966b J. Roy. Statist. Soc. Ser. B, 288, 190.201. Markov renewal programming II : Infinite return models, example. 1963b On the matrix renewal functions for Markov renewal pro- Operations Res., 1_!, 94%971. MR : 29-678, Zbl : 126-159. cesses. 1969a Limiting covariance in Markov renewal processes. 1964a Ann. Math. Statist. 400, 1901-1907. MR : 40-8144, Zbl : ORC 64-16, Operations Research Center, University of 193-453. California, Berkeley. Keilson Julian and Subba Ran S. Markov renewal models in trafic flow theory. 1965a A process with chain dependent growth rate. 1970a (Abstract). Vehicular Traffic Science, Proc. Third Int. Syrup. J. Appl. Probability, 7, 699-711. ST : 12-646, MR : 43- Theory of Traffic Flow, LC. Edie, R. Herman, R. Rothery, 8141, Zbl : 239-407. Elsevier, N.Y. 95-96. A process with chain dependent growth rate. Part II : The A note on Markov renewal programming. 1966a ruin and ergodic problems. 1971a ORC 66-41, Operations Research Center, Univ. of Califor- Advances Appl. Probability, 3, 315-338. ST : 14-788, MR : nia, Berkeley. 45-7838. Fluctuations of a renewal reward process. 1967a J. Math. Anal., 1_.99, 309-329. MR : 35-7426, Zbl : 153-200. Keilson Julian and Wishart D.M.G. Markov-renewal programming I, II. 1967b A central limit theorem for processes defined on a finite Russian. Kibernet. Sbornik, n. Ser., 4, 97-137. Zbl : 166- Markov chain. 1964a 156. Proc. Cambridge Philos. Soc., 60, 547-567. ST : 12-265 and 266, MR : 29-6523, Zbl : 126-335. Kao Edward P.C. Boundary problems for additive processes defined on a Optimal replacement under semi-Markov deteriorations. finite Markov chain. 1965a 1971a Proc. Cambridge Philos. Soc. 61, 173-190. ST : 12-648, MR : 30-2538, Zbl : 138-407. Ph.D. Dissertation, Stanford University. Addenda to processes defined on a finite Markov chain.1967a A semi-Markovian populations model with application to Proc. Cambridge Philos., 63, 18%193. MR : 34-3648, Zbl : hospital planning. 1973a 147-164. IEEE Trans. Systems Man Cybernetics SMC-3, 327-336. Optimal replacement rules when changes of state are semi- Kesten Harry Occupation times for Markov and semi-Markov chains.1962a Markovian, 1973b Trans. Amer. Math. Soc., 103, 82-112. MR : 25-1569, Zbl : Operations Res., 21, 1231-1249, Zbl : 276-506. 122-366.

Journal of Computational and Applied Mathematics, volume 2, no "2, 1976. 134 The sojourn time in a given state of the simplest semi-Mar- Renewal theory for functionals of a Markov chain with kov system. 1970a general state space. 1974a (Russian). Teor. Veroja.tnost i Mat. Statist., 1, 100-108. Ann. Probability, 2, 355-386. Zbl : 303-375. MR : 43-1285, Zbl : 223-430.

~c~.~hheim A. and Matzke H. and Mfiller K.H. _Kredentsjer B.P. Zur Steuerung halbmarkovscher Prozesse fiber einen unend- Estimation of the security of systems with ample machinery lichen Zeitraum. 1975a and time capacities and immediate discovery of breakdown. Math. Struct.,Comput., Math, Math. Modelling, dedicated L. 1971a Iliev's 60 th anniversary. (Russian). Kibernetika, 1972.

Ki~nig Denes and Matthes K. and Nawrotzki IC Kredentsjer B.P. and Zahatin A.M. ~rallgemeinerungen der erlangschen und engsetschen On the time that it takes for a linearly increasing with random Formeln. (Eine Methods in den Bedienungstheorie). 1967a changes to reach a prescribed level 1972a Schriftenreihe der Institute ffir Mathematik bei der Deutschen (Russian). Kibernetica, 1972, 89-94. Zbl : 267-392. Akademie der Wissenschaften zu Berlin, geihe B; Angewand- te Mathematik und Mechnaik, 5. Berlin, Akademie Verlag. K shirsagar Anant M. MR : 41-2799, Zbl : 189-178. Poisson counts of a Markov renewal process. 1970a South African Statist. j., 4, 67-72. ST : 12-657, Zbl : 223- K~ni 8 Denes 578. See also Gnedenko B.V. Life estimation and renewal theory. 1970b J. Indian Statist. Assoc., 8. Koroliuk V.S. ~lolding time of a semi-Markov process in a fixed set of Kshirsagar A.M. and Wysocki K. states. 1965a Some distribution and moment formulae for the Markov Ukrain Math. 7.., 3, 123-128. renewal process. 1970a Semi-Markov processes in reliability theory problems. 1967a Proc. Cambridge Philos. Soc., 68,159-166.. ST : 13=314, Math. Methods in Quality Control and Reliability. Proc. All. MR : 41-7775, Zbl : 196-191. Union Colloq. Tashkent, (Russian). 51-57 : Izdat. "Fan" Uzbek SSK, Tashkent, MR : 43-4443. Distribution of transition frequencies of a Markov renewal process, over an arbitrary interval of time. 1970b On asymptotic behaviour of the duration of a semi-Markov Metron, 2_88, 147-155. MR : 13-1584, Zbl : 231-393. process in a subset of states. 1969a Ukrain Math. J., 21,705-707. MR : 40-5021, Zbl : 185- .Kshirsagar A.M. 462. see also Arseven E., Brock D.B.~ Gupta Y.P.

