Abstract
Multi-server queue with a finite buffer and Batch Markov Arrival Process (BMAP) is considered. Customers, which do not succeed to enter the system upon arrival (due to unavailability of servers and buffer space), move to orbit to make repeated attempts in exponentially distributed time intervals. Customers in a buffer are impatient. After exponentially distributed amount of time they may leave the system without a service or go to the orbit. Stability condition of the system is derived, steady state distribution is computed, expressions for key performance measures and for waiting time distribution are given. Numerical illustrations are presented.
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References
Artalejo, J.R., Comez-Corral, A.: Retrial queueing systems: a computational approach. Springer, Heidelberg (2008)
Breuer, L., Dudin, A.N., Klimenok, V.I.: A retrial BMAP/PH/N system. Queueing Systems 40, 433–457 (2002)
Breuer, L., Klimenok, V.I., Birukov, A.A., Dudin, A.N., Krieger, U.: Modeling the access to a wireless network at hot spots. European Transactions on Telecommunications 16, 309–316 (2005)
Chakravarthy, S.R.: The batch Markovian arrival process: a review and future work. In: Krishnamoorthy, A., et al. (eds.) Proc. of Advances in Probability Theory and Stochastic Process: Proc., pp. 21–49. Notable Publications, NJ (2001)
Dudin, A.N., Klimenok, V.I.: Queueing System BMAP/G/1 with repeated calls. Mathematical and Computer Modelling 30, 115–128 (1999)
Dudin, A.N., Klimenok, V.I.: A retrial BMAP/SM/1 system with linear repeated requests. Queueing Systems 34, 47–66 (2000)
Falin, G.I., Templeton, J.G.C.: Retrial queues. Chapman and Hall, London (1997)
Gomez-Corral, A.: A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research 141, 163–191 (2006)
Kim, C.S., Mushko, V.V., Dudin, A.N.: Computation of the steady state distribution for multi-server retrial queues with phase type service process. Annals of Operations Research 201, 307–323 (2012)
Klimenok, V.I., Dudin, A.N.: Multi-dimensional asymptotically quasi-toeplitz Markov chains and their application in queueing theory. Queueing Systems 54, 245–259 (2006)
Klimenok, V.I., Orlovsky, D.S., Dudin, A.N.: A BMAP/PH/N system with impatient repeated calls. Asia-Pacific Journal of Operational Research 24, 293–312 (2007)
Klimenok, V.I., Orlovsky, D.S., Kim, C.S.: The BMAP/PH/N/N + R retrial queueing system with different disciplines of retrials. In: Proceedings of 11th International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2004), Magdeburg, Germany, June 13-16, pp. 93–98 (2004)
Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Communications in Statistics-Stochastic Models 7, 1–46 (1991)
Neuts, M.F.: Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York (1989)
Ramaswami, V., Lucantoni, D.: Algorithm for the multi-server queue with phase-type service. Communications in Statistics-Stochastic Models 1, 393–417 (1985)
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Kim, C.S., Klimenok, V., Dudin, A. (2013). Retrial Queueing System with Correlated Input, Finite Buffer, and Impatient Customers. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_19
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DOI: https://doi.org/10.1007/978-3-642-39408-9_19
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