Abstract
In this paper we survey work related to queues with interruptions that occur due to many reasons such as server breakdowns, servers taking emergency breaks, and customers having incomplete information or getting distracted. We look at both continuous and discrete time queueing models with interruptions in this survey.
Similar content being viewed by others
References
Aissani A (1988) On the M/G/1/1 queueing system with repeated orders and unreliable server. J Technol 6:98–123
Aissani A (1993) Unreliable queueing with repeated orders. Microelectron Reliab 33:2093–2106
Aissani A (1994) A retrial queue with redundancy and unreliable server. Queueing Syst 17:431–449
Aissani A, Artalejo JR (1998) On the single server retrial queue subject to breakdowns. Queueing Syst, Theory Appl 30(3–4):309–321
Alfa AS (2002) Discrete time queues and matrix-analytic methods. TOP, Span J Stat Oper Res 10(2):147–185
Altiok T (1989) Queueing modelling of a single processor with failures. Perform Eval 9:93–102
Altiok T, Vu-Duy C, Baykal-Gursoy M (1998) Two load sharing processors with failures. Comput Oper Res 25(3):183–189
Anisimov VV, Atadzhanov KL (1994) Diffusion approximation of the systems with repeated call and unreliable server. J Math Sci 72:3032–3034
Artalejo JR, Gomez-Correl A, He QM (2010) Markovian arrivals in stochastic modelling: a survey and some new results. SORT 34(2):101–144
Atencia I, Moreno P (2006) A discrete-time Geo/G/1 retrial queue with the server subject to starting failures. Ann Oper Res 141:85–107
Atencia I, Bouza G, Moreno P (2008) An M [X]/G/1 retrial queue with server breakdowns and constant rate of repeated attempts. Ann Oper Res 157(1):225–243
Avi-Itzhak B, Naor P (1963) Some queueing problems with the service station subject to breakdowns. Oper Res 11:303–320
Baccelli F, Trivedi KS (1985) A single server queue in a hard-real-time environment. Oper Res Lett 4:161–168
Balaustegui Goitia CF, Batlle L (2008) Explicit solution of a queue with nonexhaustive service interruption to model multiuser access interference. In: 3rd International symposium on communications, control, and signal processing, ISCCSP, pp 79–82
Baykal-Gursoy M, Duan Z (2006) M/M/C queues with Markov modulated service processes. ACM Int Conf Proc Ser 180:119-143
Baykal-Gursoy M, Xiao W (2004) Stochastic decomposition in M/M/∞ queues with Markov modulated service rates. Queueing Syst 48:75–88
Baykal-Gursoy M, Xiao W, Ozbay K (2009) Modeling traffic flow interrupted by incidents. Eur J Oper Res 195:127–138
Bhat UN (1992) Switched Poisson process/G/1 queue with service interruptions. Comput Oper Res 19(8):751–756
Bocharov PP (1991) Matrix-geometric queue distribution under LCFS discipline with interruption and phase type distributions. Avtom Telemeh 9:112–122
Bocharov PP, Pavlova OI (1992a) Analysis of the queue with phase type distributions and inverse service discipline with interruptions. Avtom Telemeh 11:83–92
Bocharov PP, Pavlova OI (1992b) Matrix-geometric distributions of a queue under the LCFS discipline with interruptions and distributions of the phase type. Autom Remote Control 52:1265–1273
Boxma OJ (1989) Workloads and waiting times in single-server systems with multiple customer classes. Queueing Syst 5:185–214
Boxma OJ, Konheim AG (1980) Approximate analysis of exponential queueing systems with blocking. Acta Inform 15(1):19–66
Bruneel H (1983) On the behavior of buffers with random server interruptions. Perform Eval 3:165–175
Bruneel H (1984a) Analysis of an infinite buffer system with random server interruption. Comput Oper Res 11:373–386
Bruneel H (1984b) Buffers with correlated input and output interruptions. Oper Res Lett 3:149–152
