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Single-channel system with circular access or processor-sharing and branching processes. (English. Russian original) Zbl 0715.60121

Math. Notes 44, No. 3-4, 716-724 (1988); translation from Mat. Zametki 44, No. 4, 433-448 (1988).
See the review in Zbl 0661.60114.

MSC:

60K25 Queueing theory (aspects of probability theory)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Citations:

Zbl 0661.60114
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Full Text: DOI

References:

[1] M. Yu. Kitaev and S. F. Yashkov, ?The distribution of the conditional sojourn time in a system with sharing of service time,? Izv. Akad. Nauk SSSR, Ser. Tekh. Kib., No. 4, 211-215 (1978).
[2] S. F. Yashkov, ?A derivation of response time distribution for a M|G|l processor-sharing queue,? Probl. Control Inf. Theory,12, No. 2, 133-148 (1983). · Zbl 0519.68052
[3] R. Schassberger, ?A new approach to the M|G|l processor-sharing queue,? Adv. Appl. Probab.,16, No. 1, 202-213 (1984). · Zbl 0529.68015 · doi:10.2307/1427231
[4] T. Ott, ?The sojourn time distribution in the M|G|l queue with processor sharing,? J. Appl. Probab.,21, No. 2, 360-378 (1984). · Zbl 0544.60087 · doi:10.2307/3213646
[5] E. Coffman, R. Muntz, and H. Trotter, ?Waiting time distributions for processorsharing systems,? J. Assoc. Comput. Machin.,17, No. 1, 123-130 (1970). · Zbl 0197.15304
[6] A. G. Pakes, ?Some limit theorems for the total progeny of branching process,? Adv. Appl. Probab.,3, No. 1, 176-192 (1971). · Zbl 0218.60075 · doi:10.2307/1426333
[7] A. G. Pakes, ?Further results on the critical Galton-Watson process with immigration,? J. Austral. Math. Soc.,13, No. 3, 277-290 (1972). · Zbl 0235.60078 · doi:10.1017/S1446788700013690
[8] B. A. Sevast’yanov, Branching Processes [in Russian], Nauka, Moscow (1971).
[9] P. Jagers, Branching Processes with Biological Applications, Wiley, London (1975). · Zbl 0356.60039
[10] B. V. Gnedenko and Gussein Fakhim, ?A certain transfer theorem,? Dokl. Akad. Nauk SSSR,187, No. 1, 15-18 (1969).
[11] P. S. Puri, ?Some limit theorems on branching processes and certain related processes,? Sankhya,A31, No. 1, 57-75 (1969). · Zbl 0181.43903
[12] A. G. Pakes, ?Limit theorems for the integrals of some branching processes,? Stochas. Proces. Appl.,3, No. 1, 89-111 (1975). · Zbl 0299.60067 · doi:10.1016/0304-4149(75)90009-5
[13] K. Athreya and P. Ney, Branching Processes, Springer, Berlin (1972). · Zbl 0259.60002
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