Koroliuk V.S. and Tomusyak A.A. Kumagai Michikazu Description of the working of dams by use of a semi-Markov Reliability analysis for systems with repair. 1971a process. 1965a J. Operations Res. Soc. Japan, 1~4, 53-71, gbl : 258-521. (Russian) Kibernetika, 1965, 55-59. Zbl : 156-186. Certain stationary characteristics of semi-Markovian pro- Kurtz Thomas G. cesses. 1971a Comparison of semi-Markov and Markov processes. 1971a (Russian). Kibernetika, 1971, 65-68. MR : 46-2754, Zbl : Ann. Math. Statist., 42, 991-1002. MR : 43-4112, Zbl : 236-406. 217-504.

Koroljuk Vladimir S. and Turbin A.F. Lambotte .lean-Pierre The asymptotic behaviour of the sojourn time of a semi-Mar- Processus semi-Markoviens. 1964a kov process in a reducible subset of states. 1970a Licence Thesis, Univ. Libre de Bruxelles. (Russian). Teor. Verojamost. i Mat. Statist., 2, 133-143. Processus semi-Markoviens et files d'attente. 1968a MR : 44-1125, Zbl : 25%365. Cahiers Centre Etudes Recherche Op&., 10, 21-31. ST : On one method to prove limit theorems for some functionals 10-624, MR : 3%7014. on the semi-Markov pro~sses. 1972a (Russian) Ukrain Math. Z., 24, 234-239. MR : 46-972, Lambotte Jean-pierre and Teghem Jean Zbl : 246-417. Utilisation de la th~orie des processus semi-Markoviens dans l'&ude de prpbl~mes de files d'attente. 1967a Koroljuk Vladimir S. and Politsjuk L.I. and Tomusyak A.A. Queueinf Theory, Recent Developments and Applications, On a limit theorem concerning semi-Markov processes.1969a The English Universities Press Ltd, London, 61-64. (Russian). Kibernetika, i-969, 144-145. MR: 46-971,Zbi :245-367. Lambotte Jean-Pierre and Teghem Jean and Loris-Teghem Koroljuk Vladimir S. Jacqueline. see also Brodi S.M., Ezov E.I., Gusak D.V. Moddles d'Attente M/G/I et GI/M/I ~ Arriudes et Services en Groupes. 1969a Koutsky Zdenek Springer-Verlag, Berlin. MR : 40-6663, ZB1 : 172-216. Zwei Probleme Markowschen und halb-Marhowschen Opti- mierun&. "1968a Lambotte Jean-pierre Acta Tech. CSAV, 1__33, 597-603. MR : 40-6950. see also Cheong C.K.

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Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 135 Lee Christopher Marshall Albert W. Dynamic probabilistic systems with continuous semi-Mar- see Barlow R.E. kov processes. 1974a Ph.D. Thesis, Southern Methodist University, U.S.A. Masol V.I. ~symptotic distributions of the non-failure operation time Lev G.S. of a queueing system with constraints. 1972a Semi-Markov processes of multiplication with drift. 1972a (Russian). Kibernetica, 1972, 108-111. MR : 46-6505, Zbl • (Russian). Theory Probability Appl., 17, 159-164. MR : 273-378. 46-6495, Zbl : 285-376. Convergence of semi-Markov multiplication processes with Matheron G. drift to a diffusion process. 1972b Ensembles ferm& al~atoires, ensembles semi-Markoviens et Theory Probability Appl., 17, 551-556. MR : 46-4622, poly~dres Poissoniens. 1972a Zbl : 299-404. Adv. Appl. Prob., 4, 508-541. MR : 50-1314, Zbl : 283- 315. Asymptotic properties of the probability of degeneracy for semi-Markov multiplication processes. 1973a Matthes K. (Russian). Theory Probability Appl., 17, 740-752. MR : 48- see Gnedenko B.V., KSnig D. 5201. Matthews Jane P. .L&y Paul A study of processes associated with a finite Markov Syst~mes semi-Markoviens ~ au plus une infinit~ dtnom- chain. brable d'&ats possibles. 1954a 1971a Ph. Thesis. University of Sheffield. Proc. Int. Congr. Math. Amsterdam, 2, 294. MR : 19-469, Zbl • 73-347. Matzke H. Processus semi-Markoviens. 1954b see Kirchheim A. Proc. Int. Congr. Math. Amsterdam, 3, 416-426. MR : 19- 469, Zbl : 73-347. Mazumdar Sati On waiting-time distributions in priority queues when ser- Lewis P.A.W. and Shedler G.S. vice orientation times occur. 1967a A cyclic-queue model of system overhead in multiprogramm- Ph. D. Thesis Cornell University, 97 pp. in 4 °. ed computer systems. 1971a J. Assoc. Comput. Machin., 18, 199-200. MR : 43-8276. McLean Robert A. The integral of a function, defined on a semi-Markov pro- Lewis P.A.W. cess. 1965a see also Cox D.R. Ph.D. Thesis. Purdue University.