Bruneel H (1984c) Analysis of discrete-time buffers with one single output channel subjected to a general interruption process. In: Proceedings of the 10th international symposium on computer performance, Paris, France, December 19–21. Performance, vol 84, pp 103–115
Bruneel H (1986) A general treatment of discrete-time buffers with one randomly interrupted output line. Eur J Oper Res 27(1):67–81
Bruneel H (1991) Exact derivation of transient behavior for buffers with random output interruptions. Comput Netw ISDN Syst 22(4):277–285
Bruneel H, Kim BG (1993) Discrete-time models for communication systems including ATM. Kluwer Academic, Boston
Cascone A, Manzo R, Pechinkin AV, Shorgin AY (2010) A Geom/G/1/n queueing system with LIFO discipline, service interruptions and resumption and restrictions on the total volume of demands. In: Proceedings of the world congress on engineering 2010, Vol. III, WCE, London, UK, 30 June–2 July 2010, p 30
Chakravarthy SR (2001) The batch Markovian arrival process: a review and future work. In: Krishnamoorthy A, Raju N, Ramaswami V (eds) Advances in probability and stochastic processes. Notable, New Jersey, pp 21–49
Chakravarthy SR (2010) Markovian arrival processes. Wiley encyclopedia of operations research and management science. Wiley, New York
Chan WC, Chung WK (1972) Computer-controlled queuing system with service interruptions. Proc Inst Electr Eng 119(9):1262–1268
Chan WC, Chung WK, Maa DY (1975) Discrete-time queueing system with instantaneous defection and service interruption. Proc Inst Electr Eng 122(12):1372–1376
Chan W, Bartoszynski R, Pearl D (1993) Queues with breakdowns and customer discouragement. Probab Math Stat 14:77–87
Chopra AS (2003) Ayurveda. In: Selin H (ed) Medicine across cultures: history and practice of medicine in non-western cultures. Kluwer, Norwell, pp 75–83
Choudhary G, Deka K (2008) An M/G/1 retrial queueing system with two phases of service subject to the server breakdowns and repair. Perform Eval 65(10):714–724
Choudhary G, Tadj L, Deka K (2010) A batch arrival retrial queueing system with two phases of service and service interruption. Comput Math Appl 59(1):437–450
Choudhury G, Tadj L (2009) An M/G/1 queue with two phases of service subject to the server breakdowns and delayed repair. Appl Math Model 33(6):2699–2709
Choudhury G, Ke J-C, Tadj L (2009) N-policy for an unreliable server with delaying repair and two phases of service. J Comput Appl Math 231(1):349–364
Co HC, Abdelaziz A (1991) Age-maintenance of an M/G/1 production system. Int J Prod Res 29(10):2135–2149
Cox DR (1955) The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Math Proc Camb Philos Soc 51:433–441
D’Auria B (2005) M/M/∞ queue with on-off service speeds. In: Proceedings of the seminar on stability problems for stochastic models. Part II, Maiori, Italy. Springer, Berlin. doi:1072-3374/05/1314-1
Demoor T, Fiems D, Walraevens J, Bruneel H (2010) The preemptive repeat hybrid server interruption model. In: Analytical and stochastic modeling techniques and applications. Lecture notes in computer science, vol 6148, pp 59–71
Doshi BT (1986) Queueing systems with vacations—a survey. Queueing Syst, Theory Appl 1(1):29–66
Dragalin VP, Mishkoy GK (1984) Servicing with mixed priority and orientation. Eng Cybern 22(5):9–15
Drekic S (2003) A preemptive resume queue with an expiry time for retained service. Perform Eval 54(1):59–74
Economou A, Kantaa S (2008) Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper Res Lett 36(6):696–699
Efrosinin D, Semenova O (2009) Queueing model with non-reliable server and threshold-based recovery. In: Conference proceedings, MMR2009, Moscow, pp 546–550
El-Taha M (2003) Allocation of service time in a two-server system. Comput Oper Res 30(5):683–693
