A matrix continued fraction approach to multiserver retrial queues
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We consider basic M/M/c/c (c≥1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c retrial queues with large value of c.
- Aguir, S., Karaesmen, F., Aksin, O. Z., & Chauvet, F. (2004). The impact of retrials on call center performance. OR Spectrum, 26, 353–376. CrossRef
- Alfa, A. S., & Li, W. (2002). PCS networks with correlated arrival process and retrial phenomenon. IEEE Transactions on Wireless Communications, 1, 630–637. CrossRef
- Anisimov, V. V., & Artalejo, J. R. (2002). Approximation of multiserver retrial queues by means of generalized truncated models. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 10, 51–66.
- Artalejo, J. R., & Gomez-Corral, A. (2008). Retrial queueing systems: a computational approach. Berlin/Heidelberg: Springer. CrossRef
- Artalejo, J. R., & Lopez-Herrero, M. J. (2010). Cellular mobile networks with repeated calls operating in random environment. Computers & Operations Research, 37, 1158–1166. CrossRef
- Artalejo, J. R., & Pla, V. (2009). On the impact of customer balking, impatience and retrials in telecommunication systems. Computer and Mathematics with Applications, 57, 217–229. CrossRef
- Artalejo, J. R., & Pozo, M. (2002). Numerical calculation of the stationary distribution of the main multiserver retrial queue. Annals of Operations Research, 116, 41–56. CrossRef
- Baumann, H., & Sandmann, W. (2010). Numerical solution of level dependent quasi-birth-and-death processes. Procedia Computer Science, 1, 1555–1563. CrossRef
- Breuer, L., Dudin, A., & Klimenok, V. (2002). A retrial BMAP/PH/N system. Queueing Systems, 40, 433–457. CrossRef
- Bright, L., & Taylor, P. G. (1995). Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes. Stochastic Models, 11, 497–525. CrossRef
- Cuyt, A., Petersen, V. B., Verdonk, B., Waadeland, H., & Jones, W. B. (2008). Handbook of continued fractions for special functions. Berlin: Springer Science+Business Media B.V.
- Choi, B. D., Chang, Y., & Kim, B. (1999). MAP1, MAP2/M/c retrial queue with guard channels and its application to cellular networks. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 7, 231–248.
- Domenech-Benlloch, M. J., Gimenez-Guzman, J. M., Pla, V., Martinez-Bauset, J., & Casares-Giner, V. (2008). Generalized truncated methods for an efficient solution of retrial systems. Mathematical Problems in Engineering, doi:10.1155/2008/183089.
- Falin, G. I., & Templeton, J. G. C. (1997). Retrial queues. London: Chapman & Hall.
- Fair, W. (1971). Noncommutative continued fractions. SIAM Journal of Mathematical Analysis, 2, 226–232. CrossRef
- Fair, W. (1972). A convergence theorem for noncommunitative continued fractions. Journal of Approximation Theory, 5, 74–76. CrossRef
- Gomez-Corral, A. (2006). A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research, 141, 163–191. CrossRef
- Hanschke, T. (1987). Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. Journal of Applied Probability, 24, 486–494. CrossRef
- Hanschke, T. (1999). A matrix continued fraction algorithm for the multiserver repeated order queue. Mathematical and Computer Modelling, 30, 159–170. CrossRef
- Klimenok, V., & Dudin, A. (2006). Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory. Queueing Systems, 54, 245–259. CrossRef
- Koole, G., & Mandelbaum, A. (2002). Queueing models of call centers: an introduction. Annals of Operations Research, 113, 41–59. CrossRef
- Gans, N., Koole, G., & Mandelbaum, A. (2003). Telephone call centers: tutorial, review, and research prospects. Manufacturing & Service Operations Management, 5, 79–141. CrossRef
- Liu, B., & Zhao, Y. Q. (2010). Analyzing retrial queues by censoring. Queueing Systems, 64, 203–225. CrossRef
- Marsan, M. A., de Carolis, G., Leonardi, E., Lo Cigno, R., & Meo, M. (2001). Efficient estimation of call blocking probabilities in cellular mobile telephony networks with customer retrials. IEEE Journal on Selected Areas in Communications, 19, 332–346. CrossRef
- Neuts, M. F., & Rao, B. M. (1990). Numerical investigation of a multiserver retrial model. Queueing Systems, 7, 169–190. CrossRef
- Peng, S. T., & Hessel, A. (1975). Convergence of noncommutative continued fraction. SIAM Journal of Mathematical Analysis, 6, 724–727. CrossRef
- Phung-Duc, T., Masuyama, H., Kasahara, S., & Takahashi, Y. (2009a). Performance analysis of optical burst switched networks with limited-range wavelength conversion, retransmission and burst segmentation. Journal of the Operations Research Society of Japan, 52, 58–74.
- Phung-Duc, T., Masuyama, H., Kasahara, S., & Takahashi, Y. (2009b). M/M/3/3 and M/M/4/4 retrial queues. Journal of Industrial and Management Optimization, 5, 431–451. CrossRef
- Phung-Duc, T., Masuyama, H., Kasahara, S., & Takahashi, Y. (2010a). State-dependent M/M/c/c+r retrial queues with Bernoulli abandonment. Journal of Industrial and Management Optimization, 6, 517–540. CrossRef
- Phung-Duc, T., Masuyama, H., Kasahara, S., & Takahashi, Y. (2010b). A simple algorithm for the rate matrices of level-dependent QBD processes. In Proceedings of the 5th International Conference on Queueing Theory and Network Applications, pp. 46–52.
- Tran-Gia, P., & Mandjes, M. (1997). Modeling of customer retrial phenomenon in cellular mobile networks. IEEE Journal on Selected Areas in Communications, 15, 1406–1414. CrossRef
- Stepanov, S. N. (1999). Markov models with retrials: the calculation of stationary performance measures based on concept of truncation. Mathematical and Computer Modelling, 30, 207–228. CrossRef
- A matrix continued fraction approach to multiserver retrial queues
Annals of Operations Research
Volume 202, Issue 1 , pp 161-183
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Multiserver retrial queue
- Level-dependent QBD
- Matrix continued fraction
- Call center
- Resource dimensioning
- System planning
- Industry Sectors