~.ippman Steven A. McLean Robert A. and Neuts Marcel F. Maximal average reward policies for semi-Markov decision ~l~he integral of a step function defined on a semi-Markov processes with arbitrary state and action space. 1971a process. 1967a Ann. Math. Star., 42, 1717-1726. Zbl : 231-532. SIAM J. Appl. Math., 15, 726-737. MR : 35-6204, Zbl : 166-143. Semi-Markov decision with unbounded rewards. 1973a Management ScL, 19, 717-731. Zbl : 259-406, MR : 49- McNickle D.C. 2109. The number of departures from a semi-Markov queue.1974a On dynamic programming with unbounded rewards. 1973b J. Appl. Probability, 11,825-828. Western Manag. Inst., Univ. California, Working Paper n ° 212, 1973. Mecke J. Station~e Verteilungen fiir alas erlangsche ModelL 1973a Loris - Teshem Jacqueline Math. Nachr., 58, 1-7. Zbl : 273-379. see .Lambotte J.P. Mevert Paul Maradudin A.A. and Weiss George Two-class priority system with setup times. 1966a Some problems in trafic delay. 1967a Ph.D. Thesis, Case Inst. of Tech., Cleveland, Ohio. Tech. Operations Res., 10, 74-104. Rep., n ° 72.

Marcus Allan H. Miller Hilton D. Stochastic models of some environmental impact of high- A generalization of Wald's identity with application to way traffic, I : a two sided filtered Markov renewal pro- random walk. 1961a cess; II : noise 1971a Ann. Math. Stat. 32, 549-560. The John Hopkins Univ., Techn. Report, no, 159. A convexity property in the theory of random variables de- Traffic noise as a filtered Markov renewal process. 1973a fined on a finite Markov chain. 1961b J. Appl. Probability, 10,377-386, MR : 50-8743, Zbl : Ann. Math. Statist., 32, 1260-1270. 275-401. A matrix formulation problem in the theory of random A stochastic model for microsale air pollution from high- variables defined on a finite Markov chain. 1962a way traffic. 1973b Proc. Camb. Philos. Soc. 58, 268-285. Technometrics, 1__~, 353-363. Zbl : 258-395. Absorption probabilities for sums of random variables de- Environmental impacts of highway traffic as two-sided fil- fined on a finite Markov chain. 1962b tered Markov renewal processes. 1974a Proc. Camb. Philos. Soc., 58, 26. J.R. Statist. Soc., B 36, 426-429. Zbl : 292-409. Mine Hisaski and Osaki Shunji Marlin Paul G. Linear programming algorithms for semi-Markovian decision Limit theorems for Markov chains and their application to processes. 1968a queueing systems with state-dependent arrival patterns.1972a J. Math. Anal. Appl., 22, 356-381. MR : 39-5149, Zbl : Ph.D. thesis, The George Washington Univ., Washington 182-532. D.C., U.S.A.

