Tuan Phung-Duc
ABSTRACT
This paper considers a state-dependent M/M/c/c + r retrial queue with Bernoulli abandonment, where the number of servers is equal to c, the capacity of the buffer is equal to r and that of the virtual waiting room for retrial customers is infinite. We call the virtual waiting room by orbit hereafter. We assume that the arrival and service rates depend on the number of customers in the system (the servers and buffer). Such retrial queues cover conventional M/M/c/c retrial queues without abandonment, as special cases. By a continued fraction approach, we derive analytical solutions for the stationary joint distribution of the queue length in the system and that in the orbit, assuming that the capacity of the system is less than or equal to 4. We also show that our analytical solutions can be numerically computed with any accuracy.
- S. Aguir, F. Karaesmen, O. Z. Aksin, and F. Chauvet. The impact of retrials on call center performance. OR Spectrum, 26:353--376, 2004.Google Scholar
Cross Ref
- B. D. Choi and Y. C. Kim. The M/M/c retrial queue with geometric loss and feedback. Computers&Mathematics with Applications, 36:41--52, 1998.Google ScholarCross Ref
- A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland, and W. B. Jones. Handbook of Continued Fractions for Special Functions. Springer, 2008. Google ScholarDigital Library
- G. I. Falin. A survey of retrial queues. Queueing Systems, 7:127--168, 1990. Google ScholarDigital Library
- G. I. Falin and J. G. C. Templeton. Retrial Queues. Chapman&Hall, London, 1997.Google Scholar
- A. Gomez-Corral. A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research, 141:163--191, 2006.Google ScholarCross Ref
- A. Gomez-Corral and M. F. Ramalhoto. The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems. Mathematical and Computer Modelling, 30:141--158, 1999. Google ScholarDigital Library
- T. Hanschke. Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. Journal of Applied Probability, 24:486--494, 1987.Google ScholarCross Ref
- W. B. Jones and W. J. Thron. Continued Fractions: Analytic Theory and Applications. Addison-Wesley, Massachusetts, 1980.Google Scholar
- Y. C. Kim. On M/M/3/3 retrial queueing system. Honam Mathematical Journal, 17:141--147, 1995.Google Scholar
- C. E. M. Pearce. Extended continued fractions, recurrence relations and two-dimensional Markov processes. Advances in Applied Probability, 21:357--375, 1989.Google ScholarCross Ref
- T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. M/M/3/3 and M/M/4/4 retrial queues. Journal of Industrial and Management Optimization, 5:431--451, 2009.Google ScholarCross Ref
- T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. 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, 2009.Google ScholarCross Ref
- P. Tran-Gia and M. Mandjes. Modeling of customer retrial phenomenon in cellular mobile networks. IEEE Journal on Selected Areas in Communications, 15:1406--1414, 1997. Google ScholarDigital Library
- H. S. Wall. Analytic Theory of Continued Fractions. AMS Chelsea Publishing, Providence, Rhode Island, 2000.Google Scholar
- T. Yang and J. G. C. Templeton. A survey on retrial queues. Queueing Systems, 2:201--233, 1987. Google ScholarDigital Library
Index Terms
- Analytical solutions for state-dependent M/M/c/c+r retrial queues with Bernoulli abandonment
Recommendations
Performance analysis of call centers with abandonment, retrial and after-call work
This paper considers a multiserver queueing model with abandonment, retrial and after-call work for call centers. Upon a phone call, customers that find a free call line occupy the line immediately while those who see all the call lines busy are blocked ...
A multiserver retrial queue: regenerative stability analysis
We consider a multiserver retrial GI / G / m queue with renewal input of primary customers, interarrival time with rate $\lambda=1/\mathsf{E}\tau$ , service time S , and exponential retrial times of customers blocked in the orbit. In the model, an arriving primary ...
Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers
We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the system (servers ...
Comments