An Invariance Relation and a Unified Method to Derive Stationary Queue-Length Distributions

References

• Abate J., Whitt W. Numerical inversion of probability generating functions. Oper. Res. Lett. (1992) 12:245–251Crossref, Google Scholar
• Abolnikov L., Dshalalow J. H. On a multilevel controlled bulk queueing system MX/Gr, R/1. J. Appl. Math. Stochastic Anal. (1992) 5:237–260Crossref, Google Scholar
• Bertsimas D., Mourtzinou G. A unified method to analyze overtake free queueing systems. Adv. Appl. Probab. (1996) 28:588–625Crossref, Google Scholar
• Bertsimas D., Nakazato D. The distributional Little's law and its applications. Oper. Res. (1995) 43:298–310Link, Google Scholar
• Blondia C., Casals O. Statistical multiplexing of VBR sources: A matrix-analytic approach. Performance Evaluation (1992) 16:5–20Crossref, Google Scholar
• Boxma O. J., Groenendijk W. P. Waiting times in discrete-time cyclic-service systems. IEEE Trans. Comm. (1988) COM-36:164–170Crossref, Google Scholar
• Bruneel H., Kim B. G.Discrete-Time Models for Communication Systems Including ATM (1993) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
• Bruneel H., Wuyts I. Analysis of discrete-time multiserver queueing models with constant service times. Oper. Res. Lett. (1994) 15:231–236Crossref, Google Scholar
• Chang S. H., Chae K. C., Lee H. W., Takine T. Factorization properties in the discrete-time BMAP/G/1 queue with generalized vacations. (2002a) . Technical report 2002-04, Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Daejon, Korea. http://OSL7.kaist.ac.kr/freedom/OR/DBMAPG1GV.pdf.Google Scholar
• Chang S. H., Takine T., Chae K. C., Lee H. W. A unified queue length formula for BAMP/G/1 queue with generalized vacations. Stochastic Models (2002b) 18:369–386Crossref, Google Scholar
• Chaudhry M. L., Kim N. K. A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times. Oper. Res. Lett. (2003) 31:101–107Crossref, Google Scholar
• Chaudhry M. L., Templeton J. G. C.A First Course in Bulk Queues (1983) (John Wiley and Sons, New York) Google Scholar
• Daigle J. N., Tang S. C. The queue length distribution for multiserver discrete-time queues with batch Markovian arrivals. Stochastic Models (1992) 8:665–683Crossref, Google Scholar
• Haji R., Newell G. F. A relation between stationary queue and waiting time distributions. J. Appl. Probab. (1971) 8:617–620Crossref, Google Scholar
• Hunter J. J.Mathematical Techniques of Applied Probability, Vol 2: Discrete Time Models: Techniques and Applications (1983) (Academic Press, New York) Google Scholar
• Keilson J., Servi L. D. The distributional form of Little's law and the Fuhrmann-Cooper decomposition. Oper. Res. Lett. (1990) 9:239–247Crossref, Google Scholar
• Kim N. K., Chae K. C., Lee H. W. A note on the relationships among the queue lengths at various epochs of a queue with BMAP arrivals. Internat. J. Management Sci. (2003) 9:1–12Google Scholar
• Kim N. K., Chang S. H., Chae K. C. On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals. Oper. Res. Lett. (2002) 30:25–32Crossref, Google Scholar
• Lucantoni D. M. New results on the single server queue with a batch Markovian arrival process. Stochastic Models (1991) 7:1–46Crossref, Google Scholar
• Medhi J.Recent Developments in Bulk Queueing Models (1984) (Wiley Eastern Limited, New Delhi, India) Google Scholar
• Neuts M. F.Structured Stochastic Matrices of M/G/1 Type and Their Applications (1989) (Marcel Dekker, New York) Google Scholar
• Powell W. B., Humblet P. The bulk service queue with a general control strategy: Theoretical analysis and a new computational procedure. Oper. Res. (1986) 34:267–275Link, Google Scholar
• Sohraby K., Zhang J. Spectral decomposition approach for transient analysis of multi-server discrete-time queues. Performance Evaluation (1994) 21:131–150Crossref, Google Scholar
• Takagi H.Queueing Analysis, Vol 1: Vacation and Priority Systems, Part 1 (1991) (North-Holland, Amsterdam, The Netherlands) Google Scholar
• Takagi H.Queueing Analysis, Vol 3: Discrete-Time Systems (1993) (North-Holland, Amsterdam, The Netherlands) Google Scholar
• Takine T., Takahashi Y. On the relationship between queue lengths at a random instant and at a departure in the stationary queue with BMAP arrivals. Stochastic Models (1998) 14:601–610Crossref, Google Scholar
• Wolff R. W.Stochastic Modeling and the Theory of Queues (1989) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar