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Joint distribution of waiting time and queue size for single server queues

Seria
Rozprawy Matematyczne tom/nr w serii: 248 wydano: 1986
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Warianty tytułu
Abstrakty
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CONTENTS
1. Introduction...................................................................5
2. Preliminaries................................................................11
3. Departure process......................................................19
4. Joint distribution of waiting time and queue size..........32
5. New forms of Little's formula.......................................38
References.....................................................................53
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 248
Liczba stron
53
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXLVIII
Daty
wydano
1986
Twórcy
Bibliografia
  • [1] P. B. Billingsley. Convergence of Probability Measures. Wiley. New York 1968.
  • [2] A. A. Borovkov, Stochastic Processes in Queueing Theory (in Russian). Nauka. Moskva 1971.
  • [3] S. L. Brumelle, On the relation between customer and time averages in queues, J. Appl. Probab. 8 (1971), 508-520.
  • [4] S. L. Brumelle, A generalization of L = λW to moments of queue length and waiting time, Oper. Res. 20 (1972), 1127-1136.
  • [5] J. W. Cohen, The Single Server Queue, North-Holland, Amsterdam 1969.
  • [6] S. Eilon, A simpler proof of L = λW, Oper. Res. 17 (1969), 915-917.
  • [7] P. Franken, Einige Anwendungen der Theorie zufälliger Punktprozesse in der Bedienungs-theorie I, Math. Nachr. 70 (1975), 303-319.
  • [8] R. Haji and G. F. Newell, A relation between stationary queue and waiting time distributions, J. Appl. Probab. 8 (1971), 617-620.
  • [9] D. L. Iglehart and W. Whitt, Multiple channel queues in heavy traffic I, II, Adv. in Appl. Probab. 2 (1970), 150-177 and 355-369.
  • [10] W. S. Jewell, A simple proof of: L = λW, Oper. Res. 15 (1967), 1109-1116.
  • [11] A. J. Lemoine, On two stationary distributions for the stable GI/G/1 queue, J. Appl. Probab. 11 (1974), 849-852.
  • [12] T. Lindvall. Weak convergence of probability measures and random functions in the function space D [0,∞), ibid. 10 (1973), 109-121.
  • [13] J. D. C. Little, A proof for the queueing formula: L = λW, Oper. Res. 9 (1961), 383-387.
  • [14] K. T. Marshal and R. Wolff, Customer average and time average queue length and waiting times, J. Appl. Probab. 8 (1971), 535-542.
  • [15] M. Miyazawa, A formal approach to queueing processes in the steady state and their applications, ibid. 16 (1979), 332-346.
  • [16] M. Mori, Some bounds for queues, J. Oper. Res. Soc. Japan 18 (1975), 152-181.
  • [17] M. Mori, Relations between queue-size and waiting-time distributions, J. Appl. Probab. 17 (1980), 822 830.
  • [18] V. V. Petrov, Sums of Independent Random Variables, (in Russian), Nauka, Moskva 1972.
  • [19] T. Rolski and R. Szekli, Networks of work-conserving normal queues, in: Applied Probability-Computer Science, The Interface, vol. II, BirkhSuser, Boston 1982, 477-497.
  • [20] R. F. Serfozo, Functional limit theorems for stochastic processes based on embedded processes, Adv. in. Appl. Probab. 7 (1975), 123-139.
  • [21] S. Stidham, Jr., L = λW: A discounted analogue and a new proof, Oper. Res. 20 (1972), 1115-1126.
  • [22] D. Stoyan, Further stochastic order relations among GI/G/1 queues with a common traffic intensity, Math. Operationsforsch. Statist. Ser. Optim. 8 (1977), 541-548.
  • [23] W. Szczotka, Immediate service in a Beneš-type G/G/1 queueing system, Zastos. Mat. 14 (1974), 357-363.
  • [24] W. Szczotka, An invariance principle for queues in heavy traffic, Math. Operationsforsch. Statist. Ser. Optim. 8 (1977), 591-631.
  • [25] W. Whitt, Heavy traffic limit theorems for queues: a survey, in: Lecture Notes in Econom. and Math. Systems 98 (1974), 307-350.
  • [26] W. Whitt, Some useful functions for functional limit theorems. Math. Oper. Res. 5 (1980), 67-85.
Języki publikacji
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Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-6c15d1b7-db7e-467d-80ac-693e9131d94a
Identyfikatory
ISBN
83-01-06690-3
ISSN
0012-3862
Kolekcja
DML-PL
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