El-Taha M, Maddah B (2006) Allocation of service time in a multiserver system. Manag Sci 52(4):623–637
Federgruen A, Green L (1986) Queueing systems with service interruptions. Oper Res 34:752–768
Federgruen A, Green L (1988) Queueing systems with service interruptions II. Nav Res Logist Q 35:345–358
Fiems D, Steyaert B, Bruneel H (2000a) Discrete-time queues with general service times and general server interruptions. In: Internet performance and control of network systems. Proceedings of SPIE, vol. 4211, Boston, USA
Fiems D, Steyaert B, Bruneel H (2000b) Discrete-time queues with general service times and general server interruptions. In: Internet quality and performance and control of network systems Boston. Proceedings of SPIE, 6–7 November, vol 4211, pp 93–104
Fiems D, Steyaert B, Bruneel H (2001) Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue. Comput Oper Res 28(13):1299–1313
Fiems D, Steyaert B, Bruneel H (2002) Randomly interrupted GI-G-1 queues: service strategies and stability issues. Ann Oper Res 112:171–183
Fiems D, Steyaert B, Bruneel H (2003) Analysis of a discrete-time GI-G-I queueing model subjected to bursty interruptions. Comput Oper Res 30(1):139–153
Fiems D, Steyaert B, Bruneel H (2004) Discrete-time queues with generally distributed service times and renewal-type server interruptions. Perform Eval 55:277–298
Fiems D, Maertens T, Brunee H (2008) Queueing systems with different types of interruptions. Eur J Oper Res 188(3):838–845
Fischer MJ (1977) An approximation to queueing systems with interruptions. Manag Sci 24:338–344
Gaver DP (1962) A waiting line with interrupted service including priority. J Rl Stat Soc B 24:73–90
Gaver DP (1968) Diffusion approximation and models for certain congestion problems. J Appl Probab 5:607–623
Gelenbe E (1977) Existence and uniqueness of stationary distributions in a model of roll-back recovery. In: Lecture notes in control and information sciences, vol 2: New trends in systems analysis, pp 516–529
Gelenbe E, Derochette D (1978) Performance of rollback recovery systems under intermittent failures. Commun ACM 21(6):493–499
Georganas ND (1976) Buffer behavior with poisson arrivals and bulk geometric service. IEEE Trans Commun Technol 24:938–940
Gerasimov VI (1973) Optimum time-sharing algorithm for a servicing device in a queuing system with interruptions. Autom Control Comput Sci 7(6):50–55
Gorelov GV, Kazanskii NA, Lukova ON (1993) Communication quality assessment in speech packet transmission networks with random service interrupts. Autom Control Comput Sci 27(1):62–64
Gray WJ, Wang PP, Scott M (2003) A queueing model with service breakdowns and multiple stages of repair. J Appl Stat Sci 12(1):75–89
Gray WJ, Wang PP, Scott M (2004) A queueing model with multiple types of server breakdowns. Qual Technol Quant Manag 1(2):245–255
Greenberg AG, Srikant R, Whitt W (1999) Resource sharing for book-ahead and instantaneous-request calls. IEEE/ACM Trans Netw 7(1):10–22
Gupta SM, Kavusturucu A (2000) Production systems with interruptions, arbitrary topology and finite buffers. Ann Oper Res 93:145–176
Haridass M, Arumuganathan R (2008) Analysis of a bulk queue with unreliable server and single vacation. Int J Open Problems Comput Math 1:130–148
Heines TS (1979) Buffer behavior in computer communication systems. IEEE Trans Comput 28:573–576
Hsieh Y-C, Andersland MS (1995) Repairable single server systems with multiple breakdowns modes. Microelectron Reliab 35:309–318
Hsu J (1974) Buffer behavior with Poisson arrival and geometric output processes. IEEE Trans Commun Technol 22:1940–1941
Ibe OC, Trivedi KS (1990) Two queues with alternating service and server breakdowns. Queueing Syst 7(3–4):253–268