Journal of Computational and Applied Mathematics, volume 2, no ~, 1976. 136 Mine Hisaski and Osaki Shunji Optimum preventive maintenance policies maximizing the ~ogramming co~iderations on Markovian decision mean time to the first system failure for a two-unit standby processes with no discounting. 1969b redundant system. 1974a j. Math. Anal. Apl)l,, 2__@6,221-232. MR : 38-6839, Zbl : J. Opt. Th. Appl.. 14, 115-129. Zbl : 264-391. 169-515. N~ce Richard E. Mode Charles ). see Bhat U.N. ~orems for infinite systems of renewal type integral equations in age-dependent branching processes. 1972a Nawrotzki K. Math. Bio-sciences, 13.3, 165.177. Zbl : 228-339. see Gnedenko B.V.,KSnig D.. A study of a Malthusian parameter in relation to some stochastic model of human reproduction. 1972b Neuts Marcel F. Theoret. Population Biology, 3, 300-323. Erratum, 4_, 491. Generating functions for Markov renewal processes. 1964a MR : 49-10402 and 10403. Ann. Math. Statist., 35,431-434. ST : 7-846, Zbl : 123-353. Limit theorems for the output of certain types of traffic Moore Erwin and Pyke Ronald queues. 1965a Estimation of the transition distributions of a Markov-rene- Vehicular Traffic Science, Prec. Third, Int. Syrup., Theory wal process. 1968a of Traffic Flow, ed. L.C, Edie, K, Herman, R, gothery, Ann. Inst. Statist. Math,, 20,411-424. ST : 13.685, Zbl : Elsevier New York, 193-194. Zbl : 178-230, 196-191. The busy period of a queue with batch service. 1965b Moose Richard L. Operations Kes., 13, 815-819. MR : 32-3164, Zbl : 133- adaptive state estimation solution to the maneuvering 113. target problem. 1975a Semi-Marker analysis of a bulk queue. 1966a IEEE Trans. Automatic Control AC-20, 359-362. Zbl : (French summary). Bull. Soc. Math. Belg., 18, 28-42. ST : 301-526. 8-441 and 9-236, MR : 33-6722, Zbl : 141-159. The single server queue with Poisson input and semi-Marker Mori To~io service times. 1966b ~e Huron H. J. Appl. Probability, 3, 202-230. ST : 8-422, MR : 34- Morton Richard 877, Zbl : 204-200. Optimal control of stationary Markov processes. 1973a A general class of bulk queues with Poisson input. • 1967a Stoch. Prec. Appl., 1, 237-249. Zbl : 263-502. Ann. Math. Statist., 38, 759-770. ST : 13-690, MR : 35-2375, Zbl : 157-252. Morton Thomas E. Two Markov chains arising from examples of queues with Undiscounted Markov renewal programming via modified state-dependent service timeg 1967b successive approximations. 1971a Sankhy~" A, 29, 259-264. ST : 10.1060, MR : 37-982, Operations Res., 19, 1081-1089. MR : 45.9776. Zbl : 155-245. Two queues in series with a finite intermediate waiting Miiiler K.H. room. 1968a see Kirchheim A. J. AppL Probability, 5, 123-142. ST : 10-1058, MR : 37-995, Zbl : 157-254. Mfirmann M. A semi-Markovian model for the Brownian motion. 1973a A working bibliography on Marker renewal processes and Lecture Notes in Mathematics, vet. 321, S~minaire de Pro- their applications. 1968b babilitts VII, 248-272. Zbl : 271-382. Purdue Mimeograph series, nO 140, Purdue Univ. The queue with Poisson input and general service times, Nair Sreekantan S. treated as a branching process. 1969 Semi-Markov analysis of two queues in series attended by Duke Maih. J.~ 36, 215-23I. Zbl : 183-494. a single server. 1970a BUlL Soc. Math. Be1., 22,355-367. MR : 44-6077, Zbl : Two servers in series, treated in terms of a Markov renewal 226-421. branching process. 1970a Advances AppL Probability, 2, 110-149. ST : 12-283, MR : A single server tandem queue. 1971a 42-1240, gbl : 208-439. J. Appl. Probability, 8, 95-109. MR : 43-5636. A queue subject to extraneous phase changes. 1971a Two queues in series attended by a single server. 1973a Advances Appl. Probability, 3, 78-119. ST : 12-1286, MR : Bull. Soc. Math. Belg., 25, 160-176. MR : 48-12663. 44-1132, Zbl : 218-424. Nair Sreekantan S. and Neuts Marcel F. The Markov renewal branching process. 1974a A priority rule based on the ranking of the service times Proc. Conf. on Math. Methods in the Theory of Queues, for the M/G/1 queue. 1969a Kalamazoo, Springer-Verlag, N.Y., 1-21. Operations Res., 1_7_7,466-477. Zbl : 174-215. Moment formulas for the Markov renewal branching pro. An exact comparison of the waiting times under three cess. 1975a priority rules. 1971a Purdue Mimeograph Series, nr. 434, Purdue University, Operations Reg, 19, 414-423. Zbl : 221-432. U.S.A. Distribution of occupation time and virtual waiting time Neuts Marcel F. and Purdue peter of a general class of bulk queues. 1972a Multivariate semi-Marker matrices. 1971a Sankhy~-, A, 34, 17-22. MR : 49-1616. J. Austr. Math. S0c., 13, 107-113. ST : 14-386, MR : 47. 2686, Zbl : 236-406. Nakagawa T. and Osaki Shunji On a two-unit Strmdby redundant system with standby Neuts Marcel F. and Kesnick S.l. failure. 1971a Limit laws for maxima 0fa sequence of random variables O.R., 1_99, 510.523. defined on a Markov chain. 1970a Advances Appl. Probability, 2, 323.343. ST : 12-378, MK; 41-9332, Zbl : 205-450.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 137 Neuts Marcel F. and Teugels Jozef L. Pearce Chris Exponential ergodicity of the M/G/1 queue. 1969a A queueing system with non-recurrent input and batch ser- SIAM J. Appl. Math., 17,921-929. ST : 11-1041, MR : 40- vicing. 1965a 6658, Zbl : 183-493. J. Appl. Probability, 2, 442-448. ST : 8-444, MR : 32-3165.

