Abstract
This paper considers a single server retrial queueing system with search, abandonment and flush out of customers from the system (system clearance) periodically with exponentially distributed duration. A customer on arrival, enters for service, if the server is found to be idle and enter into an orbit of infinite capacity if the server is busy. Orbital customers receive service either by successful retrials or by an orbital search. At the epoch of completion of a service, sever goes for search with probability p as long as the orbit size is atmost L-1. Search stops the moment there are L or more customers in the orbit. Further orbital customers are assumed to renege with certain probability on an unsuccessful retrial. In addition, clearance of system takes place each time a random duration following exponential distribution, expires. The customers arrive to the system according to Markovian arrival Process, inter-retrial times are exponentially distributed and service time follows phase type distribution. We analyze the resulting GI/M/1 Type queue. Steady-state analysis of the model is performed. Some performance measures are evaluated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-78725-9
Artalejo, J.R.: Accessible bibliography of research on retrial queues. Math. Comput. Model. 30, 1–6 (1999)
Artalejo, J.R.: A classified bibliography of research on retrial queues. Progress in 1990–1999. Top 7, 187–211 (1999)
Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Rev. Math. Comput. 15, 101–129 (2002)
Artalejo, J.R., Joshua, V.C., Krishnamoorthy, A.: An M/G/1 retrial queue with orbital search by server. In: Advances in Stochastic Modelling, pp. 41–54. Notable Publications, New Jersey (2002)
Artalejo, J.R., Phung-Duc, T.: Single server retrial queues with two way communication. Appl. Math. Model. 37, 1811–1822 (2013)
Chakravarthy, S.R., Krishnamoorthy, A., Joshua, V.C.: Analysis of a multi-server retrial queue with search of customers from the orbit. Perf. Eval. 63(8), 776–798 (2006)
Dudin, A.N., Krishnamoorthy, A., Joshua, V.C., Tsarenkov, G.: Analysis of BMAP/G/1 retrial system with search of customers from the orbit. Euro. J. Oper. Res. 157, 169–179 (2004)
Falin, G.I.: A survey of retrial queues. Queueing Syst. 7(2), 127–167 (1990)
Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman and Hall, London (1997)
Krishnamoorthy, A., Joshua, V.C.: Excursion between classical and retrial queue
Krishnamoorthy, A., Deepak, T.G., Joshua, V.C.: An M/G/1 retrial queue with non persistent customers and orbital search. Stoch. Anal. Appl. 23, 975–997 (2005)
Krishnamoorthy, A., Shajin, D., Lakshmi, B.: GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time. Indian J. Pure Appl. Math. 47(2), 357–388 (2016)
Krishnamoorthy, A., Joshua, V.C., Babu, D.: A MAP/PH/1 retrial queue with search and abandonment. In: Accepted for ECQT conference (2018)
Latouche, G., Ramaswami, V.: Introduction to Matrix analytic Methods in Stochastic Modelling. American Statistical Association, Siam, Alexandria, Philadelphia (1999)
Neuts, M.F., Ramalhoto, M.F.: A service model in which the server is required to search for customers. J. Appl. Probab. 21, 157–166 (1984)
Neuts, M.F.: Probability distributions of phase type. In: Liber Amicorum Professor Emeritus H. Florin, Department of Mathematics, University of Louvain, pp. 173–206 (1975)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach. The Johns Hopkins University Press, Baltimore and London (1981)
Neuts, M.F.: Markov chains with applications in queueing theory which have a matrix- geometric invariant probability vector. Adv. Appl. probab. 10, 185–212 (1978)
Yang, T., Templeton, J.G.: A survey on retrial queues. Queueing Syst. 2, 201–233 (1987)
Acknowledgments
The work of the third author is supported by the Maulana Azad National fellowship \([F1-17.1/2015-16/MANF-2015-17-KER-65493]\) of University Grants commission, India.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Babu, D., Krishnamoorthy, A., Joshua, V.C. (2018). MAP/PH/1 Retrial Queue with Abandonment, Flush Out and Search of Customers. In: Vishnevskiy, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science, vol 919. Springer, Cham. https://doi.org/10.1007/978-3-319-99447-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-99447-5_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99446-8
Online ISBN: 978-3-319-99447-5
eBook Packages: Computer ScienceComputer Science (R0)