Ishizaki F (2004) Decomposition property in a discrete-time queue with multiple input streams and service interruptions. J Appl Probab 41(2):524–534
Ishizaki F (2006) Loss probability in a finite queue with service interruptions and queue length distribution in the corresponding infinite queue. Perform Eval 63(7):682–699
Ishizaki F, Takine T, Takahashi Y, Hasegawa T (1994) A generalized SBBP/G/1 queue and its applications. Perform Eval 21:163–181
Izmailov R, Lee D-S, Sengupta B (1997) Design and analysis of a congestion-free overlay on a high-speed network. IEEE/ACM Trans Netw 5(6):970–980
Jain M, Bhargava C (2008) Bulk arrival retrial queue with unreliable server and priority subscribers. Int J Oper Res 5(4):242–259
Jain M, Jain A (2010) Working vacations queueing model with multiple types of server breakdowns. Appl Math Model 34:1–13
Jaiswal NK (1961) Preemptive resume priority queue. Oper Res, 9:732–742
Jayawardene AK, Kella O (1996) M/G/∞ with alternating renewal breakdowns. Queueing Syst 22:79–95
Jeyaraman D, Nadarajan R, Sitrarasu MR (1994) A general bulk service queue with arrival rate dependent on server breakdowns. Appl Math Model 18:156–160
Kamoun F (2008) Performance analysis of a non-preemptive priority queuing system subjected to a correlated Markovian interruption process. Comput Oper Res 35(12):3969–3988
Kamoun F (2009) Performance evaluation of a queuing system with correlated packet-trains and server interruption. Telecommun Syst 41(4):267–277
Karlin S, Taylor HE (1975) A first course in stochastic processes, 2nd edn. Academic Press, San Diego
Ke JC (2004) Bi-level control for batch arrival queues with an early startup and un-reliable server. Appl Math Model 28:469–485
Ke JC (2005) Modified T Vacation policy for an M/G/1 queueing system with an un-reliable server and startup. Math Comput Model 41:1267–1277
Ke JC (2006a) An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server. Math Methods Oper Res 63(2):357–369
Ke JC (2006b) On M/G/1 system under N-T policies with breakdowns, startup and closedown. Appl Math Model 30:49–66
Ke JC (2007) Batch arrival queues under vacation policies with server breakdowns and startup/closedown times. Appl Math Model 31(7):1282–1292
Ke JC, Pearn WL (2004) Optimal management policy for heterogeneous arrival queueing system with server breakdowns and vacations. Qual Technol Quant Manag 1:149–162
Keilson J (1962) Queues subject to service interruptions. Ann Math Stat 33(4):1314–1322
Kekre HB, Saxena CL (1978) A finite waiting room queueing model with multiple servers having Markovian interruptions and its applications to computer communications. Comput Electr Eng 5:51–65
Kendall DG (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann Math Stat 24:338–354
Kernane T (2009) A single server retrial queue with different types of server interruptions. E-prints, February 2009
Kim C, Klimenok VI, Orlovsky DS (2008) The BMAP/PH/N retrial queue with Markovian flow of breakdowns. Eur J Oper Res 189:1057–1072
Klimenok VK Dudin AN (2012) A BMAP/PH/N queue with negative customers and partial protection of service. Commun Stat Simul Comput 41 doi:10.1080/03610918.2012.625802
Koba EV (2001) On a queueing system with repetition and pushing calls out. J Autom Inf Sci 33(3):48–51
Krishnakumar B, Vijay-Kumar A, Arivudainambi D (2002) An M/G/1 retrial queuing system with two phase service and preemptive resume. Ann Oper Res 113:61–79
Krishnamoorthy A, Pramod PK (2010) On a discrete time queue with interruptions and repeat or resumption of service. Submitted for publication
Krishnamoorthy A, Gopakumar B, Viswanath CN (2009a) A queueing model with interruption resumption/restart and reneging. Bull Kerala Math Assoc, Special issue, 29–45, October 2009
