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2014 | 24 | 3 | 471-484
Tytuł artykułu

A discrete-time system with service control and repairs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper discusses a discrete-time queueing system with starting failures in which an arriving customer follows three different strategies. Two of them correspond to the LCFS (Last Come First Served) discipline, in which displacements or expulsions of customers occur. The third strategy acts as a signal, that is, it becomes a negative customer. Also examined is the possibility of failures at each service commencement epoch. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. We obtain the generating functions of the number of customers in the queue and in the system. The generating functions of the busy period as well as the sojourn times of a customer at the server, in the queue and in the system, are also provided. We present the main performance measures of the model. The versatility of this model allows us to mention several special cases of interest. Finally, we prove the convergence to the continuous-time counterpart and give some numerical results that show the behavior of some performance measures with respect to the most significant parameters of the system.
Rocznik
Tom
24
Numer
3
Strony
471-484
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-08-19
poprawiono
2014-01-30
poprawiono
2014-03-26
Twórcy
autor
  • Department of Applied Mathematics, University of Malaga, Campus de Teatinos, 29071 Malaga, Spain
Bibliografia
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  • Atencia, I., Fortes, I. and Sánchez, S. (2013b). Discrete-time queueing system with expulsions, Communications in Computer and Information Science 356(1): 20-25.
  • Atencia, I. and Moreno, P. (2004). The discrete-time Geo/Geo/1 queue with negative customers and disasters, Computers and Operations Research 31(9): 1537-1548.
  • Atencia, I. and Moreno, P. (2005). A single-server G-queue in discrete-time with geometrical arrival and service process, Performance Evaluation 59(1): 85-97.
  • Atencia, I. and Pechinkin, A. (2012). A discrete-time queueing system with optional LCFS discipline, Annals Operation Research 202(1): 3-17.
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  • Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks: Customers, Signals and Product form Solutions, John Wiley and Sons, Chichester.
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  • Fiems, D., Steyaert, B. and Bruneel, H. (2004). Discrete-time queues with generally distributed service times and renewal-type server interruptions, Performance Evaluation 55(3-4): 277-298.
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  • Kleinrock, L. (1976). Queueing Systems, Vol. 2, John Wiley and Sons, New York, NY.
  • Krishna Kumar, B., Pavai Madheswari, S. and Vijayakumar, A. (2002). The M/G/1 retrial queue with feedback and starting failures, Applied Mathematical Modelling 26(11): 1057-1075.
  • Krishnamoorthy, A., Pramod, P. and Deepak, T. (2009). On a queue with interruptions and repeat or resumption of service, Nonlinear Analysis: Theory, Methods & Applications 71(12): 1673-1683.
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  • Park, H.M., Yang, W.S. and Chae, K.C. (2009). The Geo/G/1 queue with negative customers and disasters, Stochastic Models 25(4): 673-688.
  • Pechinkin, A. and Shorgin, S. (2008). A Geo/G/1/∞ system with a non-standard discipline for the service, Informatics and Its Applications 2(1): 55-62, (in Russian).
  • Pechinkin, A. and Svischeva, T. (2004). The stationary state probability in the BM AP/G/1/r queueing system with inverse discipline and probabilistic priority, Transactions of the XXIV International Seminar on Stability Problems for Stochastic Models, Jurmala, Latvia, pp. 141-174.
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Typ dokumentu
Bibliografia
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