Neuts Marcel F. and Yadin Micha Perera A.G.A.D. The transient behaviour of the queue with alternating priori- see Fabens AJ. ties, with special reference to the waiting times. 1968a Bull. Soc. Math. Belg., 20, 343-376. ST : 11-329, MR : 39- Perrin E.B. and Sheps M.C. 4960, Zbh 181-467. bluman reproduction: a stochastic process. 1964a Biometrics, 20, 28-45. Neuts Marcel F. see also Chen S., Fabens A.J., McLean R., Nair S.S. Further results from a human fertility model with a variety of pregnancy outwares. 1966a Neveu Jacques Human Biol., 38, 180-193. Une g~n~ralisation des processus ~ accroissements positifs ind~pendants. 1961a Pinsky Mark A. Abh. Math. Sem. Univ. Hamburg, 25, 36-61. Differential equations with a small parameter and the central limit theorem for functions defined on a Markov chain. Newbould Martin 1968a A classification of a random walk defined on a finite Mar- Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 9, 101- kov chain. 1973a 111. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 26, 95- Multiplicative operator functionals and their asymptotic 104. Zbl : 247-403. properties. 1972a Advances in Probability HI, Marcel Dekker, New York, Vol. O'Brien George !.. 3, 1-100. The limiting distribution of maxima of random variables defined on a denumerable Markov chain. 1974a see also ~inlar E. Ann. Probability, 2, 103-111. MR : 50-8656, Zbl : 287- 408. Pittel B.G. see Burtha Yu. D. Limit theorems for sums of chain-dependent processes.1974b J. Appl. Probability, 11,582-587. Zbl : 293-409. Plucinska A. O~den P.H. and Shedler Gerald S. On the joint limiting distribution of times spent in particular A model of memory contention in a paging machine. 1972a states by a Markov process. 1962a Comm. Assoc. Comput. Machin., 15, 761-771. Colloq. Math., 9,347-360. ST : 4-546, MR : 25-5548, Zbl : 124-88. Oodaira Hirohisa see Hatori H. Pogosjan LA. see Akimov A.P., Brodi S.M. Orey Steven Change of time scale for Markov processes. 1961a Politsjuk L.I. and Turbin A.F. Trans. Amer. Math. Soc., 99, 384-397. MR : 26-3116, The convergence of a semi-Markov process depending on a Zbl : 102-140. small parameter to a non-stationary continuous-time Markov process. 1974a Osaki Shunji (Russian). Teor. Slu~ain. Proces., respubL megvedomst. System reliability analysis by Markov renewal processes. Sbornik, 2 , 104-109. Zbl : 291-408. 1969a Politsjuk L.I. J. Operations Res. Soc. Japan, 12, 127-188.MK : 41-9367, see also Koroliuk V.S. Zbl : 233-530. Study on system analysis and synthesis by Markov renewal Prasard J.S. processes. 1970a Markov renewal programming under incomplete informa- Doctoral Dissertation, Kyoto Univ., Japan. tion. 1971a A note on a two-unit standby redundant system. 1970b Ph.D. Dissertation, Texas Technical University. Journal of the Operations Research Society of Japan, 12, 43-51. Prehn Uwe Gleichverteilungseigenschaften yon Verteilungsgesetzen zu- Reliability analysis of a standby redundant system with F~liger Summen, deren Summanden einer veralgemeinerten preventive maintenance (Japanese). 1970c Markowschen Abh~ingigheit unterworfen shad. 1971a Keiei-Kagaku, 14,233-345. MR : 47-6291. Math. Nachr., 49, 2%40. MR : 46-6409, Zbl : 271-353. Signal flow graphs in reliability theory. 1974a Minoetectronics and Reliability, 13, 539-541. presman E.L. Boundary problems for sums of lattice random variables, see also Asakura T., Mine H., Nakagawa T. defined on a fmite regular Markov chain. 1967a Theor. Probability AppL, 12,323.328. MR: 35-4993,Zbl: 174-497. Ott Teunis J. Factorization methods and boundary problems for sums of Infinite divisibility and stability of finite semi-Markov ma- random variables given on Markov chains. 1969a trices. 1973a Math. USSR - Izv., 3,815-852. MR : 41-1123, Zbl : 192- Center of System Science, Univ. Rochester CSS, 73-11. 551. Infinite divisibility and imbeddability of semi-Markov matrices on certain topological groups. 1975a Prizva G.I. Advances Appl. Probability, 7, 256-257. A limit theorem for semi-Markov processes. 1972a Dopovidi Akad. Nauk. Ukrain. RSK. Ser. A., 820-824. Se- lected Transl. Math. Statist. and Prob., 10, 22-27. MR : 39- 6400, Zbl : 165-196.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 138 prizva G.I. and Simonova S.N. Queile Gisbert ~-the distribution of a variable of first transition. 1967a Uber Polnische Entscheidungsmodetle und Optimierung in (Russian). Ukrain Mat. ~., 199, 117-121. Selected Transl. einigen semi-Markoffschen Entscheidungsmodellen. 1970a Math. Statist. and Prob., 9, 1970, 177-182. Zbl : 221-428. UnverSffentlichte Diplomarbeit, Universit/it Hamburg. Prizva G.I. and Tihomirova L.V. Dynamische Optimierung semi-Markoffscher Entscheidungs- class of functionals on Markov renewal processes.1973a modelle : Stationari~tseigenschaften, Varianzen, Pr/iventive (Russian). Teor. Verojatuost. i Mat. Statist., 8, 138-144. Aktionen. 1973a Ph.D. Dissertation, Universit~t Hamburg. see also Arseni~vRi G.L., E~ov I.I. Ra]amannan G. and Srinivasan S. Kidambi Selective interaction between two independent stationary Proschan F. recurrent point pro~esses. 1970a ~e Barlow R.E. J. Appl. Prob., 7, 476-482.