Krishnamoorthy A, Pramod PK, Deepak TG (2009b) On a queue with interruptions and repeat or resumption of service. Nonlinear Anal Theory Methods Appl 71(12):1673–1683
Krishnamoorthy A, Gopakumar B, Viswanath CN (2010a) An M/E n /1 queue with protected and unprotected phases of service from interruption. Presented at QTNA conference held in Beijing, June 2010
Krishnamoorthy A, Gopakumar B, Viswanath CN (2010b) A retrial queue with server interruptions, resume and restart of service. Presented at the VII International Workshop on Retrial Queues held in Beijing, June 2010
Krishnamoorthy A, Pramod PK, Chakravarthy SR (2011) On a queue with interruption controlled by a super clock and bound on maximum number of interruptions. Submitted for publication
Kroese DP, Nicola VF (1999) Efficient estimation of overflow probabilities in queues with breakdowns. Perform Eval 36–37:471–484
Kulkarni VG, Choi BD (1990) Retrial queues with server subject to breakdowns and reairs. Queueing Syst, Theory Appl 7(2):191–208
Kulkarni VG, Nicola NF, Trivedi KS (1986) On modelling the performance and reliability of multimode computer systems. J Syst Softw 6(1–2):175–182
Kulkarni VG, Nicola NF, Trivedi KS (1987) The completion time of a job in multimode systems. Adv Appl Probab 19:932–954
Laevens K, Bruneel H (1995) Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers. Eur J Oper Res 85:161–177
Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modelling. ASA-SIAM, Philadelphia
Lee DS (1997) Analysis of a single server queue with semi-Markovian service interruption. Queueing Syst 27:153–178
Li JH, Wang J-T (2006) M/M/N queue system with balking reneging and server breakdowns. J Beijing Jiaotong Univ 30(3):84–87. Beijing Jiaotong Daxue Xuebao
Li H, Zhao YQ (2005) A retrial queue with a constant retrial rate, server breakdowns and impatient customers. Stoch Models 21(2–3):531–550
Li Q, Yu Y, Zhao YQ (2006) A BMAP/G/1 retrial queue with a server subject to breakdowns and repairs. Ann Oper Res 141:233–270
Liu Z, Wu J, Yang G (2009) An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs. Comput Math Appl 58(9):1792–1807
Lucatoni D (1991) New results on the single server queue with a batch Markovian arrival process. Stoch Models 7:1–46
Lv S, Li J, Yue D, Xiao X (2008) The M/M/2 repairable queueing system. In: 2007 IEEE international conference on control and automation, ICCA, pp 2071–2075
Lv SL, Li JB, Yue DQ (2009) The M/M/1 repairable queueing system with variable breakdowns rates. In: Chinese control and decision conference, CCDC, pp 2635–2637
Madan KC (1973) A priority queueing system with service interruptions. Stat Neerl 27:115–123
Madan KC (1976) Interrupted service queueing with arrivals and departures in batches of variable size. Math Operforsch Stat 7(1):139–149
Madan KC (1989) A single channel queue with bulk service subject to interruptions. Microelectron Reliab 29:813–818
Madan KC (1992) A bulk queueing system with random failures and two phase repairs. Microelectron Reliab 32:669–677
Madan KC (2000) An M/G/1 queue with second optional service. Queueing Syst, Theory Appl 31(1):37–46
Masuyama H, Takine T (2003) Stationary queue length in a FIFO single server queue with service interruptions and multiple batch Markovian arrival streams. J Oper Res Soc Jpn 46(3):319–341
Medhi J (2002) A single server Poisson input queue with a second optional channel. Queueing Syst 42(1):239–242
Mehmet-Ali M, Zhang X, Hayes JF (2003) A performance analysis of a discrete-time queueing system with server interruption for modeling wireless ATM multiplexer. Perform Eval 51(1):1–31
Milovanova TA (2007a) BMAP/G/1/r System with last come first served probabilistic priority. In: Inform protsessy, pp 153–167
Milovanova TA (2007b) Stationary characteristics related to the time of customer sojourn in the BMAP/G/1/r/LCFSPP system. In: Inform protsessy, pp 411–424
