Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs

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

Al-Seedy, R.O., El-Sherbiny, A.A., El-Shehawy, S.A., Ammar, S.I.: Transient solution of the M/M/c queue with balking and reneging. Comput. Math. Appl. 57, 1280–1285 (2009)

Ammar, S.I.: Transient analysis of a two-heterogeneous servers queue with impatient behavior. J. Egypt. Math. Soc. 22, 90–95 (2014)

Ammar, S.I., El-Sherbiny, A.A., El-Shehawy, S.A., Al-Seedy, R.O.: A matrix approach for the transient solution of an M/M/1/N queue with discouraged arrivals and reneging. Int. J. Comput. Math. 89(4), 482–491 (2012)

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

Ancker Jr., C.J., Gafarian, A.V.: Some queueing problems with balking and reneging: II. Metrika 11, 928–937 (1963)

Atencia, I., Moreno, P.: The discrete time Geo/Geo/1 queue with negative customers and disasters. Comput. Oper. Res. 31(9), 1537–1548 (2004)

Chao, X.: A queuing network model with catastrophes and its product form solution. Oper. Res. Lett. 18, 75–79 (1995)

Chao, X., Mayazawa, M., Pinedo, M.: Queueing networks: customers, signals and product form solutions. Wiley, Chichester (1993)

Chen, A., Renshaw, E.: The M/M/1 queue with mass exodus and mass arrivals when empty. J. Appl. Prob. 34, 192–207 (1997)

Choudhry, A., Medhi, P.: Balking and reneging in multiserver Markovian queueing system. Int. J. Math. Oper. Res. 3(4), 377–394 (2011)

DiCrescenzo, A., Giorno, V., Nobile, A.G.: On the M/M/1 queue with catastrophes and its continuous approximation. Que. Syst. 43, 329–347 (2003)

DiCrescenzo, A., Giorno, V., Nobile, A.G., Ricciardi, L.M.: A note on birth-death processes with catastrophes. Stat. Probab. Lett. 78, 2248–2257 (2008)

DiCrescenzo, A., Giorno, V., Kumar, B.K., Nobile, A.G.: A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation. Methodol. Comput. Appl. Probab. 14, 937–954 (2012)

Dimou, S., Economou, A.: The single server queue with catastrophesand geometric reneging. Methodol. Comput. Appl. Probab. 15, 595–621 (2013)

Gelenbe, E.: Product form queueing networks with positive and negative customers. J. Appl. Probab. 28(3), 656–663 (1991)

Giorno, V., Nobile, A.G., Spina, S.: On some time non-homogeneous queueing systems with catastrophes. Appl. Math. Comput. 245, 220–234 (2014)

Haghighi, A.M., Medhi, J., Mohanty, S.G.: On a multi-server Markovian queueing system with balking and reneging. Comput. Oper. Res. 13, 421–425 (1986)

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

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

Jain, G., Sigman, K.: A Pollaczek–Khintchine formula for M/G/1 queues with disasters. J. Appl. Probab. 33(4), 1191–1200 (1996)

Kalidass, K., Gopinath, S., Gnanaraj, J., Ramanath, K.: Time dependent analysis of an M/M/1/N queue with catastrophes and a repairable server. Opsearch 49, 39–61 (2012)

Krishna Kumar, B., Arivudainambi, D.: Transient solution of an M/M/1 queue with catastrophes. Comput. Math. Appl. 10, 1233–1240 (2000)

Krishana Kumar, B., Krishnamoorthy, A., Pvavi Madeshwari, S., Sadiq Basha, S.: Transient analysis of a single server queue with catastrophes, failures and repairs. Que. Syst. 56(3–4), 133–141 (2007)

Krishna Kumar, B., Parthasarathy, P.R., Sharafali, M.: Transient solution of an M/M/1 queue with balking and reneging. Que. Syst. Theory Appl. 13, 441–448 (1993)

Krishna Kumar, B., Pavai Madheswari, S.: Transient analysis of an M/M/1 queue subject to catastrophes and server failures. Stochastic Anal. Appl. 23, 329–340 (2005)

Neuts, M.F., Lucantoni, D.M.: A Markovian queue with N servers subjects to breakdowns and repairs. Manage. Sci. 25(9), 849–861 (1979)

Pollett, P., Zhang, H., Cairns, B.J.: A note on extinction times for the general birth, death and catastrophe process. J. Appl. Probab. 44, 566–569 (2007)

Sudesh, R.: Transient analysis of a queue with system disasters and customer impatience. Que. Syst. 66(1), 95–105 (2010)

Tarabia, A.M.K.: Transient and steady-state analysis of an M/M/1 queue with balking, catastrophes, server failures and repairs. J. Ind. Manag. Optim. 7, 811–823 (2011)

Towsley, D., Tripathi, S.K.: A single server priority queue with server failures and queue flushing. Oper. Res. Lett. 10, 353–362 (1991)

Vijaya Laxmi, P., Goswami, V., Jyothsna, K.: Analysis of finite buffer Markovian queue with balking, reneging and working vacations. Int. J. Strategic Decis. Sci. 4(1), 11–24 (2013)

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