Algorithms for computing waiting time distributions under different queue disciplines for the D-BMAP/PH/1

Naval Research Logistics

Volumn 44, Issue 6, 1997, Pages 559-576

  Frigui, Imed ^a   Alfa, Attahiru Suie ^a   Xu, Xiaoyi ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Customer waiting time; Discrete batch Markovian arrival process; Phase distribution

Indexed keywords

ALGORITHMS; MARKOV PROCESSES; QUEUEING THEORY;

DISCRETE BATCH MARKOVIAN ARRIVAL PROCESS (D BMAP); PHASE DISTRIBUTION; WAITING TIME DISTRIBUTIONS;

LOGISTICS;

EID: 0031234204     PISSN: 0894069X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1520-6750(199709)44:6<559::AID-NAV3>3.0.CO;2-2     Document Type: Article

References (30)

1. Alfa, A.S., and Chakravarthy, S., "A Discrete Queue with the Markovian Arrival Process and Phase Type Primary and Secondary Services," Stochastic Models, 10, 437-451 (1994).
2. Alfa, A.S., and Frigui, I., "Discrete NT-Policy Single Server Queue with Markovian Arrival Process and Phase Type Service," European Journal of Operational Research, 88, 599-613 (1996).
3. Allen, B., Andersen, R.S., and Seneta, E., "Computation of Stationary Measures for Infinite Markov Chains," TIMS Studies in the Management Science, 7, 13-23 (1977).
4. Blondia, C., "A Discrete-Time Markovian Arrival Process," RACE Document, PRLB_123_0015_CC_CD, August 1989.
5. Blondia, C., "A Discrete-Time Batch Markovian Arrival Process as B-ISDN Traffic Model," Belgian Journal of Operations Research, Statistics and Computer Science, 32, 3-23 (1994).
6. Blondia, C., and Theimer, T., "A Discrete-Time Model for ATM Traffic," RACE Document, PRLB_123_0018_CC_CD/UST_123_0022_CC_CD, October 1989.
7. Hashida, O., Takahashi, Y., and Shimogawa, S., "Switched Batch Bernoulli Process (SBBP) and the Discrete-Time SBBP/G/1 Queue with Application to Statistical Multiplexer Performance," IEEE Journal of Selected Areas in Communications, 9, 394-401 (1991).
8. Heffes, H., and Lucantoni, D.M., "A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance," IEEE Journal of Selected Areas in Communications, 4, 856-868 (1986).
9. Herrmann, C., "Analysis of the Discrete-Time SMP/D/1/s Finite Buffer Queue with Applications in ATM," in INEOCOM-93, 1993, pp. 160-167.
10. Johnson, M.A., and Luhman, J.L., "Behavior of Queueing Approximations Based on Sample Moments," Technical report. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1994.
11. Johnson, M.A., and Taaffe, M.R., "Matching Moments to Phase Distributions: Nonlinear Programming Approaches," Stochastic Models, 6, 258-281 (1989).
12. Kroner, H., Theimer, T., and Briem, U., "Queueing Models for ATM Systems - A Comparison," Contribution to the 7th ITC Seminar, Morristown, October 1990.
13. Lucantoni, D.M., "New Results on the Single Server Queue with a Batch Markovian Arrival Process," Stoch. Mod., 7, 1-46 (1991).
14. Lucantoni, D.M., and Neuts, M.F., "The Customer Delay in a Single Server Queue with a Batch Markovian Arrival Process," working paper, 1994.
15. Meir-Hellstern, K.S., Lucantoni, D.M., and Neuts, M.F., "A Single Server Queue with Server Vacation and a Class of Non-Renewal Arrival Processes," Advances in Applied Probability, 22, 676-705 (1990).
16. Neuts, M.F., "Moment Formulas for the Markov Renewal Branching Process," Advances in Applied Probability, 8, 690-711 (1976).
17. Neuts, M.F., "Algorithms for the Waiting Time Distributions under Various Queue Disciplines in the M/G/1 Queue with Service Time Distribution of Phase Type," TIMS Studies in the Management Science, 7, 177-197 (1977).
18. Neuts, M.F., "A Versatile Markovian Point Process," Journal of Applied Probability, 16, 764-779 (1979).
19. Neuts, M.F., Matrix-Geomatric Solutions in Stochastic Models - An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, Maryland, 1981.
20. Neuts, M.F., Structured Stochastic Matrices of M/G/1 Type and Their Applications, Marcel Dekker, New York, 1989.
21. Rumaswami, V., "Stable Recursion for the Steady State Vector for Markov Chains of M/G/ 1 Type," Stoch. Mod., 4, 183-188 (1988).
22. Sen, P., Maglaris, B., Rikli, N.E., and Anastasiou, D., "Models for Packet Switching of Variable-Bit-Rate Video Sources," IEEE Journal of Selected Areas in Communications, 7, 865-869 (1989).
23. Seneta, E., Non-Negative Matrices and Markov Chains, Springer-Verlag, New York, 1981.
24. Seneta, E., and Vere-Jones, D., "On Quasi-Stationary Distributions in Discrete Time Markov Chains with Denumerable Infinity of States," Journal of Applied Probability, 3, 403-434 (1966).
25. Sriram, K., and Whitt, W., "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data," IEEE Journal of Selected Areas in Communications, 4, 833-846 (1986).
26. Steyaert, B., Bruneel, H., and Xiong, Y., "A General Relationship between Buffer Occupancy and Delay in Discrete-Time Multiserver Queueing Models, Applicable in ATM Networks," in INFOCOM-93, 1993, pp. 1250-1258.
27. Takacs, L., "Delay Distributions for One Line with Poisson Input, General Holding Times and Various Orders of Service," Bell Systems Technical Journal, 42, 487-503 (1963).
28. Tsuchiya, T., and Takahashi, Y., "On Discrete-Time Single Server Queues with Markov Modulated Batch Bernoulli Input and Finite Capacity," Journal of the Operations Research Society of Japan, 36, 29-45 (1993).
29. Tweedie, R.L., "Truncation Procedures for Non-Negative Matrices," Journal of Applied Probability, 8, 311-320 (1971).
30. Yegenoglu, F., and Jabbari, B., "Performance Evaluation of MMPP/D/1/K Queues for Aggregate ATM Traffic Models," in INFOCOM-93, 1993, pp. 1314-1319.