ANALYSIS OF DISCRETE-TIME QUEUE WITH TWO HETEROGENEOUS SERVERS SUBJECT TO CATASTROPHES

This paper studies a discrete-time queueing system with two heterogeneous servers subject to catastrophes. We obtain explicit expressions for the steady-state probabilities at arbitrary epoch using displacement operator method. The waiting time distribution and outside observer’s observation epoch probabilities are deduced. Various performance measures and numerical results have been investigated

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  • Chao, X., (1995), A queueing network model with catastrophes and product form solution, Oper. Res. Lett., 18 (2), 75–79.
  • Chen, A. and Renshaw, E., (1997), The M/M/1 queue with mass exodus and mass arrivals when empty, J. Appl. Probab., 34 (1), 192–207.
  • Di Crescenzo, A. Giorno, V. Nobile A. G. and Ricciardi, L. M., (2003), On the M/M/1 queue with catastrophes and its continuous approximation, Queueing Syst., 43 (4), 329–347.
  • Boudali, O. and Economou, A., (2012), Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes, Eur. J. Oper. Res., 218 (3), 708–715.
  • Krishna Kumar, B. and Arivudainambi, D., (2000), Transient solution of an M/M/1 queue with catastrophes, Comput. Math. Appl., 40(10-11), pp.1233–1240.
  • Krishna Kumar, B. and Pavai Madheswari, S., (2002), Transient behaviour of the M/M/2 queue with catastrophes, STATISTICA, 62 (1), 129–136.
  • Krishna Kumar, B., Krishnamoorthy, A., Pavai Madheswari, S. and Sadiq Basha S., (2007a)
  • Transient analysis of a single server queue with catastrophes, failures and repairs, Queueing Syst., (3-4), 133–141. Guo, P. and Hassin, R., (2012), Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers, Eur. J. Oper. Res., 222 (2), 278–286.
  • Larsen, R. L. and Agrawala, A. K., (1983), Control of a heterogeneous two-server exponential queueing system, IEEE Trans. Software Eng., 9(4), 522–526.
  • Lin, W. and Kumar, P. R., (1984), Optimal control of a queueing system with two heterogeneous servers, IEEE Trans. Autom. Control., 29(8), 696–703.
  • Krishna Kumar, B., Madheswari, S. P. and Venkatakrishnan, K. S., (2007b), Transient Solution of an M/M/2 Queue with Heterogeneous Servers Subject to Catastrophes, Int. J. Infor. Manage. Sci., 18 (1), 63–80.
  • Hunter, J. J., (1983), Mathematical Techniques of Applied Probability, Vol. II, Discrete-Time
  • Models: Techniques and Applications, Academic Press, New York. Gravey, A. and H´ebuterne, G., (1992), Simultaneity in discrete time single server queues with
  • Bernoulli inputs, Perf. Eval., 14(2), 123–131. Bruneel, H. and Kim, B. G., (1993), Discrete-Time Models for Communication Systems Including
  • ATM, Kluwer Academic Publishers, Boston. Takagi, H., (1993), Queueing Analysis – A Foundation of Performance Evaluation : Volume 3
  • Discrete-Time Systems, North Holland, Amsterdam. Woodward, M. E., (1994), Communication and Computer Networks: Modelling with Discrete
  • Time Queues, Los Alamitos, CA: IEEE Computer Society Press. Atencia, I. and Moreno, P. A., (2004), The discrete-time Geo/Geo/1 queue with negative customers and disasters, Comput. Oper. Res., 31(9), 1537–1548.
  • Goswami, V. and Gupta, U. C., (1998), Analyzing the Discrete-time Multiserver Queue
  • Geom/Geom/m Queue with Late and Early Arrivals, Int. J. Infor. Manage. Sci., 9 (2), 55–66. Artalejo, J. R. and Hern´andez-Lerma, O., (2003), Performance analysis and optimal control of the Geo/Geo/c queue, Perf. Eval., 52(1), 15–39.
  • Goswami, V. and Samanta, S. K., (2009), Discrete-time bulk-service queue with two heterogeneous servers, Comp. Indus. Engg., 56 (4), 1348-1356.