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Articles

Analysis of stationary queue-length distributions of the BMAP/R(a,b)/1 queue

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Pages 198-223 | Received 30 Nov 2019, Accepted 29 May 2020, Published online: 29 Jul 2020

References

  • N. Akar and E. Arikan, A numerically efficient method for the MAP/D/1/K queue via rational approximations, Queueing Syst. 22(1) (1996), pp. 97–120.
  • F. Avram and A. Gómez-Corral, On bulk-service MAP/PH(L,N)/1/N G-Queues with repeated attempts, Ann. Oper. Res. 141(1) (2006), pp. 109–137.
  • N.T.J. Bailey, On queueing process with bulk service, J. R. Stat. Soc. Ser. B(Methodological) 16(1) (1954), pp. 80–87.
  • A. Banerjee and U.C. Gupta, Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service, Perform. Evaluation 69 (2012), pp. 53–70.
  • A. Banerjee, U.C. Gupta, and S.R. Chakravarthy, Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service, Comput. Oper. Res. 60 (2015), pp. 138–149.
  • A.D. Banik, Queueing analysis and optimal control of BMAP/G(a,b)/1/N and BMAP/MSP(a,b)/1/N systems, Comput. Ind. Eng. 57(3) (2009), pp. 748–761.
  • A.D. Banik, Single server queues with a batch markovian arrival process and bulk renewal or non-renewal service, J. Syst. Sci. Syst. Eng. 24(3) (2015), pp. 337–363.
  • B. Bank, S.K. Samanta, Analytical and computational studies of the BMAP/G(a,Y)/1 queue. Commun. Stat.-Theory Methods (2020). doi:10.1080/03610926.2019.1708941.
  • S.K. Bar-Lev, M. Parlar, D. Perry, W. Stadje, and F.A. Van der Duyn Schouten, Applications of bulk queues to group testing model with incomplete identification, Eur. J. Oper. Res. 183(1) (2007), pp. 226–237.
  • T. Battestilli and H. Perros, An introduction to optical burst switching, IEEE Commun. Maga. 41(8) (2003), pp. S10–S15.
  • S.M. Brown, T. Hanschke, I. Meents, B.R. Wheeler, and H. Zisgen, Queueing model improves IBM's semiconductor capacity and lead-time management, Interface 40(5) (2010), pp. 519–551.
  • S. Chakravarthy, Analysis of a finite MAP/G/1 queue with group services, Queueing Syst. 13(4) (1993), pp. 385–407.
  • M.L. Chaudhry and U.C. Gupta, Analysis of a finite-buffer bulk-service queue with discrete-Markovian arrival process: D-MAP/Ga,b/1/N, Nav. Res. Logist. 50(4) (2003), pp. 345–363.
  • M.L. Chaudhry, G. Singh, and U.C. Gupta, A simple and complete computational analysis of MAP/R/1 queue using roots, Methodol. Comput. Appl. Probab. 15(3) (2013), pp. 563–582.
  • M.L. Chaudhry, J.G.C. Templeton, A First Course in Bulk Queues, John Wiley & Sons Inc, New York, 1983.
  • M.L. Chaudhry, B.K. Yoon, and N.K. Kim, On the distribution of the number of customers in the D-BMAP/G(a,b)/1/M queue a simple approach to a complex problem, Infor 48(2) (2010), pp. 121–132.
  • Y. Chen, C. Qiao, and X. Yu, Optical burst switching: a new area in optical networking research, IEEE Netw. 18(3) (2004), pp. 16–23.
  • D. Claeys, B. Steyaert, J. Walraevens, K. Laevens, and H. Bruneel, Analysis of a versatile batch-service queueing model with correlation in the arrival process, Perform. Evaluation 70(4) (2013), pp. 300–316.
  • A. Dudin and S. Chakravarthy, Optimal hysteretic control for the BMAP/G/1 system with single and group service modes, Ann. Oper. Res. 112 (2002), pp. 153–169.
  • H.R. Gail, S.L. Hantler, and B.A. Taylor, Spectral analysis of M/G/1 and G/M/1 type Markov chains, Adv. Appl. Probab. 28(1) (1996), pp. 114–165.
  • V. Goswami, J.R. Mohanty, and S.K. Samanta, Discrete-time bulk-service queues with accessible and non-accessible batches, Appl. Math. Comput. 182(1) (2006), pp. 898–906.
  • U.C. Gupta and S. Pradhan, A computational approach for determination of system length distribution of a batch arrival and batch service queue. The 6th International Conference on Computational Methods (ICCM2015), Auckland, New Zealand.
