Abstract
This paper discusses multiserver feedback retrial queues with balking and control retrial rate. This system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition for stability of the system is discussed. Some interesting system performance measures are obtained using matrix geometric method. The effects of various parameters on the system performance measures are illustrated numerically. Finally, the optimization of the retrial rate and specific probabilistic descriptors of the system are investigated.
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References
Artalejo, J.R. (1999). “Accessible Bibliography on Retrial Queues.” Mathematical and Computer Modeling 30, 1–6.
Artalejo, J.R., A. Gomez-Corral, and M.F. Neuts. (2000). “Numerical Analysis of Multiserver Retrial Queues Operating Under Full Access Policy.” In G. Latouche and Peter Taylor (eds.), Advances in Algorithmic Methods for Stochastic Models. Notable Publications Inc., New Jersey, USA, pp. 1–19.
Artalejo, J.R., A. Gomez-Corral, and M.F. Neuts. (2001). “Analysis of Multiserver Queues with Constant Retrial Rate.” Euporean Journal of Operations Research 135, 569–581.
Artalejo, J.R. and M.J. Lopez-Herrero. (2000).“On the Single Server Retrial Queue with Balking.” INFOR 38, 35–50.
Artalejo, J.R. and M. Pozo. (2002). “Numberical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue.” Annals of Operations Research 116, 41–56.
Bright, L. and P.G. Taylor. (1995). “Calculating the Equilibrium Distribution in Level Dependent Quasi-birth-and-death Processes.” Stochastic Models 11, 495–525.
Choi, B.D. and V.G. Kulkarni. (1992). “Feedback Retrial Queueing Systems.” In U.N. Bhat and I.V. Basawa (eds.), Queueing and Related Models. Oxford University Press, New York, pp. 93–105.
Choi, B.D., Y.W. Shin and W.C. Ahn. (1992). “Retrial Queues with Collision Arising from Unslotted CSMA/CD Protocol.” Queueing Systems 11, 335–356.
Choi, B.D. and Y. Chang, (1999). “Single Server Retrial Queues with Priority Calls.” Mathematical and Computer Modeling 30, 7–32.
Choi, B.D., K.H. Rhee, and K.K. Park. (1993). “The M/G/1 Retrial Queue with Retrial Rate Control Policy.” Probability in the Engineering and Information Sciences 7, 29–46.
Choi, B.D., Y.G. Kim, and Y.W. Lee. (1998). “The M/M/c Retrial Queue with Geometric Loss and Feedback.” Computer Mathematics and Applications 36, 41–52.
Cohen, J.W. (1957). “Basic Problems of Telephone Traffic Theory and the Influence of Repeated Calls.” Phillips Telecommunictaion Review 18, 49–100.
Falin, G.I. and Templeton, J.G.C. (1997). Retrial Queues. Chapman and Hall, London.
Falin, G.I. (1983). “Calculation of Probability Characteristic of a Multiline System with Repeat Calls.” Mascow University Computational Mathematics and Cybernetics 1, 43–49.
Falin, G.I. (1990). “A Survey of Retrial Queues.” Queueing Systems 7, 127–168.
Falin, G.I. and J.R. Artalejo. (1995). “Approximations for Multiserver Queues with Balking/Retrial Discipline.” OR Spektrum 17, 239–244.
Farahmand, K. (1990). “Single Server Line Queue with Repeated Demands.” Queueing Systems 6, 223–228.
Fayolle, G. (1986). “A Simple Telephone Exchange with Delayed Feedbacks.” In O.J. Boxma, J.W. Cohen, and H.C. Tijms (eds.), Teletraffic analysis and computer performance evaluation. vol.7, Elsevier, Amsterdam, pp. 245–253.
Gomez-Corral, A. and M.F. Ramalhoto. (1999). “On the Stationary Distribution of a Markovian Process Arising in the Theory of Multiserver Retrial Queueing Systems.” Mathematical and Computer Modeling 30, 141–158.
Gomez-Corral, A. and M.F. Ramalhoto. (2000). “On the Waiting Time Distribution and the Busy Period of a Retrial Queue with Constant Retrial Rate.” Stochastic Modelling and Applications 3(2), 37–47.
Khalil, Z., G. Falin and T. Yang. (1992). “Some Analytical Results for Congestion in Subscriber Line Modules.” Queueing Systems 10, 381–402.
Krishna Kumar, B., S. Pavai Madheswari, and A. Vijayakumar. (2002). “The M/G/1 retrial queue with feedback and starting failures.” Applied Mathematical Modelling 26, 1057–1075.
Kulkarni, V.G. and H.M. Liang. (1997). “Retrial Queues Revisited.” In J.H. Dshalalow (ed.), Frontiers in Queueing. CRC Press, New York, pp. 19–34.
Latouche, G. and V. Ramaswami. (1999). Introduction to Matrix Analytic Methods in Stochastic Modelling. ASA-SIAM, Philadelphia.
Neuts, M.F. (1981). Matrix-Geometric Solutions in Stochastic Models -An Algorithmic Approach. John Hopkins University Press, Baltimore, MD.
Neuts, M.F. and Rao, B.M. (1990). “Numerical Investigation of a Multiserver Retrial Model.” Queueing Systems 7, 169–190.
Pearce, C.E.M. (1989). “Extended Continued Fractions, Recurrence Relations and two Diamensional Markov Processes.” Advances in Applied Probability 21, 357–375.
Ramalhoto, M.F. and A. Gomez-Corral. (1998). “Some Decomposition Formulae for M/M/r/r+d Queues and Without Retrials.” Communications in Statistics — Stochastic Models 14(1&2), 123–145.
Stepanov, S.N. (1999). “Markov Models with Retrials: The Calculation of Stationary Performance Measures Based on the Concept of Truncation.” Mathematical and Computer Modeling 30, 207–228.
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Kumar, B.K., Raja, J. On multiserver feedback retrial queues with balking and control retrial rate. Ann Oper Res 141, 211–232 (2006). https://doi.org/10.1007/s10479-006-5300-1
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DOI: https://doi.org/10.1007/s10479-006-5300-1