Transient laws of non-stationary queueing systems and their applications

Queueing Systems

Volumn 25, Issue 1-4, 1997, Pages 115-155

  Bertsimas, Dimitris ^a,b   Mourtzinou, Georgia ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Little's law; Non homogeneous Poisson process; Non stationary systems; Transient analysis

Indexed keywords

INTEGRAL EQUATIONS; QUEUEING NETWORKS; QUEUEING THEORY;

ASYMPTOTIC EXPANSION; COMPUTATIONAL RESULTS; LITTLE'S LAW; NON HOMOGENEOUS POISSON PROCESS; NONSTATIONARY SYSTEMS; NUMERICAL TECHNIQUES; PERFORMANCE MEASURE; STRUCTURAL RELATIONSHIP;

TRANSIENT ANALYSIS;

EID: 0031483143     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019100301115     Document Type: Article

References (31)

1. J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, Journal on Computing 7 (1995) 36-43.
2. M.S. Bartlett, Some evolutionary stochastic processes, J. Roy. Statist. Soc. Ser. B 11 (1949) 211-229.
3. V.E. Beněs, On queues with Poisson arrivals, Annals of Mathematical Statistics 28 (1956) 670-677.
4. D. Bertsimas and G. Mourtzinou, Multiclass queueing systems in heavy traffic: An asymptotic approach based on distributional and conservation laws, working paper, Operations Research Center, MIT (1993) to appear in Oper. Res.
5. D. Bertsimas and G. Mourtzinou, A unified method to analyze overtake-free queueing systems, Adv. Appl. Probab. 28 (1996) 588-625.
6. D. Bertsimas and D. Nakazato, Transient and busy period analysis of the GI/G/1 queue: The method of stages, Queueing Systems 10 (1992) 153-184.
7. D. Bertsimas and D. Nakazato, The distributional Little's law and its applications, Oper. Res. 43 (1995) 298-310.
8. D.M. Choudhury, G.L. Lucantoni and W. Whitt, Numerical solution of M(t)/G(t)/1 queues, working paper, AT&T Bell Labs (1993).
9. D.R. Cox, Renewal Theory (Chapman and Hall, New York, 1962).
10. D.R. Cox and V. Isham, Point Processes (Chapman and Hall, New York, 1980).
11. J.L. Doob, Stochastic Processes (John Wiley, New York, 1953).
12. P. Green, L. Kolesar and A. Svoronos, Some effects of nonstationarity on multiserver markovian systems, Oper. Res. 39 (1991) 502-511.
13. R. Haji and G. Newell, A relation between stationary queue and waiting time distributions, J. Appl. Probab. 8 (1971) 617-620.
14. D. Heyman and M. Sobel, Stochastic Models in Operations Research: Vol. 1 (McGraw-Hill, New York, 1982).
15. T. Hosono, Numerical inversion of Laplace transform and some applications to wave optics, Radio Science 16 (1981) 1015-1019.
16. k/D/r queues with FIFO, Oper. Res. Lett. 2 (1983) 20-21.
17. J. Keilson and L. Servi, A distributional form of Little's law, Oper. Res. Lett. 7 (1988) 223-227.
18. J. Keilson and L. Servi, The distributional form of Little's law and the Fuhrmann-Cooper decomposition, Oper. Res. Lett. 9 (1990) 239-247.
19. A. Y. Khintchine, Mathematical Methods in the Theory of Queues (in Russian, Trudy Mat. Inst. Steklov, 49; English translation by Charles Griffin & Co, London, 1955).
20. L. Kleinrock, Queueing Systems; Vol. 1: Theory (Wiley, New York, 1975).
21. J. Little, A proof of the theorem L = λW, Oper. Res. 9 (1961) 383-387.
22. K.M Malone, Dynamic queueing systems: behavior and approximations for individual queues and for networks, Ph.D. thesis, Massachusetts Institute of Technology (Cambridge, MA, 1995).
23. W.A. Massey and W. Whitt, Networks of infinite-server queues with non-stationary Poisson input, Queueing Systems 13 (1993) 183-250.
24. G. Mourtzinou, An axiomatic approach to queueing systems, Ph.D. thesis, Massachusetts Institute of Technology (Cambridge, MA, 1995).
25. A. Odoni and E. Roth, An empirical investigation of the transient behavior of stationary queueing systems, Oper. Res. 31 (1983) 432-455.
26. K.L. Ong and M.R. Taaffee, Non-stationay queues with interrupted Poisson arrivals and unreliable/repairable servers, Queueing Systems 4 (1989) 27-46.
27. C. Palm, Intensity variations in telephone traffic, Ericson Technics 44 (1943) 1-189 (in German, English translation by North-Holland, Amsterdam, 1988).
28. A. Prékopa, On secondary processes generated by a random point distribution of Poisson type, Annales Univ. Sci. Budapest de Eötvös Nom. Sectio. Math. 1 (1958) 153-170.
29. S. Ross, Introduction to Probability Models, 5th edn. (Academic Press, London, 1993).
30. S. Stidham Jr., A last word on L = λW, Oper. Res. 22 (1974) 417-421.
31. L. Takács, Investigation of waiting time problems by reduction to Markov processes, Acta. Math. Acad. Sci. Hung. 6 (1955) 101-129.