Purdue Peter Reinschke Kurt O~n the use of analytic matrix functions in queueing theory. Zuverlissigkeit yon Systemen. Band 1 : Systeme mit end- 1971a lich vielen Zust/inden. 1973a Technical Report nr. 28, Dept. Statistics, Univ. Kentucky. Theoretische Grundlagen der technischen Kybernetik.Berlin. VEB, 1973. Zbl : 261-490. The M/G/1 queue subject to extraneous phase changes.1973a Technical Report, nr. 41, Dept. Statistics, Univ. Kentucky. Resnick Sidney I. Non-linear integral equations of Volterra type in queueing Maxima of a sequence of random variables defined on a Mar- kov chain. 1970a theory. 1973b J. Appl. Probability, 1_.0, 644-655. Zbl : 272-397. Ph.D. Thesis, Purdue Univ., Lafayette (Ind.), U.S.A., Dept. Statist., mimeoseries n°217. The M/M/1 queue in a Markovian environment. 1974a Oper. Res., 2_22, 562-569. Tail equivalence and its applications. 1971a J. Appl. Probability, 8, 136-156. MR : 43-4093, Zbl : 217- The single server queue in a markovian environment. 1974b 499. Lecture Notes Economics Math. Syst., 9_88, 395.364. Zbl : Asymptotic location and recurrence properties of maxima of 302-410. a sequence of random variables defined on a Markov chain. A queue with Poisson input and semi-Markov service times : 1971b busy period analysis. 1975a Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 18, 197- J. Appl. Probability, 12,353-357. 217. ST : 12-1298, Zbl : 196-201. Stability of maxima of random variables defined on a Markov see also Neuts M.F. chain. 1972a Purl Prem S. Advances Appl. Probability, 4, 285-295. ST : 14-1259. Zbl : 26%392. A generalization of a formula of PoUaczek and Spitzer as applied to a storage model. 1973a Resnick Sidney I. and Tomkins R.J. (abstract). Bull. Institute Math. Statist., 2,56-57. Almost sure stability of maxima. 1973a Purl Prem S. and Senmria Jerome J. Appl. Probability, 1_O0,387-401. Zbl : 258-376. A semi-Markov storage model. 1973a gesnick Sidney I. Adv. AppL Probability, 5, 362-378. MR : 49-11670, Zbl : see also Neuts M.F. 261-359. Reuver H.A. and Ten Hoopen M. Pyke Ronald Selective interaction of two independent recurrent pro- Markov renewal processes : definitions and preliminary cesses. 1965a properties. 1961a J. Appl. Probability, 2, 286-292. ST : 8-465, MR : 31-6294. Ann. Math. Statist., 32, 1231-1242. ST : 5-496, MR : Zbl : 137-67. 24-3712, Zbl : 26%391. On a waitingtime problem in physiology. 1965b Markov renewal processes with finitely many states.1961b Statistica Neerlandica, 19, 27-34. ST : 7-212. Ann. Math. Statist., 32, 1243-1259. ST : 5-497, MR : 27- 4273, Zbl : 201-499. On a first passage problem in stochastic storage with total release. 1967a Markov renewal processes of zero order and their applica- J. AppL Probability, 4, 409-412. ST : 9-527, MR : 36-3426, tion to counter theory. 1962a Zbl : 137-145. Studies in AppL Prob. and Management Sc.ed. Arrow, Kar- fin, Scarf, Stanford University Press, Stanford, Cal. 173- Ro~osin B.A. 183. Zbl : 134-136. see Borovkov A.A.

