On queues with Markov modulated service rates

Queueing Systems

Volumn 51, Issue 1-2, 2005, Pages 89-113

  Mahabhashyam, Sai Rajesh ^a   Gautam, Natarajan ^a,b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

First step analysis; Large deviations; Markov modulated processes; Matrix geometric method

Indexed keywords

GEOMETRY; MARKOV PROCESSES; QUEUEING THEORY;

CLOSED-FORM EXPRESSION; EXTERNAL ENVIRONMENTS; LARGE DEVIATIONS; MARKOV MODULATED PROCESS; MARKOV-MODULATED SERVICE; MATRIX GEOMETRIC METHODS; QUEUE LENGTH DISTRIBUTION; STEP ANALYSIS;

NUMERICAL METHODS;

EID: 30844463691     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-005-2158-x     Document Type: Article

References (56)

1. I.J.B.F. Adan and V.G. Kulkarni, Single server queue with markov dependent interarrivai and service times, Queueing Systems 45(2) (2003) 113-134.
2. S. Ahn and J. Jeon, Large deviation results for queues with continuous time markov modulated arrivals, Engineering Simulation 18(1) (2000) 67-74.
3. M. Baykal-Gursoy and W. Xiao, Stochastic decomposition in M/M/∞ queues with Markov modulated service rates, Queueing Systems 48 (2004) 75-88.
4. T. Bonald and A. Proutiere, Insensitive bandwidth sharing in data networks, Queueing Systems 44 (2003) 69-100.
5. O.J. Boxma and I.A. Kurkova, The M/G/1 queue with two service speeds, Adv. Applied Probability 33(2001)520-540.
6. I. Cidon, R. Gu'erin, A. Khamisy, and M. Sidi, On queues with inter-arrival times proportional to service times, Technion, EE PUB (1991) (811).
7. T. Collings and C. Stoneman, The M/M/∞ queue with varying arrival and service rates, Operations Research 24 (1976) 760-773.
8. C. Courcoubetis and R. Weber, Effective bandwidths for stationary sources, Prob. Eng. Inf. Sci. 9 (1995)285-296.
9. K. Dorman, karindorman.stat.iastate.edu/stat432/2003-09-12.pdf.
10. A.I. Elwalid and D. Mitra, Effective bandwidth of general Markovian traffic sources and admission control of high speed networks, IEEE/ACM Transactions on Networking 1(3) (1993) 329-343.
11. N. Gautam, V.G. Kulkarni, T. Rolski, and Z. Palmowski, Bounds for fluid models driven by semi-Markov inputs, Probability in Engineering and Informational Sciences 13(4) (1999) 429-475.
12. J.S. Kaufman, Blocking in shared resource environment, IEEE Transactions on Communications 29(10) (1981) 1494-1481.
13. F.P. Kelly, Notes on Effective Bandwidth, Stochastic Networks: Theory and Applications, (Oxford University Press, 1996).
14. G. Kesidis, J. Walrand, and C-S. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE/ACM Transactions on Networking 1(3) (1993) 424-428.
15. V.G. Kulkarni, Modeling and Analysis of Stochastic Systems. Chapman and Hall texts in Statistical series, CRC press, (1995).
16. V.G. Kulkarni, Effective bandwidths for Markov regenerative sources, Queueing Systems 24 (1997) 137-153.
17. G. Latouche, C. Pierce, and P. Taylor, Invariant measures for quasi-birth and death processes, Stochastic Models (1997).
18. W. Massey, The analysis of queues with time-varying rates for telecommunication models, Telecommunication Systems 21(2-4) (2002) 173-204.
19. M.F. Neuts, Matrix geometric Solutions in Stochastic models: An algorithmic Approach, (Johns Hopkins University Press, Baltimore, 1981).
20. R. Núñez-Queija, Steady state analysis of a queue with varying service rate, Technical Report PNA-R9712, CWI (1997).
21. V. Ramaswami, Algorithmic analysis of stochastic models: The changing face of mathematics, Ramanujam Endowment Lecture at Anna University, Chennai, India (2000).
22. A. Riska and E. Smirni, Mamsolver: A matrix analytical method tool, in the Proceedings of the 12th International Conference on Modeling Techniques and Tools for Computer and Communication Systems Performance Evaluation, LNCS 2324 (2002) 205-211.
23. J.W. Roberts, A Service system with heterogeneous user requirements, Performance of Data Communication Systems and their Applications (1981) 423-431.
24. K.W. Ross, Multiservice Loss Models for Broadband Telecommunication Networks (New York: Springer-Verlag, 1995).
25. V. Sharma, Queues with service rate controlled by a delayed feedback, Queueing Systems 39(4) (2001) 303-315.
26. H. Takahashi and L. Wang, Approximate analysis of a queueing system with Markov modulated arrivals, Electronics and Communications in Japan, Part 1 73(11) (1990) 12-21.
