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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

  • Aissani, A. and Artalejo, J. (1998). On the single server retrial queue subject to breakdowns, Queueing Systems 30(3-4): 309-321.
  • Alfa, A. (2010). Queueing Theory for Telecommunications, 1: Discrete Time Modelling of a Single Node System, Springer, New York, NY.
  • Artalejo, J. (1994). New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandica 48(1): 23-36.
  • Artalejo, J. (2000). G-networks: A versatile approach for work removal in queueing networks, European Journal of Operational Research 126(2): 233-249.
  • Atencia, I., Fortes, I., Pechinkin, A. and Sánchez, S. (2013a). A discrete-time queueing system with different types of displacement, 27th European Conference on Modelling and Simulation, Alesund, Norway, pp. 558-564.
  • 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.
  • Bruneel, H. and Kim, B. (1993). Discrete-time Models for Communication Systems Including ATM, Kluwer Academic Publishers, Boston, MA.
  • Cascone, A., Manzo, P., Pechinkin, A. and Shorgin, S. (2011). A Geoₘ/G/1/n system with a LIFO discipline without interruptions in the service and with a limitation for the total capacity for the customers, Avtomatika i Telemejanika 1(1): 107-120, (in Russian).
  • Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks: Customers, Signals and Product form Solutions, John Wiley and Sons, Chichester.
  • Fiems, D., Steyaert, B. and Bruneel, H. (2002). Randomly interrupted GI/G/1 queues: Service strategies and stability issues, Annals of Operations Research 112(1-4): 171-183.
  • 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.
  • Gelenbe, E. and Label, A. (1998). G-networks with multiple classes of signals and positive customers, European Journal of Operational Research 108(2): 293-305.
  • Gravey, A. and Hébuterne, G. (1992). Simultaneity in discrete-time single server queues with Bernoulli inputs, Performance Evaluation 14(2): 123-131.
  • Harrison, P.G., Patel, N.M. and Pitel, E. (2000). Reliability modelling using g-queues, European Journal of Operational Research 126(2): 273-287.
  • Hunter, J. (1983). Mathematical Techniques of Applied Probability, Academic Press, New York, NY.
  • Kendall, D. (1951a). Some problems in the theory of queues, Royal Statistical Society Series 13(2): 151-185.
  • Kendall, D. (1951b). Stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chains, Annals of Mathematical Statistics 24(3): 338-354.
  • 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.
  • Kulkarni, V. and Choi, B. (1990). Retrial queues with server subject to breakdowns and repairs, Queueing Systems 7(2): 191-208.
  • Meisling, T. (1958). Discrete time queueing theory, Operations Research 6(1): 96-105.
  • Morozov, E., Fiems, D. and Bruneel, H. (2011). Stability analysis of multiserver discrete-time queueing systems with renewal-type server interruptions, Performance Evaluation 68(12): 1261-1275.
  • Oniszczuk, W. (2009). Semi-Markov-based approach for the analysis of open tandem networks with blocking and truncation, International Journal of Applied Mathematics and Computer Science 19(1): 151-163, DOI: 10.2478/v10006-009-0014-6.
  • 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.
  • Piórkowski, A. and Werewka, J. (2010). Minimization of the total completion time for asynchronous transmission in a packet data-transmission system, International Journal of Applied Mathematics and Computer Science 20(2): 391-400, DOI: 10.2478/v10006-010-0029-z.
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  • Vinck, B. and Bruneel, H. (2006). System delay versus system content for discrete-time queueing systems subject to server interruptions, European Journal of Operational Research 175(1): 362-375.
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  • Yang, T. and Li, H. (1994). The M/G/1 retrial queue with the server subject to starting failures, Queueing Systems 16(1-2): 83-96.
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Typ dokumentu

Bibliografia

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