Pyke Ronald and Schaufele Ronald A. Rolph John E. Limit theorems for Markov renewal processes. 1964a see Fox Bcnneth L. Ann. Math. Statist., 35, 1746-1764. ST : 8-453, MR : 29- 5291, Zbl : 134-346. Romanovskii LV. The existence and uniqueness of stationary measures for Turnpike theorems for semi-markovian decision processes. Markov renewal processes. 1966a 1970a Ann. Math. Statist., 37, 1439-1462. MR : 34-3658; Zbl : (Russian). Trudy Mat. Inst. Steklov, III, 208-223. MR : 45- 154-429. 1584, Zbl : 265-390.

~ke Ronald Rosenblit P. Ya see also Gideon R. see Andronov A.M. see also .Moore E.H.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 139 Ross Sheldon M. see also Pyke R. Average cost semi-Markov decision processes. 1970a J. Appl. Prob., 7, 649-656. ST : 12-380, MR : 46-2771, Scheaffer R.L. Zbl : 204.517. Asymptotic properties of sample proportions under a Mar- kovian renewal structure. 1973a Applied probab~ity models with optimization applications. Commun. Statist., 2, 167-184. Zbl : 261-382. 1970b San Francisco, Holden-Day. MR : 41-9383. Schellhaas H. Regenerative stochastische Entscheidungsprozesse mit end- see also Brown M. lich vielen Zustfmden. 1971a Operations Res.-Verf. 13, IV, Oberwohlfach Tag., Opera- Rudemo Mats tions Res., 332-357. Zbl : 251-525. State estimation for partially observed Markov chains. 1974a J. Math. Anal. Appl., 44, 581-611. Zbt : 271-373. Zur Extrapolation in Markoffschen Entscheidungsmodellen mit Diskontierung. 1974a Runggaldier W. Z. Operat. Res., _A, 18, 91-104. Zbl : 288-531. see Finkbeiner B. Schnepps-Schneppe M.A. (Sneps-Sneppe M.A.) Shkol'nyy Ye.I. Rykov V.V. On the accuracy of statistical simulation of queueing sys- see Jastrebeneckii M.A. tems described by semi-Markov birth and death processes. 1973a Safonov I.V. Izv. Akad. Nauk SSR Tehn. Kibernetika ,1973, 60-65. MR : The application of the theory of multidimensional stochas- 50-11528. tic matrices to the investigation of random processes. 1969a Cybernetics, 1, 78-86. MR : 46-10089. Schweitzer P.J. Perturbation theory and Markovian decision processes.1965a Sapagovas I. Ph.D. Thesis MIT. On the reliability of a replacement system with dependent Perturbation theory and undiscounted Markov renewal pro- dements. 1969a gramming. 1969a (Russian). Litovsk. Mat. Sb., 9, 589-604. MR : 42-6951, Operations Res., 19, 716-727. MR : 41-1377, Zbl : 176-500. Zbl : 199-526. Iterative solution of the functional equations of undiscount- Convergence of sums of Markov renewal processes through ed Markov renewal programming. 1971a a multi-dimensional Poisson-process. 1969b J. Math. Anal. Appl., 34,495.501. MR : 43-2981, Zbl : 218- (Russian). Litovsk. Mat. Sb., 9, 817-826. MR : 42-2554, 583. Zbl : 186-503. Multiple policy improvements in undiscounted Markov rene- Convergence of sums of Markov renewal processes to a wal programming. 1971b Poisson-process. 1970a Operations Res., 19, 784-793. ST : 14-899. Litovsk. Mat. Sb., 6, 1966, 271-277. Sdected Translat. in Math. Statist. and Probability, 9, 251-260, Zbl : 295-372. Iterative solution of the functional equations of undiscounted Markov renewal programming. 1971c Schgl Manfred J. Math. Anal. Appl., 34, 495-501. Markoffsche Erneuerungsprozesse mit Hilfspfaden. 1969a Annotated bibliography on Markov decision processes.1973a Doctor's Thesis. University of Hamburg. Working copy. Markov renewal processes with auxiliary paths. 1970a Randomized maximal-gain policies for undiscounted Markov Ann. Math. Statist., 41, 1604-1624. ST : 12-1304, MR : renewal programming. 1974a 42-8561, Zbl : 223-429. (to appear). Rates of convergence in Markov renewal processes with auxiliary paths. 1970b Senturia Jerome Z. Wahrscheinlichkeitstheorie verw. Gebiete, 16, 29-38. A semi-Markov model in dam theory. 1972a ST : 12-1305, MR : 44-2283, Zbl : 192-546. (Abstract). Bull. Institute Math. Statistics, 1, 95-96. The analysis of the queueing system M/G/1 with state de- see also Purl P.S. pendent service times and the queueing system GIIM/1 with state dependent input by Markov renewal processes with Serfozo Richard F. auxiliary paths. 1970c Time and space transformations of semi-Markov processes. preprint. 1969a The analysis of queues with state dependent parameters by Ph.D. Thesis, Northwestern Univ., Evanston (III.) U.S.A. Markov renewal processes. 1971a Functions of semi-Markov processes. 1971a Advances Appl. Probability, 3, 155-175. ST : 12-1303. SIAM J. Appl. Math., 20, 530-535. ST : 14.1265, MR : MR : 44.4827, Zbl : 218-422. 45-7812, Zbl : 217-504. A generalized stationary decisio~ model of dynamic optimi- Random time transformations of semi-Markov processes~ zation. 1971b 1971b Operat. Res. Verfahren 10, 145.162. ST : 13-415. Ann. Math. Statist., 42, 176-188. ST : 14-843, MR : 44- Dynamische Optimierung unter Stetigkeits- und Habilita- 6058, Zbl : 217-504. tionsschrift, 1972a Semi-stationary processes. 1972a Univ. Hamburg. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 23, 125- On continuous dynamic programming with discrete time 132. ST : 14-844. MR : 47-5942, Zbl : 236-395. parameter. 1972b Weak convergence of superpositions of randomly selected Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21, 279- partial sums. 1973a 288. ST : 13-1197, Zbl : 213-454. Ann. Probability, 1, 1044-1056. Zbl : 271-360.

