Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneing

References

• Arndt , K . Construction of a class of stationary processes with applications in reliablity . Zast. Mat , To appear in
   Google Scholar
• Brown , M and Ross , S.M . 1972 . Asymptotic properties of cumulative processes . SIAM J. Appl Math , 22 : 93 – 105 .
   Web of Science ®Google Scholar
• Cohen , J.W . 1969 . The single server queue , Amsterdam : North Holland Publ .
   Google Scholar
• Cohen , J.W . 1976 . “ On regenerative processes in queueing theory ” . In Lect. Notes in Econ.Math.Syst , Vol. 121 , Berlin : Springer-Verlag . Heideiberg/New York
   Google Scholar
• Franken , P . 1975 . On stationary state probabilities of queueing systems at several points in time . Izv. AN SSSR Techn. Kib. 1975 , 1 : 101 – 107 . Russian
   Google Scholar
• Franken , P . 1976 . Einige Anwendungen der Theorie zufälliger Punktprozesse in der Bedienungstheorie . I. Math. Nachr , 70 : 309 – 319 .
   Google Scholar
• Franken , P . 1976 . A new approach to investigation of stationary queueing systems . Math. Operation Res , 70 Submitted to
   Google Scholar
• Herrmann , U . 1965 . Ein Approximationssatz für Verteilungen stationlirer zufälliger Punktfolgen . Math. Nachr , 30 : 377 – 381 .
   Web of Science ®Google Scholar
• Jankiewicz , M and Kopocinski , B . 1976 . Steady-state distributions of piecewise Markov processes . Zast. Mat , 15 : 25 – 32 .
   Google Scholar
• Jankiewicz , M and Rolski , T . 1977 . Piecewise Markov processes on a general state space . Zast Mat , 15 : 421 – 436 .
   Google Scholar
• Kendall , D.G . 1953 . Stochastic processes occuring in the theory of queues and their analysis by the method of the imbedded Markov chains . Ann. Math. Statist , 24 : 338 – 354 .
   Google Scholar
• Kerstan , J , Matthes , K and Mecke , J . 1974 . Unbegrenzt teilbare Punktprozesse , Berlin : Akadenlie-Verlag .
   Google Scholar
• König , D , Matthes , K and Nawrotzki , K . 1967 . Verallgemeinerungen der ERLANGschen und ENGSETschen Formeln , Berlin : Akademie-Verlag . Eine Methode in der Bedienungstheorie
   Google Scholar
• König , D , Schmidt , V and Stoyan , D . 1976 . On some relations between stationary distributions of queue lengths and imbedded queue lengths in G/G/s queueing systems . Math. Operationsforsch. Statist , 7 : 577 – 586 .
   Google Scholar
• Kopocinska , I and Kopocinski , B . 1971 . Queueing systems with feedback . Bull. Acad.Polon. Sci. Ser. Sci. Math. Astronom. Phys , 19 : 397 – 401 .
   Google Scholar
• Kopocinska , I and Kopocinski , B . 1972 . Queueing systems with feedback . Zast. Mat , 12 : 373 – 384 .
   Google Scholar
• Kopocinski , B and Rolski , T . 1977 . A note on the virtual waiting time in the GI/G/s queue . Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys , 25 : 1279 – 1280 .
   Google Scholar
• Kuczura , A . 1973 . Piecewise Markov processes . SIAM. J. Appl. Math , 24 : 169 – 181 .
   Web of Science ®Google Scholar
• Lemoine , A.J . 1974 . On two stationary distributions for the stable GI/G/1 queue . J. Appl.Prob , 11 : 849 – 852 .
   Web of Science ®Google Scholar
• Litvinov , M.L . 1975 . KENDALL's method and the determination of characteristics of service models . Russian. Izv. AN SSSR, Techn. Kib. 1975 , 6 : 74 – 79 .
   Google Scholar
• Miyazawa , M . 1976 . Stochastic order relations among GI/G/1 queues with a common traffic intensity . J. Operations Res. Soc. Japan , 19 : 193 – 208 .
   Google Scholar
• Miyazawa , M . 1977 . Time and customer processes in queues with stationary inputs . J. Appl. Prob , 14 : 349 – 357 .
   Web of Science ®Google Scholar
• Miyazawa , M . 1976 . Conservation laws in queueing theory and their applications to the finiteness of moments , Tokyo Institute of Technology . Research Report on Information Sciences B-28
   Google Scholar
• Nawrotzki , K . 1975 . Markov random marked streams and their application to problems of queueing theory . Math. Operationsforsch. u. Statist , 6 : 445 – 477 . Russian
   Google Scholar
• Pyke , R and Schaufele , R . 1966 . The existence and uniqueness of stationary measures for Markov renewal processes . Ann. Math. Statlist , 37 : 1439 – 1462 .
   Google Scholar
• Rolski , T . 1977 . A relation between imbedded Markov chains in piecewise Markov processes . Bull. Acad. Poion. Sci. Ser. Sci. Math. Astronom. Phys , 25 : 181 – 199 .
   Google Scholar
• Schäl , M . 1970 . Markov renewal processes with auxiliary paths . Ann. Math. Statist , 41 : 1604 – 1623 .
   Google Scholar
• Schäl , M . 1971 . The analysis of queues with state-dependent parameters by Markov renewal processes . Adv. Appl. Prob , 3 : 155 – 175 .
   Google Scholar
• Schrage , L . 1970 . An alternative proof of a conservation law for the queue G/G/l . Operations Res , 18 : 185 – 187 .
   Web of Science ®Google Scholar
• Stidham , S . 1970 . Regenerative processes in the theory of queues with applications to the alternating priority queue . Adv. Appl. Prob , 4 : 542 – 577 .
   Google Scholar
• Stidham , S . 1974 . A last word on L = &lamda;W . Operations Res , 22 : 417 – 421 .
   Web of Science ®Google Scholar
• Takas , L . 1962 . Introduction to the theory of queues , New York : Oxford University Press .
   Google Scholar
• Takas , L . 1963 . The limiting distribution of the virtuni waiting time end the queue size for a single-server queue with recurrent input and general service times , 25 : 91 – 100 . Sankhya A
   Google Scholar