Abstract
In this paper we consider the analysis of an M/G/1 queue with working vacation. In contrast to the previous literature where the working vacation starts when all customers are served (exhaustive discipline) we consider the case where the vacation period starts when the customers present at the system at beginning of the service period are served (gated discipline). The analysis of the model with gated discipline requires a different approach than the one with exhaustive discipline.
We present the probability-generating function of the number of customers in the system and the Laplace-Stieljes transform of the stationary waiting time.
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References
Baba, Y.: Analysis of a GI/M/1 queue with multiple working vacations. Operation Research Letters 33, 201–209 (2005)
Bertsimas, D., Nakazato, D.: The distributional Little’s law and its application. Operations Research 43, 298–310 (1995)
Borst, S.C., Boxma, O.J.: Polling models with and without switchover times. Operations Research 45, 536–543 (1997)
Doshi, B.T.: Queueing systems with vacations - a survey. Queueing Systems 1, 29–66 (1986)
Fuhrmann, S.W., Cooper, R.B.: Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations. Operations Research 33, 1117–1129 (1985)
Kim, T.S., Chang, S.H., Chae, K.C.: Performance Analysis of a Discrete-Time Two-Phase Queueing System. ETRI Journal 25, 238–246 (2003)
Kuczma, M.: Functional equations in a single variable. PWN-Polish Scientific Publishers, Warsaw (1968)
Li, J., Jia, D., Tian, N.: A batch arrival queue with exponential working vacations. In: 5th International Conference on Queueing Theory and Network Applications (QTNA 2010), pp. 169–173 (July 2010)
Li, J., Tian, N., Zhang, Z.G., Luh, H.P.: Analysis of the M/G/1 queue with exponential working vacations - a matrix analytic approach. Queueing Systems 61, 139–166 (2009)
Liu, W., Xu, X., Tian, N.: Stochastic decompositions in the M/M/1 queue with working vacations. Operation Research Letters 35, 595–600 (2007)
Narula-Tam, A., Finn, S.G., Medard, M.: Analysis of reconfiguration in IP over WDM access networks. In: Proceedings of the Optical Fiber Communication Conference, (OFC) p. MN4.1-MN4.3 (2001)
Saffer, Z.: An introduction to classical cyclic polling model. In: Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2007), pp. 59–64 (2007)
Servi, L.D., Finn, S.G.: M / M /1 queue with working vacations(M/M/1/WV). Performance Evaluation 50, 41–52 (2002)
Takács, L.: Introduction to the Theory of Queues. Oxford University Press, New York (1962)
Takagi, H.: Analysis of Polling Systems. MIT Press, Cambridge (1986)
Takagi, H.: Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems, vol. 1. North-Holland, Amsterdam (1991)
Wolff, R.W.: Poisson Arrivals See Times Averages. Operations Research 30, 223–231 (1982)
Wu, D., Takagi, H.: M/G/1 queue with multiple working vacations. Performance Evaluation 63, 654–681 (2006)
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Saffer, Z., Telek, M. (2011). M/G/1 Queue with Exponential Working Vacation and Gated Service. In: Al-Begain, K., Balsamo, S., Fiems, D., Marin, A. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2011. Lecture Notes in Computer Science, vol 6751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21713-5_3
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DOI: https://doi.org/10.1007/978-3-642-21713-5_3
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