Analytical distribution of waiting time in the M/{iD}/1 queue

Queueing Systems

Volumn 50, Issue 2-3, 2005, Pages 185-197

  Shortle, John F ^a   Brill, Percy H ^b  

^a Krasnow Institute for Advanced Study   (United States)

^b UNIVERSITY OF WINDSOR   (Canada)

Author keywords

Integer partitions; M D 1 queue; M Discrete 1 queue; Numerical queueing methods; Waiting time

Indexed keywords

NUMERICAL METHODS;

INTEGER PARTITIONS; M/D/1 QUEUE; M/DISCRETE/1 QUEUE; NUMERICAL QUEUEING METHODS; WAITING-TIME;

QUEUEING THEORY;

EID: 23944486947     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-005-0615-1     Document Type: Article

References (20)

1. J. Abate, G. Choudhury and W. Whitt, An introduction to numerical transform inversion and its application to probability models, in: Computational Probability, ed. W. Grassmann (Kluwer, Boston, 1999) pp. 257-323.
2. M. Brahimi and D.J. Worthington, The finite capacity multi-server queue with inhomogeneous arrival rate and discrete service time distribution-and its application to continuous service time problems, European Journal of Operational Research 50 (1991) 310-324.
3. P.H. Brill, Properties of the waiting time in M/Dpj/1 queues, Technical report, Dept. of Mathematics and Statistics, University of Windsor, 2002. Report WMSR 02-01.
4. O. Brun and J. Garcia, Analytical solutions of finite capacity M/D/1 queues, Journal of Applied Probability 37 (2000) 1092-1098.
5. J. Cao, W.S. Cleveland, D. Lin and D.X. Sun, Internet traffic tends toward Poisson and independent as the load increases, in: Nonlinear Estimation and Classification, ed. D. Denison et al. (Springer, New York, 2003).
6. M.L. Chaudhry, On numerical computations of some discrete-time queues, in: Computation Probability, ed. W.K. Grassmann (Kluwer Academic, Boston, 2000) pp. 365-408.
7. C.D. Crommelin, Delay probability formulae when the holding times are constant, Post Office Electrical Engineering Journal 25 (1932) 41-50.
8. A.K. Erlang, The theory of probabilities and telephone conversations, Nyt Tidsskrift for Matematik B, 20 (1909) 33-39;
9. English translation in: The Life and Work of A.K. Erlang (The Copenhagen Telephone Company, Copenhagen, 1948).
10. G.J. Franx, A simple solution for the M/D/c waiting time distribution, Operations Research Letters 29 (2001) 221-229.
11. V.B. Iversen and L. Staalhagen, Waiting time distribution in M/D/1 queueing systems, Electronics Letters 35(25) (1999) 2184-2185.
12. D.L. Kreher and D.R. Stinson, Combinatorial. Algorithms: Generation, Enumeration, and Search (CRC Press, New York, 1999).
13. D. Newman, G. Chagnot and J. Perser, Networking the Telecom Industry, Detailed Methodology. Light Reading, 2001. www.lightreading.com/document.asp?doc_id=3972, Section 3 [accessed Jan. 15, 2004].
14. A. Nijenhuis and H.S. Wilf. Combinatorial Algorithms for Computers and Calculators 2nd edn. (Academic Press, New York, 1978).
15. S. Niu and R. Cooper, Transform-free analysis of M/G/1/K and related queues, Mathematics of Operations Research 18(2) (1993) 486-510.
16. K. Sigman, Appendix: A primer on heavy-tailed distributions, Queueing Systems 33 (1999) 261-275.
17. K. Thompson, G. Miller and R. Wilder, Wide-area Internet traffic patterns and characteristics, IEEE Network 11(6) (1997) 10-23.
18. H.C. Tijms, A First Course in Stochastic Models (Wiley, Hoboken, NJ, 2003).
19. R. Wolff, Stochastic Modeling and the Theory of Queues, (Prentice Hall, Englewood Cliffs, NJ, 1989).
20. M.E. Woodward, Communication and Computer Networks: Modelling with Discrete-Time Queues, (IEEE Computer Society Press, Los Alamitos, CA, 1994).