Abstract
The research of the queueing system with incoming MAP, n types of customers, infinite number of servers and exponential service time is proposed. Investigation of n-dimensional stochastic process that characterizes the number of busy servers for different types of customers is held by the method of initial moments. There are expressions for the characteristic function of the number of busy servers for different types of customers in the system MAP/M/ ∞ under the asymptotic condition that service time infinitely grows equivalently to each type of customers.
This work is performed under the state order No. 1.511.2014/K of the Ministry of Education and Science of the Russian Federation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Pechinkin, A.V.: Boundary of change of stationary queue in queuing systems with various service disciplines. In: Proc. of the Seminar “Problems of Stability of Stochastic Models”, vol. 109, pp. 118–121. All-Union Scientific Research Institute for System Studies, Moscow (1985) (in Russian)
Pechinkin, A.V.: The inversion procedure with probabilistic priority in queuing system with extraordinary incoming flow. Stochastic processes and their applications. Mathematical research. Shtiintsa, Kishinev (1989) (in Russian)
Pechinkin, A.V., Sokolov, I.A., Chaplygin, V.V.: Stationary characteristics of multi-line queuing system with simultaneous failures of devices. Computer Science and Applications 1(2), 28–38 (2007) (in Russian)
Abaev, P., Pechinkin, A., Razumchik, R.: On Mean Return Time in Queueing System with Constant Service Time and Bi-level Hysteric Policy. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 11–19. Springer, Heidelberg (2013)
Auria, B.D.: M|M| ∞ queues in semi-Markovian random environment. Queueing Systems 58(3), 221–237 (2008)
Baum, D.: The infinite server queue with Markov additive arrivals in space. In: Proc. of the International Conference on Probabilistic Analysis of Rare Events, Riga, pp. 136–142 (1999)
Baum, D., Breuer, L.: The Inhomogeneous BMAP|G| ∞ queue. In: Proc. of the 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems (MMB 2001), Aachen, pp. 209–223 (2001)
Bojarovich, J., Marchenko, L.: An open queueing network with temporarily non-active customers and rounds. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 33–36. Springer, Heidelberg (2013)
Doorn, E.A., Jagers, A.A.: Note on the GI|GI| ∞ system with identical service and interarrival-time distributions. Journal of Queueing Systems 47, 45–52 (2004)
Duffield, N.G.: Queueing at large resources driven by long-tailed M|G| ∞-modulated processes. Queueing Systems 28(1-3), 245–266 (1998)
Fricker, C., Jaïbi, M.R.: On the fluid limit of the M|G| ∞ queue. Queueing Systems 56(3-4), 255–265 (2007)
Girlich, E., Kovalev, M.M., Listopad, N.I.: Optimal choice of the capacities of telecommunication networks to provide qoS-routing. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 93–104. Springer, Heidelberg (2013)
Jayawardene, A.K., Kella, O.: M|G| ∞ with alternating renewal breakdowns. Queueing Systems 22(1-2), 79–95 (1996)
Parulekar, M., Makowski, A.M.: Tail probabilities for M|G| ∞ input processes: I. Preliminary asymptotics. Queueing Systems 27(3-4), 271–296 (1997)
Basharin, G.P., Samouylov, K.E., Yarkina, N.V., Gudkova, I.A.: A new stage in mathematical teletraffic theory. Automation and Remote Control 70(12), 1954–1964 (2009)
Movaghar, A.: Analysis of a Dynamic Assignment of Impatient Customers to Parallel Queues. Queueing Systems 67(3), 251–273 (2011)
Kargahi, M., Movaghar, A.: Utility Accrual Dynamic Routing in Real-Time Parallel Systems. Transactions on Parallel and Distributed Systems (TDPS) 21(12), 1822–1835 (2010)
Knessl, C.A., Morrison, J.: Heavy Traffic Analysis of Two Coupled Processors. Queueing Systems 43(3), 173–220 (2003)
Down, D.G., Wu, R.: Multi-layered round robin routing for parallel servers. Queueing Systems 53(4), 177–188 (2006)
Bambos, N., Michailidis, G.: Queueing Networks of Random Link Topology: Stationary Dynamics of Maximal Throughput Schedules. Queueing Systems 50(1), 5–52 (2005)
Ivanovskaya (Sinyakova), I., Moiseeva, S.: Investigation of the queuing system MMP (2)|M 2| ∞ by method of the moments. In: Proc. of The Third International Conference, Problems of Cybernetics and Informatics, Baku, vol. 2, pp. 196–199 (2010)
Sinyakova, I., Moiseeva, S.: Investigation of queuing system GI (2)|M 2| ∞. In: Proc. of the International Conference, Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks, Minsk, pp. 219–225 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Pankratova, E., Moiseeva, S. (2014). Queueing System MAP/M/ ∞ with n Types of Customers. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds) Information Technologies and Mathematical Modelling. ITMM 2014. Communications in Computer and Information Science, vol 487. Springer, Cham. https://doi.org/10.1007/978-3-319-13671-4_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-13671-4_41
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13670-7
Online ISBN: 978-3-319-13671-4
eBook Packages: Computer ScienceComputer Science (R0)