Abstract
We consider the M/M/c retrial queues with multiclass of customers. We show that the stationary joint distribution for the number of customers in service facility and orbit converges to those of the ordinary M/M/c with discriminatory random order service (DROS) policy as retrial rate tends to infinity. Approximation formulae for the distributions of the number of customers in service facility, the mean number of customers in orbit and the sojourn time distribution of a customer are presented. The approximations are compared with exact and simulation results.
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References
Artalejo JR, Gómez-Corral A (2008) Retrial queueing systems, a computational approach. Springer, Hidelberg.
Artalejo JR, Phung-Duc T (2012) Markovian retrial queues with two way communication. J Indu Manag Optim 8:781–806
Artalejo JR, Phung-Duc T (2013) Single server retrial queues with two way communication. Appl Math Model 37:1811–1822
Avrachenkov K, Yechiali U (2010) On tandem blocking queues with a common retrial queue. Comput Oper Res 37:1174–1180
Bright L, Taylor PG (1995) Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes. Stoch Model 11: 497–525
Choi BD, Chang Y (1999) MAP 1,MAP 2/M/c retrial queue with the retrial group of finite capacity and geometric loss. Math Comput Model 30:99–113
Choi BD, Kim B (2004) Non-ergodicity criteria for denumerable continuous time Markov processes. Oper Res Lett 32:574–580
Choi BD, Choi, KB, Lee YW (1995) M/G/1 retrial queueing systems with two types of calls and finite capacity. Queueing Syst 19:215–229.
Cohen JW (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecomm Rev 18(2):49–100
Falin GI (1988) On a multiclass batch arrival retrial queue. Adv Appl Probab 20:483–487
Falin GI, Templeton JGC (1997) Retrial queues. Chapman and Hall, London
Falin GI, Artalejo JR, Martin M (1993) On the single server retrial queue with priority customers. Queueing Syst 14:439–455
Gharbi N, Dutheillet C, Ioualalen M (2009) Colored stochastic Petri nets for modelling and analysis of multiclass retrial systems. Math Comput Model 49:1436–1448
Grishechkin SA (1992) Multiclass batch arrival retrial queues analyzed as branching process with immigration. Queueing Syst 11:395–418
Khalil Z, Falin G, Yang T (1992) Some analytical results for congestion in subscriber line modules. Queueing Syst 10:381–402
Kim B (2011) Stability of a retrial queueing network with different classes of customers and restricted resource pooling. J Ind Manag Optim 7(3):753–765
Kim J (2009) Queue length distribution in a queue with relative priorities. Bull Kor Math Soc 46:107–116
Kim J, Kim J, Kim B (2011) Analysis of the M/G/1 queue with discriminatory random order service policy. Perform Eval 68:256–270
Kulkarni VG (1983) On queueing systems with retrials. J Appl Probab 20:380–389
Kulkarni VG (1986) Expected waiting times in a multiclass batch arrival retrial queue. J Appl Probab 23:144–154
Martin M, Artalejo JR (1995) Analysis of an M/G/1 queue with two types of impatient units. Adv Appl Probab 27:840–861.
Shin YW (2009) Fundamental matrix of transient QBD generator with finite states and level dependent transitions. Asia Pac J Oper Res 26:697–714
Tweedie RL (1975) Sufficient condition for regularity, recurrence and ergodicity of Markov processes. Math Proc Cambridge Philos Soc 78:125–136
Wolff RW (1989) Stochastic modeling and the theory of queues. Prentice Hall, New Jersey
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Shin, Y.W., Moon, D.H. M/M/c Retrial Queue with Multiclass of Customers. Methodol Comput Appl Probab 16, 931–949 (2014). https://doi.org/10.1007/s11009-013-9340-0
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DOI: https://doi.org/10.1007/s11009-013-9340-0