  • U.C. Gupta, G Singh, and M.L. Chaudhry, An alternative method for computing system-length distributions of BMAP/R/1 and BMAP/D/1 queues using roots, Perform. Evaluation 95 (2016), pp. 60–79.
  • U.C. Gupta and P. Vijaya Laxmi, Analysis of the MAP/G(a,b)/1/N queue, Queueing Syst. 38(2) (2001), pp. 109–124.
  • Q. He, Analysis of a continuous time SM[K]/PH[K]1/FCFS queue: age process, sojourn times, and queue lengths, J. Syst. Sci. Complex. 25 (2012), pp. 133–155.
  • C. Kim, A. Dudin, S. Dudin, and V. Klimenok, A queueing system with batch arrival of customers in sessions, Comput. Ind. Eng. 62(4) (2012), pp. 890–897.
  • C. Kim, V.I. Klimenok, and A.N. Dudin, Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns, Appl. Math. Comput. 314 (2017), pp. 154–172.
  • A. Klemm, C. Lindemann, and M. Lohmann, Traffic modeling and characterization for UMTS networks, In GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No. 01CH37270) 3 (2001), pp. 1741–1746.
  • A. Klemm, C. Lindemann, and M. Lohmann, Modeling IP traffic using the batch Markovian arrival process, Perform. Evaluation 54 (2003), pp. 149–173.
  • H.W. Lee, J.M. Moon, B.K. Kim, J.G. Park, and S.W. Lee, A simple eigenvalue method for low-order D-BMAP/G/1 queues, Appl. Math. Model. 29(3) (2005), pp. 277–288.
  • Q.L. Li, Z. Lian, and L. Liu, An RG-factorization approach for a BMAP/M/1 generalized processor-sharing queue, Stochastic Models 21(2-3) (2005), pp. 507–530.
  • D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Stochastic Models 7(1) (1991), pp. 1–46.
  • D.M. Lucantoni, The BMAP/G/1 queue: a tutorial, in Models and Techniques for Performance Evaluation of Computer and Communications Systems, L. Donatiello, R. Nelson, eds., Springer-Verlag, 1993, pp. 330–358.
  • M.F. Neuts, A general class of bulk queues with Poisson input, Ann. Math. Stat. 38(3) (1967), pp. 759–770.
  • M.F. Neuts, A versatile Markovian point process, J. Appl. Proba. 16(4) (1979), pp. 764–779.
  • M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, CRC Press, Marcel Dekker, New York, 1989.
  • S. Nishimura, H. Tominaga, and T. Shigeta, A computational method for the boundary vector of a BMAP/G/1 queue, J. Oper. Res. Soc. Japan 49(2) (2006), pp. 83–97.
  • S. Pradhan and U.C. Gupta, Modeling and analysis of an infinite-buffer batch-arrival queue with batch-size-dependent service: MX/Gn(a,b)/1, Perform. Evaluation 108 (2017), pp. 16–31.
  • S. Pradhan and U.C. Gupta, Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process, Ann. Oper. Res. 277 (2019), pp. 161–196.
  • P. Ramírez, R.E. Lillo, M.P. Wiper, Bayesian analysis of a queueing system with a long-tailed arrival process. Commun. Stat.-Simul. Comput. 37 (2008), pp. 697–712.
  • V. Ramaswami, The N/G/1 queue and its detailed analysis, Adv. Appl. Proba. 12(1) (1980), pp. 222–261.
  • S.K. Samanta, Waiting-time analysis of D-BMAP/G/1 queueing system, Ann. Oper. Res. 284(1) (2020), pp. 401–413.
  • S.K. Samanta, M. Chaudhry, and A. Pacheco, Analysis of BMAP/MSP/1 queue, Methodol. Comput. Appl. Proba.18(2) (2014), pp. 419–440.
  • G. Singh, U.C. Gupta, and M.L. Chaudhry, Computational analysis of bulk service queue with Markovian arrival process: MAP/R(a,b)/1 queue, Opsearch 50(4) (2013), pp. 582–603.
  • G. Singh, U.C. Gupta, and M.L. Chaudhry, Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots, J. Appl. Proba. 53(4) (2016), pp. 1078–1097.
  • J.F. Shortle, P.H. Brill, M.J. Fischer, D. Gross, and D.M.B. Masi, An algorithm to compute the waiting time distribution for the M/G/1 queue, INFORMS J. Comput. 16(2) (2004), pp. 152–161.
  • K. Sikdar and S.K. Samanta, Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and servers vacation, Opsearch 53 (2016), pp. 553–583.
  • K. De Turck, S.D. Vuyst, D. Fiems, H. Bruneel, and S. Wittevrongel, Efficient performance analysis of newly proposed sleep-mode mechanisms for IEEE 802.16m in case of correlated downlink traffic, Wirel. Netw. 19(5) (2013), pp. 831–842.

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