Schaufele Ronald A. Potentials associated with recurrent Markov renewal processes. 1966a J. Math. Anal. Appl., 13, 303-336. MR:35-7419,Zbl :144-401.

Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 140 Limit theorems for semi-Markov processes. 1971c Serfozo Richard F. w ~nalFunc limit tl~eorems for stochastic processes based (Ukrainian, English summary). Dopovidi Akad. Nauk. Ukrain. on embedded processes. 1975a RSR, Ser. A., 987-989. MR : 47-5980, Zbl : 231-393. Advances Appl. Probability, 7, i23-139. Limit theorems for sums of random variables determined on a denumerable Markov chain with absorption. 1972a see also Deb R___~ (Ukrainian, English summary). Dopovidi Akad. Nauk. Ukrain. RSR, Ser. A, 337-340. MR : 46-2746, Zbl : 233-340. Sevast~anov B.A. Estimation of the rate of convergence for sums of random ~e---'~'-Chistsee Y akov V • P " variables that are defined on a countable Markov chain with Shah B. absorption. 1972b see':-'--~son M.M. (Ukrainian, English summary). Dopovidi Akad. Nauk. Ukra~n. KSR, Ser. A, 436-488, 478. MR : 46-2724. Shedler Gerald S. and Tun 8 C. On the convergence of weakly depending processes in the Lofty in page reference strings. 1973a uniform topology I, II. 1972c SIAM J. Computing, Zbl : 232-411. (Russian). Teor. Verojatnost. i Mat. Statist., 6, 109-117 and 7, 132-145. MR : 48-1279, Zbl : 299-382. Shedler Gerald S. sc'-e also Gaver D.P., Lewis P.A.W., Ogden P.H. Limit theorems for semi-Markov processes with countably many states. 1973a (Russian). Teor. Verojatnost. i Mat. Statist., 8, 145.157. Sheps M.C. Zbl : 274-393. ~e Perrin ~.B. Simonova S.N. Shks~n~epYe~hneppe NLA. On single-line service sy~ems with priorities. 1966a (Russian). Trudy S. Naucnoi konferencii molodyk mate- Sil'vestrov D.S. matikov Ukrainy. Asymptotic behaviour of first passage time for sums of random variables controlled by a regular semi-Markov process.1969a On a multi-line system with losses with semi-Markov service Soviet. Math. Dokl. 10, 1541-1543. MR : 41-2749, Zbl : times. 1967a 211-217. (Russian). Kibernetika, 1967, 48-53. Zbl : 183-234. 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MR : 39-6420, Limit theorems for a continuous walk on the half-line that Zbl : 235-408. is controlled by a two state Markov process in a triangular scheme I. 1970c Output flow of single-line queueing systems. 1969a (Russian, English summary). Teor. Verojatnost. i Mat. Sta- (Russian). Ukrain, Math. J., 211, 428-435. MR : 42-1241, tist., 1, 205-220. Zbl : 198-250. Limit theorems for a discrete random walk on the half-line see alSO Prizva G.L controlled by a Markov chain, II. 1970d (Russian, English summary). Teor. Verojamost. i Mat. Sta- vw Sisonok-N.A. fist., 2, 158-166. MR : 43-8129a, Zbl : 236-401. see l~ikarev V.E. Limit theorems for a continuous walk on the half-line that is controlled by a two-state Markov process in a triangular Skorohod A.V. scheme II. 1970e A remark on homogeneous Markov processes with a discrete (Russian, English summary). Teor. Verojamost. i mat. Sta- component. 1970a fist., 2, 167-171. MR : 43-8129b. (Russian). Teor. Veronatnost. i Mat. Statist., 1, 216-221. 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Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 144