On feedback queueing system with reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption

Abou El-Ata, M. O.; Hariri, A.M.A.: The $$M/M/c/N$$ M / M / c / N queue with balking and reneging. Comput. Oper. Res. 19(13), 713–716 (1992)

Altman, E.; Yechiali, U.: Analysis of customers’ impatience in queues with server vacations. Queueing Syst. Theory Appl. 52(4), 261–279 (2006)

Ancker Jr., C.J.; Gafarian, A.V.: Some queuing problems with balking and reneging: I. Oper. Res. 11(1), 88–100 (1963)

Ancker Jr., C.J.; Gafarian, A.V.: Some queuing problems with balking and reneging: II. Oper. Res. 11(6), 928–937 (1963)

Ayyapan, G.; Muthu Ganapathi Subramanian, A.; Sekar, G.: $$M/M/1$$ M / M / 1 Retrial queueing system with loss and feedback under non-pre-emptive priority service by matrix Geometric method. Appl. Math. Sci. 4(48), 2379–2389 (2010)

Baba, Y.: The $$M/PH/1$$ M / P H / 1 queue with working vacations and vacation interruption. J. Syst. Sci. Syst. Eng. 19(4), 496–503 (2010)

Chen, H.; Li, J.; Tian, N.: The $$GI/M/I$$ G I / M / I queue with phase type working vacations and vacation interruption. J. Appl. Math. Comput. 30(1–2), 121–141 (2009)

D’Avignon, G.R.; Disney, R.L.: Single server queue with state dependent feedback. INFOR 14, 71–85 (1976)

El-Paoumy, M.S.; Nabwey, H.A.: The Poissonian queue with balking function, reneging and two heterogeneous servers. Int. J. Basic Appl. Sci. IJBAS-IJENS 11(6), 149–152 (2011)

Goswami, V.: Analysis of impatient customers in queues with Bernoulli schedule working vacations and vacation interruption. J. Stoch. 2014, 1–10, Article ID 207285 (2014)

Haight, F.A.: Queueing with balking. Biometrika 44, 360–369 (1957)

Haight, F.A.: Queueing with reneging. Metrika 2, 186–197 (1959)

Ke, J.C.; Wu, C.H.; Zhang, Z.G.: Recent developments in vacation queueing models: a short survey. Int. J. Oper. Res. 7(4), 3–8 (2010)

Kumar, R.; Sharma, S.K.: $$M/M/1/N$$ M / M / 1 / N queuing system with retention of reneged customers. Pak. J. Stat. Oper. Res. 8, 859–866 (2012)

Kumar, R.; Sharma, S.K.: An $$M/M/1/N$$ M / M / 1 / N queuing model with retention of reneged customers and balking. Am. J. Oper. Res. 2(1), 1–5 (2012)

Kumar, R.; Sharma, S.K.: A Markovian feedback queue with retention of reneged customers and balking. AMO—Adv. Model. Optim. 14(3), 681–688 (2012)

Laxmi, P.V.; Goswami, V.; Jyothsna, K.: Analysis of finite buffer Markovian queue with balking, reneging and working vacations. Int. J. Strateg. Decis. Sci. 4(1), 1–24 (2013)

Li, J.; Tian, N.: The $$M/M/1$$ M / M / 1 queue with working vacations and vacation interruptions. J. Syst. Sci. Syst. Eng. 16(1), 121–127 (2007)

Robert, E.: Reneging phenomenon of single channel queues. Math. Oper. Res. 4(2), 162–178 (1979)

Santhakumaran, A.; Thangaraj, V.A.: Single server queue with impatient and feedback customers. Inf. Manag. Sci. 11(3), 71–79 (2000)

Selvaraju, N.; Goswami, C.: Impatient customers in an $$M/M/1$$ M / M / 1 queue with single and multiple working vacations. Comput. Ind. Eng. 65(2), 207–215 (2013)

Sharma, S.K.; Kumar, R.: A Markovian feedback queue with retention of reneged customers and balking. AMO—Adv. Model. Optim. 14(3), 681–688 (2012)

Takacs, L.: A single server queue with feedback. Bell Syst. Tech. J. 42, 134–149 (1963)

Thangaraj, V.; Vanitha, S.: On the analysis of $$M/M/1$$ M / M / 1 feedback queue with catastrophes using continued fractions. Int. J. Pure Appl. Math. 53(1), 131–151 (2009)

Tian, N.; Zhang, Z.G.: Vacation Queueing Models. Springer, New York (2006)

Wang, K.-H.; Chang, Y.-C.: Cost analysis of a finite $$M/M/R$$ M / M / R queueing system with balking, reneging and server breakdowns. Math. Methods Oper. Res. 56(2), 169–180 (2002)

Yue, D.; Zhang, Y.; Yue, W.: Optimal performance analysis of an $$M/M/1/N$$ M / M / 1 / N queue system with balking, reneging and server vacation. Int. J. Pure Appl. Math. 28(1), 101–115 (2006)

Yue, D.; Yue, W.; Xu, G.: Analysis of customers’ impatience in an $$M/M/1$$ M / M / 1 queue with working vacations. J. Ind. Manag. Optim. 8(4), 895–908 (2012)

Zhang, M.; Hou, Z.: Performance analysis of $$M/G/1$$ M / G / 1 queue with working vacations and vacation interruption. J. Comput. Appl. Math. 234(10), 2977–2985 (2010)

Zhang, H.; Shi, D.: The $$M/M/1$$ M / M / 1 queue with Bernoulli schedule-controlled vacation and vacation interruption. Int. J. Inf. Manag. Sci. 20(4), 579–587 (2009)