Publication: On the single server retrial queue with balking
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2000-02
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Abstract
We are concerned with the M/G/1 retrial queue with balking. The ergodicity condition is first investigated making use Of classical mean drift criteria. The limiting distribution of the number of customers in the system is determined with the help of a recursive approach based on the theory of regenerative processes. Many closed form expressions are obtained when we reduce to the M/M/1 queue for some representative balking policies.
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The authors thank the referees for their suggestions that greatly improved the readability of this paper. This research was supported by DGICYT through operating grant PB98-0837, the Complutense University through grant PR64/99-8501 and the European Commission through INTAS grant 96-0828.
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Abou-El-ata, M.O. and Hariri, A.M.A. (1995). Estimation and confidence intervals of the M/M/2/N queue with balking and heterogeneity, American Journal of Mathematics and Management Science, 15, 35-55.
Artalejo, J.R. (1994). New results in retrial queueing systems with breakdown of the servers, Staiistica NeeHandica, 48, 23-36.
Artalejo, J.R. (1995). A queueing system with returning customers and waiting line. Operations Research Letters, 17, 191-199.
Artalejo, J.R. and Gomez-Corral, A. (1997). Steady state solution of a single server queue with linear repeated requests. Journal of Applied Probability, 34, 223-233.
Choi, B.D., Shin, Y.W. and Ahn, W.C (1992). Retrial queues with collision arising from unslotted CSMA/CD protocol, Queueing Systems, 11, 335-356.
Qinlar, E. (1975). Introduction to Stochastic Processes, Prentice-Hall, Inc., Englewood Cliffs.
Cohen, J.W. (1957). Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Review, 18, 49-100.
Cox, D.R. and Isham, V. (1980). Point Processes, Chapman and Hall, London.
Falin, G.I. (1990). A survey of retrial queues, Queueing Systems, 7, 127-167.
Falin, G.I. and Artalejo, J.R. (1995). Approximations for multiserver queu^ with balking/ retrial discipline, OR Spektrum, 17, 239-244.
Falin G.I. and Templeton, J.G.C. (1997). Retrial Queues, Chapman and Hall, London.
Grassmann, W.K. (1974). The steady state behaviour of the M/Ek/l queue, with state dependent arrival rates, Infor, 12, 163-173.
Haight, F.A. (1957). Queueing with balking, Biometrika, 44, 360-369.
Ikeda, Z. and Nishida, T. (1988). M/G/1 queue with balking, Mathematica Japonica, 33, 707-711.
Janssens, G.K. (1997). The quasi-random input queueing system with repeated attempts as a model for collision-avoidance star local area network, IEEE Transactions on Communications, 45, 360-364.
Khomichkov,I.I.(1995.Calculation of the characteristics of local axea network with p-persistent protocol of multiple random access. Automation and Remote Control, 56,208-218.
Kleinrock, L. (1975). Queueing Systems, Vol. I: Theory, John Wiley and Sons, New York.
Kok, A.G. de (1984). Algorithmic methods for single server systems with repeated attempts, Statistica NeeHandica, 38, 23-32.
Krishna Kumar, B., Parthasarathy, P.R. and Sharafali, M. (1993). Transient solution of an M/M/1 queue with balking, Queueing Systems, 13, 441-448.
Kulkarni, V.G. (1995). Modeling and Analysis of Stochastic Systems, Chapman and Hall, London.
Martin, M. and Artalejo, J.R. (1995). Analysis of an M/G/1 queue with two types of impatient units. Advances in Applied Probability, 27, 840-861.
Schellhaas, H. (1983). Computation of the state probabilities in M/G/1 queues with state dependent input arid state dependent service, OR Spektrum, 5, 223-228.
Schellhaas,H.(1986).Computation of the state probabilities in a class of semi-regenerative queueing models, in: Semi-Markov Models: heory and Applications (Jansen, J. ed.) Plenum Press, 111-130.
Sennott, L.I., Humblet, P.A. and Tweedie, R.L. (1983). Mean drifts and the nonergodicity of Markov chains. Operations Research, 31, 783-789.
Subba Rao, S. and Jaiswal, N.K. (1965). A queueing model with balking, reneging and limited servers' availability, Opsearch, 2, 31-43.
Tijms, H.C. (1994). Stochastic Models: An Algorithmic Approach, John Wiley and Sons, Chichester.
Yang, T. and Templeton, J.G.C. (1987). A survey on retrial queues, Queueing Systems, 2, 201-233.