Milovanova TA (2009) BMAP/G/1/∞ System with last come first served probabilistic priority. Autom Remote Control 70:885–896
Mitrani LL, Avi-Itzhak B (1968) A many server queue with service interruptions. Oper Res 16:628–638
Mohebbi E (2003) Supply interruptions in a lost-sales inventory system with random lead time. Comput Oper Res 30(3):411–426
Nain P (1983) Queueing systems with service interruptions: an approximation model. Perform Eval 3:123–129
Neuts MF (1979) A versatile Markovian point process. J Appl Probab 16:764–779
Neuts MF (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore [1994 version is Dover Edition]
Neuts MF (1989) Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York
Neuts MF, Lucatoni D (1979) A Markovian queue with N servers subject to breakdowns and repairs. Manag Sci 25:849–861
Nicola VF (1986) A single server queue with mixed types of interruptions. Acta Inf 23:465–486
Nicola VF (1983) Single server queue with mixed types of interruptions: application to the modelling of check pointing and recovery in a transactional system. EUT report—Eindhoven University of Technology, Department of Electrical Engineering
Nunez-Queija R (2000) Sojourn times in a processor sharing queue with service interruptions. Queueing Syst 34:351–386
Pang G, Whitt W (2009) Heavy-traffic limits for many-server queues with service interruptions. Queueing Syst 61:167–202
Pechinkin A, Shorgin S (2010) A Geo m /G/1/n queueing system with lifo discipline. In: Service interruptions and repeat again service, and restrictions on the total volume of demands. Lecture notes in computer science, vol 6235. Springer, Berlin, pp 98–106 Multiple Access Communications
Pechinkin AV, Svishcheva TA (2002) MAP/G/1/r system with LCFS probabilistic priority. In: Vestn Ross univ druzhby narodov, ser prikl mat inf, pp 80–89
Pechinkin AV, Svishcheva TA (2003) MAP/G/1/∞ system with LCFS probabilistic priority. In: Vestn Ross univ druzhby narodov, ser prikl mat inf, pp 109–118
Pramod PK (2010) GEO/G/1 queue with service interruption. Bull Kerala Math Assoc 6(1):9–16
Pyke R (1961) Markov renewal processes: Definitions and preliminary properties. Ann Math Stat 32:1231–1242
Ramaswami V (1980) The N/G/1 queue and its detailed analysis. Adv Appl Probab 12:222–261
Robert P, Mitrani I, King PJB (1988) An intermittently served discrete time queue with applications to meteor scatter communications. Queueing Syst 3(1):25–40
Samira T, Aissani A (2010) Unreliable M/G/1 retrial queue: monotonicity and comparability. Queueing Syst 64:227–252
Sandhu D, Posner MJM (1989) A priority M/G/1 queue with to voice/data communication. Eur J Oper Res 40:99–108
Sengupta B (1990) Queue with service interruptions in an alternating random environment. Oper Res 38(2):308–318
Sherman NP, Kharoufeh JP (2006) An M/M/1 retrial queue with unreliable server. Oper Res Lett 34(6):697–705
Sherman NP, Kharoufeh JP, Abramson MA (2009) An M/G/1 retrial queue with unreliable server for streaming multimedia applications. Probab Eng Inf Sci 23(2):281–304
Singh IP, Ram C (1991) Three-server bulk service queue with service interruptions and exponential repairs. Microelectron Reliab 31:257–259
Sondhi MM, Gopinath B, Mitra D (1974) Formulas on queues in burst processes – 2. Bell Syst Tech J 53(3):425–448
Tadj L, Choudhary G (2005) Optimal design and control of queues. TOP 13(2):359–412
Tadj L, Choudhary G (2009) A quorum queueing system with an unreliable server. Appl Math Lett 22:1710–1714
Takagi H (1991) Queueing analysis: a foundation of performance evaluation, vol. 1: Vacation and priority systems, Part 1. Amsterdam, Elsevier
Takagi H (1993) Queueing analysis, vol 3: Discrete-time systems. Amsterdam, Elsevier
