Abstract
The research of wide class of retrial queuing systems faces the problem of calculating characteristics of the system in stationary regime. Markov chain that describes service process in such system is multidimensional and its transaction matrix usually does not have special properties that would streamline the explicit solution of Kolmogorov set of equations. In addition, the probabilities of transition between states of the controlled system depend on its current state that complicates their obtaining even more. Therefore, only the simplest models are explicitly researched on this moment.
In this paper we consider a finitesource retrial queue with c servers and controlled parameters. The primary calls arrive from n customers. Each customer after some random period of time which is exponential distributed random variable tries to get service and is served immediately if there is any free server. Service times are also exponentially distributed. The customer who finds all servers busy leaves the system and returns after an exponential time. Two- and three-dimensional Markov models that describe threshold and hysteresis control policies are taken into account. Explicit vector-matrix representations of stationary distributions are main results in both cases. Also we state and give an algorithm for solving a multi-criteria problem of maximization of total income from the system.
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References
Das, I., Lobiyal, D.K., Katti, C.P.: Queuing effect on multipath routing in mobile ad hoc networks. Int. J. Inf. Eng. Electron. Bus. (IJIEEB) 8(1), 62–68 (2016). https://doi.org/10.5815/ijieeb.2016.01.07
Tran-Gia, P., Mandjes, M.: Modeling of customer retrial phenomenon in cellular mobile networks. University of Wurzburg, Institute of Computer Science Report 142 (1996)
Saxena, D., Chauhan, R.K., Kait, R.: Dynamic fair priority optimization task scheduling algorithm in cloud computing: concepts and implementations. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 8(2), 41–48 (2016). https://doi.org/10.5815/ijcnis.2016.02.05
Rao, A.S.: Improving the serviceability of a prepaid autorickshaw counter using queuing model: an optimization approach. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 9(12), 19–27 (2017). https://doi.org/10.5815/ijitcs.2017.12.03
Adebiyi, R.F.O., Abubilal, K.A., Tekanyi, A.M.S., Adebiyi, B.H.: Management of vehicular traffic system using artificial bee colony algorithm. Int. J. Image Graph. Sig. Process. (IJIGSP) 9(11), 18–28 (2017). https://doi.org/10.5815/ijigsp.2017.11.03
Artalejo, J.R., Gómez-Corral, A.: Retrial Queuing Systems: A Computational Approach. Springer, Heidelberg (2008)
Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman and Hall, London (1997)
Gomez Corral, A.: Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority. Comput. Math. Appl. 43, 767–782 (2002)
Falin, G.I., Gomez Corral, A.: On a bivariate Markov process arising in the theory of single-server retrial queues. Stat. Neerl. 54, 67–78 (2000)
Bolch, G., Roszik, J., Sztrik, J., Wuechner, P.: Modeling finite-source retrial queueing systems with unreliable heterogeneous servers and different service policies using MOSEL. HAS-DFG (2005)
Roszik, J., Sztrik, J.: Performance analysis of finite-source retrial queueing systems with heterogeneous non-reliable servers and different service policies. Technical report 6 (2004)
Walrand, J.: An Introduction to Queueing Networks. Prentice Hall, Englewood Cliffs (1988)
Dudin, A., Klimenok, V.: Optimization of dynamic control of input load in node of informational computing network. Autom. Technol. 3, 25–31 (1991)
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Ponomarov, V., Lebedev, E. (2019). Optimal Control of Retrial Queues with Finite Population and State-Dependent Service Rate. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education. ICCSEEA 2018. Advances in Intelligent Systems and Computing, vol 754. Springer, Cham. https://doi.org/10.1007/978-3-319-91008-6_36
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DOI: https://doi.org/10.1007/978-3-319-91008-6_36
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