Publication:
Analysis of an M/G/1 Queue with Two Types of Impatient Units

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1995-09-03
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Applied Probability Trust
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Abstract
This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specificp erformancem easures,s uch as the numbero f lost customersa nd other quantities,a re also considered.T he mathematicaal nalysiso f the model is based on the theory of Markov renewal processes, in Markov chains of M/G/1 type and in expressions of 'Takacs' equation' type.
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The authors would like to thank the referee for valuable suggestions that helped to improve the presentation of this paper.
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Investigación operativa (Matemáticas)
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1207 Investigación Operativa
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Artalejo,J. R. and Martin, M. (1994) A maximum entropy analysis of the M/G/1 queue with constant repeated attempts. In Selected Topics on Stochastic Modelling. World Scientific, Singapore. Çinlar, E.(1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ. Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam. Falin, G., Artalejo, J. R. and Martin, M.(1993) On the single server retrial queue with priority customers. Queueing Systems 14, 439-455. Farahmand, K. (1990) Single line queue with repeated demands. Queueing Systems 6, 223-228. Fayolle, G. (1986) A simple telephone exchange with delayed feedbacks. In Teletraffic Analysis and Computer Performance Evaluation, ed. O. J. Boxma, J. W. Cohen and H. C. Tijms. Elsevier Science,Amsterdam. Hammon, J. L. and O'Reilly, P. J. P. (1986) Performance Analysis of Local Computer Networks. Addison-Wesley, Reading, MA. Neuts, M . F. and Ramalhoto, M. F. (1984) A service model in which the server is required to search for customers. J. Appl. Prob. 21, 157-166. Neuts, M. F. (1989) Structured Stochastic Matrices of M/G/1 Type and their Applications. Marcel Dekker, New York.
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https://hdl.handle.net/20.500.14352/57500
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