Abstract
A single-server retrial queue with a MAP flow, PH service times and a pool of finite capacity for accumulation of the customers and their group service is considered. Service to the next group is not provided until the number of customers in the pool will reach a certain predefined threshold value. The service time of a group depends on its size and it is less than the sum of the individual service times. The dependencies of the basic performance measures of the system on the capacity of the pool and the threshold are obtained. Numerical results are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abolnikov L, Dukhovny A (2003) Optimization in HIV screening problems. Int J Stoch Anal 16(4):361–374
Aggoun L, Benkherouf L, Tadj L (1998) On a bulk queueing system with impatient customers. Math Probl Eng 3(6):539–554
Alfa AS, Chakravarthy SR (1994) A finite capacity queue with Markovian arrivals and two servers with group services. J Appl Math Stoch Anal 7:161–178
Artalejo JR, Gomez-Corral A (2008) Retrial queueing systems: a computational approach. Springer, Berlin, Heidelberg
Bailey NTJ (1954) On queueing processes with bulk service. J R Stat Soc Ser B 61:80–87
Banerjee A, Chakravarthy SR, Gupta UC (2015) Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service. Comput Oper Res 60:138–149
Bar-Lev SK, Parlar M, Perry D, Stadje W, Van der Duyn Schouten FA (2007) Applications of bulk queues to group testing models with incomplete identification. Eur J Oper Res 183(1):226–237
Baumann H, Sandmann W (2013) Computing stationary expectations in level-dependent QBD processes. J Appl Probab 50(1):151–165
Baumann H, Sandmann W (2017) Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers. Eur J Oper Res 256:187–195
Bin L, Chakravarthy SR (1997) A finite capacity queue with nonrenewal input and exponential dynamic group services. INFORMS J Comput 9:276–287
Brugno A, Dudin AN, Manzo R (2017) Retrial queue with discipline of adaptive permanent pooling. Appl Math Model 50:1–16
Brugno A, Dudin AN, Manzo R (2018) Analysis of a strategy of adaptive group admission of customers to single server retrial system. J Ambient Intell Humaniz Comput 9:123–135
Bruneel H, Claeys D, Laevens K, Walraevens J (2010) A queueing model for general group screening policies and dynamic item arrivals. Eur J Oper Res 207(2):827–835
Chakravarthy SR (1992) A finite capacity \(GI/PH/1\) queue with group services. Naval Res Logist Q 39:345–357
Chakravarthy SR (1996) Analysis of the \(MAP/PH/1/K\) queue with service control. Appl Stoch Models Data Anal 12:179–191
Chakravarthy SR (1998) Analysis of a priority polling system with group services. Commun Stat Stoch Models 14:25–49
Chakravarthy SR, Dudin AN (2002) A multi-server retrial queue with \(BMAP\) arrivals and group services. Queueing Syst 42(1):5–31
Chakravarthy SR, Dudin AN (2003) Analysis of a retrial queuing model with \(MAP\) arrivals and two types of customers. Math Comput Model 37(3–4):343–363
Chaudhry M, Templeton J (1983) A first course in bulk queues. Wiley, New York
Deb RK, Serfozo RF (1973) Optimal Control of Batch Service Queues. Adv Appl Probab 5(2):340–361
Dixit VV, Islam MK, Sharma A, Vandebona U (2014) A bulk queue model for the evaluation of impact of headway variations and passenger waiting behavior on public transit performance. IEEE Trans Intell Transp Syst 15(6):2432–2442
Downton F (1955) Waiting time in bulk service queues. J R Stat Soc Ser B 17(2):256–261
Dudin SA, Dudina OS (2019) Retrial multi-server queueing system with PHF service time distribution as a model of a channel with unreliable transmission of information. Appl Math Model 65:676–695
Dudin AN, Piscopo R, Manzo R (2015) Queue with group admission of customers. Comput Oper Res 61:89–99
Falin G, Templeton J (1997) Retrial queues. Chapman and Hall, London
Graham A (1981) Kronecker products and matrix calculus with applications. Ellis Horwood, Cichester
Gupta UC, Maity A, Chakravarthy SR (2017) An \((s, S)\) inventory in a queueing system with batch service facility. Ann Oper Res 258(2):263–283
Harten AV, Schuur P, Zee DJVD (2001) On-line scheduling of multi-server batch operations. IIE Trans 33(7):569–586
Indhira K, Sasikala S (2016) Bulk service queueing models—a survey. Int J Pure Appl Math 106(6):43–56
Klimenok VI, Dudin AN (2006) Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory. Queueing Syst 54:245–259
Lucantoni DM (1991) New results on the single server queue with a batch Markovian arrival process. Commun Stat Stoch Models 7:1–46
Neuts MF (1981) Matrix-geometric solutions in stochastic models. The Johns Hopkins University Press, Baltimore
Xia CH, Zeng Y (2017) Optimal bulking threshold of batch service queues. J Appl Probab 54(2):409–423
Acknowledgements
The publication has been prepared with the support of the RUDN University Program 5-100.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
D’Arienzo, M.P., Dudin, A.N., Dudin, S.A. et al. Analysis of a retrial queue with group service of impatient customers. J Ambient Intell Human Comput 11, 2591–2599 (2020). https://doi.org/10.1007/s12652-019-01318-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-019-01318-x