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A queueing system with \(n\)-phases of service and (\(n-1\))-types of retrial customers. (English) Zbl 1188.90068

Summary: A queueing system with a single server providing \(n\)-phases of service in succession is considered. Every customer receives service in all phases. Arriving customers join a single ordinary queue, waiting to start the service procedure. When a customer completes his service in the \(i\)th phase he decides either to proceed to the next phase or to join the \(K_i\) retrial box \((i=1,2,\dots ,n-1)\), from where he repeats the demand for the \((i+1)\)th phase of service after a random amount of time and independently to the other customers in the system. Every customer can join during his service procedure a number of retrial boxes before departs from the system. When at the moment that a customer, either departs from the system or joins a retrial box and so releases the server, there are no other customers waiting in the ordinary queue, then the server departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service times are arbitrarily distributed. For such a system, the mean number of customers in the ordinary queue and in each retrial box separately are obtained, and used to investigate numerically system performance.

MSC:

90B22 Queues and service in operations research
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[1] Artalejo, J. R., A classified bibliography of research on retrial queues: progress in 1990-1999, Top, 7, 2, 187-211 (1999) · Zbl 1009.90001
[2] Artalejo, J. R.; Gomez-Corral, A., Retrial queueing systems. Retrial queueing systems, A Computational Approach (2008), Springer-Verlag: Springer-Verlag Berlin, Heidelberg · Zbl 1161.60033
[3] Choi, D. I.; Kim, T., Analysis of a two-phase queueing system with vacations and Bernoulli feedback, Stochastic Analysis and Applications, 21, 5, 1009-1019 (2003) · Zbl 1030.60082
[4] Choudhury, G., Steady state analysis of a M/G/1 queue with linear retrial policy and two-phase service under Bernoulli vacation schedule, Applied Mathematical Modelling, 32, 12, 2480-2489 (2008) · Zbl 1167.90444
[5] Choudhury, G.; Madan, K. C., A two stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modelling, 42, 71-85 (2005) · Zbl 1090.90037
[6] Dimitriou, I.; Langaris, C., Analysis of a retrial queue with two-phase service and server vacations, Queueing Systems, 60, 1-2, 111-129 (2008) · Zbl 1158.60377
[7] Doshi, B. T., Analysis of a two-phase queueing system with general service times, Operation Research Letters, 10, 265-272 (1991) · Zbl 0738.60091
[8] Falin, G. I.; Templeton, J. G.C., Retrial Queues (1997), Chapman and Hall: Chapman and Hall London · Zbl 0944.60005
[9] Falin, G. I., On a multiclass batch arrival retrial queue, Advances in Applied Probability, 20, 483-487 (1988) · Zbl 0672.60089
[10] Katayama, T.; Kobayashi, K., Sojourn time analysis of a queueing system with two-phase service and server vacations, Naval Research Logistics, 54, 1, 59-65 (2006) · Zbl 1114.60075
[11] Ke, J.-C., An \(M^{[x]}\)/G/1 system with startup server and J additional options for service, Applied Mathematical Modelling, 32, 4, 443-458 (2008) · Zbl 1162.90399
[12] Krishna, C. M.; Lee, Y. H., A study of a two-phase service, Operation Research Letters, 9, 91-97 (1990) · Zbl 0687.68014
[13] Kulkarni, V. G.; Liang, H. M., Retrial queues revisited, (Dshalalow, J. H., Frontiers in Queueing (1997), CRP Press: CRP Press Boca Raton), 19-34 · Zbl 0871.60074
[14] Krishna Kumar, A.; Vijayakumar, A.; Arivudainambi, D., An M/G/1 retrial queueing system with two-phases of service and preemptive resume, Annals of Operation Research, 113, 61-79 (2002) · Zbl 1013.90032
[15] Langaris, C.; Katsaros, A., Time depended analysis of a queue with batch arrivals and N levels of non preemptive priority, Queueing Systems, 19, 269-288 (1995) · Zbl 0833.60092
[16] Madan, K. C., On a single server queue with two stage heterogeneous service and deterministic server vacations, International Journal of Systems Science, 32, 7, 837-844 (2001) · Zbl 1006.90021
[17] Moutzoukis, E.; Langaris, C., Non-preemptive priorities and vacations in a multiclass retrial queueing system, Stochastic Models, 12, 3, 455-472 (1996) · Zbl 0858.60086
[18] Takacs, L., Introduction to the Theory of Queues (1962), Oxford University Press: Oxford University Press New York · Zbl 0118.13503
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