An invariance relation and a unified method to derive stationary queue-length distributions

Operations Research

Volumn 52, Issue 5, 2004, Pages 756-764

  Kim, Nam K ^a   Chae, Kyung C ^b   Chaudhry, Mohan L ^c  

^a Chonnam National University   (South Korea)

^b Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^c ROYAL MILITARY COLLEGE OF CANADA   (Canada)

Author keywords

Queues, batch bulk: batch arrivals, batch services, multiple servers, BMAP arrivals; Queues: invariance relation, unified method, discrete time queue

Indexed keywords

COMPUTER SYSTEMS; CUSTOMER SATISFACTION; FUNCTIONS; MARKOV PROCESSES; PROBABILITY; SERVERS;

BATCH ARRIVALS; BATCH SERVICES; BMAP ARRIVALS; DISCRETE-TIME QUEUE; INVARIANCE RELATION; MULTIPLE SERVERS; QUEUES; UNIFIED METHOD;

QUEUEING NETWORKS;

EID: 8344244597     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1040.0116     Document Type: Article

References (27)

1. Abate, J., W. Whitt. 1992. Numerical inversion of probability generating functions. Oper. Res. Lett. 12 245-251.
2. ,R/I. J. Appl. Math. Stochastic Anal. 5 237-260.
3. Bertsimas, D., G. Mourtzinou. 1996. A unified method to analyze overtake free queueing systems. Adv. Appl. Probab. 28 588-625.
4. Bertsimas, D., D. Nakazato. 1995. The distributional Little's law and its applications. Oper. Res. 43 298-310.
5. Blondia, C., O. Casals. 1992. Statistical multiplexing of VBR sources: A matrix-analytic approach. Performance Evaluation 16 5-20.
6. Boxma, O. J., W. P. Groenendijk. 1988. Waiting times in discrete-time cyclic-service systems. IEEE Trans. Comm. COM-36 164-170.
7. Bruneel, H., B. G. Kim. 1993. Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston, MA.
8. Bruneel, H., I. Wuyts. 1994. Analysis of discrete-time multiserver queueing models with constant service times. Oper. Res. Lett. 15 231-236.
9. Chang, S. H., K. C. Chae, H. W. Lee, T. Takine. 2002a. Factorization properties in the discrete-time BMAP/G/l queue with generalized vacations. Technical report 2002-04, Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Daejon, Korea. http://OSL7.kaist.ac.kr/ freedom/OR/DBMAPGlGV.pdf.
10. Chang, S. H., T. Takine, K. C. Chae, H. W. Lee. 2002b. A unified queue length formula for BAMP/G/1 queue with generalized vacations. Stochastic Models 18 369-386.
11. Chaudhry, M. L., N. K. Kim. 2003. A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times. Oper. Res. Lett. 31 101-107.
12. Chaudhry, M. L., J. G. C. Templeton. 1983. A First Course in Bulk Queues. John Wiley and Sons, New York.
13. Daigle, J. N., S. C. Tang. 1992. The queue length distribution for multiserver discrete-time queues with batch Markovian arrivals. Stochastic Models 8 665-683.
14. Haji, R., G. F. Newell. 1971. A relation between stationary queue and waiting time distributions. J. Appl. Probab. 8 617-620.
15. Hunter, J. J. 1983. Mathematical Techniques of Applied Probability, Vol 2: Discrete Time Models: Techniques and Applications. Academic Press, New York.
16. Keilson, J., L. D. Servi. 1990. The distributional form of Little's law and the Fuhrmann-Cooper decomposition. Oper. Res. Lett. 9 239-247.
17. Kim, N. K., K. C. Chae, H. W. Lee. 2003. A note on the relationships among the queue lengths at various epochs of a queue with BMAP arrivals. Internat. J. Management Sci. 9 1-12.
18. Kim, N. K., S. H. Chang, K. C. Chae. 2002. On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals. Oper. Res. Lett. 30 25-32.
19. Lucantoni, D. M. 1991. New results on the single server queue with a batch Markovian arrival process. Stochastic Models 7 1-46.
20. Medhi, J. 1984. Recent Developments in Bulk Queueing Models. Wiley Eastern Limited, New Delhi, India.
21. Neuts, M. F. 1989. Structured Stochastic Matrices of M/G/I Type and Their Applications. Marcel Dekker, New York.
22. Powell, W. B., P. Humblet. 1986. The bulk service queue with a general control strategy: Theoretical analysis and a new computational procedure. Oper. Res. 34 267-275.
23. Sohraby, K., J. Zhang. 1994. Spectral decomposition approach for transient analysis of multi-server discrete-time queues. Performance Evaluation 21 131-150.
24. Takagi, H. 1991. Queueing Analysis, Vol 1: Vacation and Priority Systems, Part I. North-Holland, Amsterdam, The Netherlands.
25. Takagi, H. 1993. Queueing Analysis, Vol 3: Discrete-Time Systems. NorthHolland, Amsterdam, The Netherlands.
26. Takine, T., Y. Takahashi. 1998. On the relationship between queue lengths at a random instant and at a departure in the stationary queue with BMAP arrivals. Stochastic Models 14 601-610.
27. Wolff, R. W. 1989. Stochastic Modeling and the Theory of Queues. Prentice-Hall, Englewood Cliffs, NJ.