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2014 | 24 | 3 | 485-501
Tytuł artykułu

Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented.
Rocznik
Tom
24
Numer
3
Strony
485-501
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-08-19
poprawiono
2014-02-24
Twórcy
autor
  • Department of Business Administration, Sangji University, Wonju, Kangwon, 220-702, Korea
  • Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus
autor
  • Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus
autor
  • Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus
Bibliografia
  • Aksin, O., Armony, M. and Mehrotra, V. (2007). The modern call centers: A multi-disciplinary perspective on operations management research, Production and Operation Management 16(6): 655-688.
  • Al-Begain, K., Dudin, A., Kazimirsky, A. and Yerima, S. (2009). Investigation of the M₂/G₂/1/∞, N queue with restricted admission of priority customers and its application to HSDPA mobile systems, Computer Networks 53(6): 1186-1201.
  • Al-Begain, K., Dudin, A. and Mushko, V. (2006). Novel queueing model for multimedia over downlink in 3.5g wireless network, Journal of Communication Software and Systems 2(2): 68-80.
  • Chakravarthy, S. (2001). The batch Markovian arrival process: A review and future work, in A. Krishnamoorthy, N. Raju and V. Ramaswami (Eds.), Advances in Probability Theory and Stochastic Processes, Notable Publications, Neshanic Station, NJ, pp. 21-49.
  • Chydziński, A. and Chróst, Ł. (2011). Analysis of AQM queues with queue size based packet dropping, International Journal of Applied Mathematics and Computer Science 21(3): 567-577, DOI: 10.2478/v10006-011-0045-7.
  • Dudin, A., Osipov, E., Dudin, S. and Schelen, O. (2013a). Socio-behavioral scheduling of time-frequency resources for modern mobile operators, Communications in Computer and Information Science 356: 69-82.
  • Dudin, S., Kim, C. and Dudina, O. (2013b). M MAP/M/N queueing system with impatient heterogeneous customers as a model of a contact center, Computers and Operations Research 40(7): 1790-1803.
  • Graham, A. (1981). Kronecker Products and Matrix Calculus with Applications, Ellis Horwood, Chichester.
  • Jouini, O., Aksin, Z. and Dallery, Y. (2011). Call centers with delay information: Models and insights, Manufacturing & Service Operations Management 13(4): 534-548.
  • Jouini, O., Dallery, Y. and Aksin, Z. (2009). Queuing models for flexible multi-class call centers with real-time anticipated delays, International Journal of Production Economics 120(2): 389-399.
  • Kesten, H. and Runnenburg, J. (1956). Priority in Waiting Line Problems, Mathematisch Centrum, Amsterdam.
  • Kim, C., Dudin, A., Klimenok, V. and Khramova, V. (2010a). Erlang loss queueing system with batch arrivals operating in a random environment, Computers and Operations Research 36(3): 674-697.
  • Kim, C., Klimenok, V., Mushko, V. and Dudin, A. (2010b). The BM AP/PH/N retrial queueing system operating in Markovian random environment, Computers and Operations Research 37(7): 1228-1237.
  • Kim, C., Dudin, S., Dudin, A. and Dudina, O. (2013a). Queueing system M AP/PH/N/R with session arrivals operating in random environment, Communications in Computer and Information Science 370: 406-415.
  • Kim, C., Dudin, S., Taramin, O. and Baek, J. (2013b). Queueing system M MAP/PH/N/N+R with impatient heterogeneous customers as a model of call center, Applied Mathematical Modelling 37(3): 958-976.
  • Kim, C., Klimenok, V., Lee, S. and Dudin, A. (2007). The BM AP/PH/1 retrial queueing system operating in random environment, Journal of Statistical Planning and Inference 137(12): 3904-3916.
  • Kim, J. and Park, S. (2010). Outsourcing strategy in two-stage call centers, Computers and Operations Research 37(4): 790-805.
  • Klimenok, V. and Dudin, A. (2006). Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory, Queueing Systems 54(4): 245-259.
  • Krieger, U., Klimenok, V., Kazimirsky, A., Breuer, L. and Dudin, A. (2005). A BM AP/PH/1 queue with feedback operating in a random environment, Mathematical and Computer Modelling 41(8-9): 867-882.
  • Lucantoni, D. (1991). New results on the single server queue with a batch Markovian arrival process, Communication in Statistics-Stochastic Models 7(1): 1-46.
  • Neuts, M. (1981). Matrix-geometric Solutions in Stochastic Models-An Algorithmic Approach, Johns Hopkins University Press, Baltimore, MD.
  • Olwal, T., Djouani, K., Kogeda, O. and van Wyk, B. (2012). Joint queue-perturbed and weakly coupled power control for wireless backbone networks, International Journal of Applied Mathematics and Computer Science 22(3): 749-764, DOI: 10.2478/v10006-012-0056-z.
  • van Danzig, D. (1955). Chaines de markof dans les ensembles abstraits et applications aux processus avec regions absorbantes et au probleme des boucles, Annals de l'Institute H. Pioncare 14(3): 145-199.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv24i3p485bwm
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