27. J.R. Thorne, Modeling complex queuing situations with markov processes, URL: charybdis.mit.csu.edu.au/mantolov/CD/ICITA2002/papers/077-1.pdf.
28. Z. Yong-Pin and G. Noah, A single-server queue with Markov modulated service times, (October 1999), URL: http://fic.wharton.upenn.edu/fic/papers/99/9940.pdf.
29. I.J.B.F. Adan and V.G. Kulkarni, Single server queue with markov dependent interarrivai and service times, Queueing Systems 45(2) (2003) 113-134.
30. S. Ahn and J. Jeon, Large deviation results for queues with continuous time markov modulated arrivals, Engineering Simulation 18(1) (2000) 67-74.
31. M. Baykal-Gursoy and W. Xiao, Stochastic decomposition in M/M/∞ queues with Markov modulated service rates, Queueing Systems 48 (2004) 75-88.
32. T. Bonald and A. Proutiere, Insensitive bandwidth sharing in data networks, Queueing Systems 44 (2003) 69-100.
33. O.J. Boxma and I.A. Kurkova, The M/G/1 queue with two service speeds, Adv. Applied Probability 33(2001)520-540.
34. I. Cidon, R. Gu'erin, A. Khamisy, and M. Sidi, On queues with inter-arrival times proportional to service times, Technion, EE PUB (1991) (811).
35. T. Collings and C. Stoneman, The M/M/∞ queue with varying arrival and service rates, Operations Research 24 (1976) 760-773.
36. C. Courcoubetis and R. Weber, Effective bandwidths for stationary sources, Prob. Eng. Inf. Sci. 9 (1995)285-296.
37. K. Dorman, karindorman.stat.iastate.edu/stat432/2003-09-12.pdf.
38. A.I. Elwalid and D. Mitra, Effective bandwidth of general Markovian traffic sources and admission control of high speed networks, IEEE/ACM Transactions on Networking 1(3) (1993) 329-343.
39. N. Gautam, V.G. Kulkarni, T. Rolski, and Z. Palmowski, Bounds for fluid models driven by semi-Markov inputs, Probability in Engineering and Informational Sciences 13(4) (1999) 429-475.
40. J.S. Kaufman, Blocking in shared resource environment, IEEE Transactions on Communications 29(10) (1981) 1494-1481.
41. F.P. Kelly, Notes on Effective Bandwidth, Stochastic Networks: Theory and Applications, (Oxford University Press, 1996).
42. G. Kesidis, J. Walrand, and C-S. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE/ACM Transactions on Networking 1(3) (1993) 424-428.
43. V.G. Kulkarni, Modeling and Analysis of Stochastic Systems. Chapman and Hall texts in Statistical series, CRC press, (1995).
44. V.G. Kulkarni, Effective bandwidths for Markov regenerative sources, Queueing Systems 24 (1997) 137-153.
45. G. Latouche, C. Pierce, and P. Taylor, Invariant measures for quasi-birth and death processes, Stochastic Models (1997).
46. W. Massey, The analysis of queues with time-varying rates for telecommunication models, Telecommunication Systems 21(2-4) (2002) 173-204.
47. M.F. Neuts, Matrix geometric Solutions in Stochastic models: An algorithmic Approach, (Johns Hopkins University Press, Baltimore, 1981).
48. R. Núñez-Queija, Steady state analysis of a queue with varying service rate, Technical Report PNA-R9712, CWI (1997).
49. V. Ramaswami, Algorithmic analysis of stochastic models: The changing face of mathematics, Ramanujam Endowment Lecture at Anna University, Chennai, India (2000).
50. A. Riska and E. Smirni, Mamsolver: A matrix analytical method tool, in the Proceedings of the 12th International Conference on Modeling Techniques and Tools for Computer and Communication Systems Performance Evaluation, LNCS 2324 (2002) 205-211.
51. J.W. Roberts, A Service system with heterogeneous user requirements, Performance of Data Communication Systems and their Applications (1981) 423-431.
52. K.W. Ross, Multiservice Loss Models for Broadband Telecommunication Networks (New York: Springer-Verlag, 1995).
53. V. Sharma, Queues with service rate controlled by a delayed feedback, Queueing Systems 39(4) (2001) 303-315.
54. H. Takahashi and L. Wang, Approximate analysis of a queueing system with Markov modulated arrivals, Electronics and Communications in Japan, Part 1 73(11) (1990) 12-21.
55. J.R. Thorne, Modeling complex queuing situations with markov processes, URL: charybdis.mit.csu.edu.au/mantolov/CD/ICITA2002/papers/077-1.pdf.
56. Z. Yong-Pin and G. Noah, A single-server queue with Markov modulated service times, (October 1999), URL: http://fic.wharton.upenn.edu/fic/papers/99/9940.pdf.