Takine T, Sengupta B (1997) A single server queue with service interruptions. Queueing Syst 26:285–300
Takine T, Sengupta B, Hasegawa T (1994) An analysis of a discrete-time queue for broadband ISDN with priorities among traffic classes. IEEE Trans Commun 42(2/3):4
Tatashev AG (1995) An inverse service discipline in a queuing system with batch input. Autom. Control Comput. Sci. 29(1):39–43
Tatashev AG (1999) Priority-service discipline in an M n /G n /1/1 system. Cybern Syst Anal 35(5):841–843
Tatashev AG (2000) A single-channel system with inverse service discipline and heterogeneous demands. Cybern Syst Anal 36(3):459–462
Tatashev AG (2001a) The \(\mathit{MAP}/G_{N_{1}}/1\) queueing system with two special service disciplines. Autom Remote Control 62(12):1958–1963
Tatashev AG (2001b) A queueing system M N |G N |1|1 with loss of interrupted requests. Cybern Syst Anal 37(4):615–617
Tatashev AG (2002) A MAP/G/1/n system of inverse service discipline and resumption of service of an interrupted customer with his initial duration. Autom Remote Control 63(11):1789–1793
Tatashev AG (2003a) Stationary probabilities of states of a queuing system with an inverse discipline and demands of three types. Cybern Syst Anal 39(6):918–920
Tatashev AG (2003b) A queueing system with inverse discipline, two types of customers and Markov input flow. Autom Remote Control 64(11):1755–1759
Thirurengadan K (1963) Queueing with breakdowns. Oper Res 11:62–71
Tian N, Zhang ZG (2006) Vacation queueing models–theory and applications. Springer international series. Springer, Berlin
Towsley D (1980) The analysis of a statistical multiplexer with nonindependent arrivals and errors. IEEE Trans Commun COM-28:65–72
Uluscu OS, Altiok T (2009) Waiting time approximation in single-class queueing systems with multiple types of interruptions: Modeling congestion at waterways entrances. Ann Oper Res 172(1):291–313
Uluscu OS, Ozbas B, Altiok T, Or I, Almaz AO (2009) Transit vessel scheduling in the Strait of Istanbul. J Navig 62:59–77
Varghese J, Chakravarthy SR, Krishnamoorthy A (2010) On a customer induced interruption in a service system. In: 8th International workshop on retrial queues, Beijing, July
Varghese J, Chakravarthy SR, Krishnamoorthy A (2012) On a customer induced interruption in a service system. To appear in J Stoch Anal Appl
Vinck B, Bruneel H (2006) System delay versus system content for discrete-time queueing systems subject to server interruptions. Eur J Oper Res 175(1):362–375
Walraevens J, Steyaert B, Bruneel H (2006) A preemptive repeat priority queue with resampling: performance analysis. Ann Oper Res 146:189–202
Wang J (2004) An M/G/1 queue with second optional service and service breakdowns. Comput Math Appl 47:1713–1723
Wang J, Cao J (2001) Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Syst, Theory Appl 38(4):363–380
Wang J, Zhao Q (2007) A discrete time Geo/G/1 retrial queue with stating failures and second optional service. Comput Math Appl 53(1):115–127
White H, Christie LS (1958) Queueing with preemptive priorities or with breakdowns. Oper Res 6:79–95
Yang OWW, Mark JW (1990) Performance analysis of integrated services on a single server system. Perform Eval 11:79–92
Yue D, Tu F (2001) On the completion time of a job processed on an unreliable machine. Acta Math Appl Sin 17(3):418–425
Acknowledgements
The authors thank the anonymous referees for their valuable suggestions that improved the presentation of the material.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krishnamoorthy, A., Pramod, P.K. & Chakravarthy, S.R. Queues with interruptions: a survey. TOP 22, 290–320 (2014). https://doi.org/10.1007/s11750-012-0256-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-012-0256-6