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, Volume 22, Issue 1, pp 290–320 | Cite as

Queues with interruptions: a survey

  • A. Krishnamoorthy
  • P. K. Pramod
  • S. R. ChakravarthyEmail author
Original Paper

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.

Keywords

Queues with interruptions Discrete- and continuous-time queues Negative customers 

Mathematics Subject Classification

60K25 

Notes

Acknowledgements

The authors thank the anonymous referees for their valuable suggestions that improved the presentation of the material.

References

  1. Aissani A (1988) On the M/G/1/1 queueing system with repeated orders and unreliable server. J Technol 6:98–123 Google Scholar
  2. Aissani A (1993) Unreliable queueing with repeated orders. Microelectron Reliab 33:2093–2106 Google Scholar
  3. Aissani A (1994) A retrial queue with redundancy and unreliable server. Queueing Syst 17:431–449 Google Scholar
  4. Aissani A, Artalejo JR (1998) On the single server retrial queue subject to breakdowns. Queueing Syst, Theory Appl 30(3–4):309–321 Google Scholar
  5. Alfa AS (2002) Discrete time queues and matrix-analytic methods. TOP, Span J Stat Oper Res 10(2):147–185 Google Scholar
  6. Altiok T (1989) Queueing modelling of a single processor with failures. Perform Eval 9:93–102 Google Scholar
  7. Altiok T, Vu-Duy C, Baykal-Gursoy M (1998) Two load sharing processors with failures. Comput Oper Res 25(3):183–189 Google Scholar
  8. Anisimov VV, Atadzhanov KL (1994) Diffusion approximation of the systems with repeated call and unreliable server. J Math Sci 72:3032–3034 Google Scholar
  9. Artalejo JR, Gomez-Correl A, He QM (2010) Markovian arrivals in stochastic modelling: a survey and some new results. SORT 34(2):101–144 Google Scholar
  10. 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 Google Scholar
  11. 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 Google Scholar
  12. Avi-Itzhak B, Naor P (1963) Some queueing problems with the service station subject to breakdowns. Oper Res 11:303–320 Google Scholar
  13. Baccelli F, Trivedi KS (1985) A single server queue in a hard-real-time environment. Oper Res Lett 4:161–168 Google Scholar
  14. 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 Google Scholar
  15. Baykal-Gursoy M, Duan Z (2006) M/M/C queues with Markov modulated service processes. ACM Int Conf Proc Ser 180:119-143 Google Scholar
  16. Baykal-Gursoy M, Xiao W (2004) Stochastic decomposition in M/M/∞ queues with Markov modulated service rates. Queueing Syst 48:75–88 Google Scholar
  17. Baykal-Gursoy M, Xiao W, Ozbay K (2009) Modeling traffic flow interrupted by incidents. Eur J Oper Res 195:127–138 Google Scholar
  18. Bhat UN (1992) Switched Poisson process/G/1 queue with service interruptions. Comput Oper Res 19(8):751–756 Google Scholar
  19. Bocharov PP (1991) Matrix-geometric queue distribution under LCFS discipline with interruption and phase type distributions. Avtom Telemeh 9:112–122 Google Scholar
  20. Bocharov PP, Pavlova OI (1992a) Analysis of the queue with phase type distributions and inverse service discipline with interruptions. Avtom Telemeh 11:83–92 Google Scholar
  21. 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 Google Scholar
  22. Boxma OJ (1989) Workloads and waiting times in single-server systems with multiple customer classes. Queueing Syst 5:185–214 Google Scholar
  23. Boxma OJ, Konheim AG (1980) Approximate analysis of exponential queueing systems with blocking. Acta Inform 15(1):19–66 Google Scholar
  24. Bruneel H (1983) On the behavior of buffers with random server interruptions. Perform Eval 3:165–175 Google Scholar
  25. Bruneel H (1984a) Analysis of an infinite buffer system with random server interruption. Comput Oper Res 11:373–386 Google Scholar
  26. Bruneel H (1984b) Buffers with correlated input and output interruptions. Oper Res Lett 3:149–152 Google Scholar
  27. 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 Google Scholar
  28. Bruneel H (1986) A general treatment of discrete-time buffers with one randomly interrupted output line. Eur J Oper Res 27(1):67–81 Google Scholar
  29. Bruneel H (1991) Exact derivation of transient behavior for buffers with random output interruptions. Comput Netw ISDN Syst 22(4):277–285 Google Scholar
  30. Bruneel H, Kim BG (1993) Discrete-time models for communication systems including ATM. Kluwer Academic, Boston Google Scholar
  31. 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 Google Scholar
  32. 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 Google Scholar
  33. Chakravarthy SR (2010) Markovian arrival processes. Wiley encyclopedia of operations research and management science. Wiley, New York Google Scholar
  34. Chan WC, Chung WK (1972) Computer-controlled queuing system with service interruptions. Proc Inst Electr Eng 119(9):1262–1268 Google Scholar
  35. 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 Google Scholar
  36. Chan W, Bartoszynski R, Pearl D (1993) Queues with breakdowns and customer discouragement. Probab Math Stat 14:77–87 Google Scholar
  37. 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 Google Scholar
  38. 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 Google Scholar
  39. 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 Google Scholar
  40. 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 Google Scholar
  41. 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 Google Scholar
  42. Co HC, Abdelaziz A (1991) Age-maintenance of an M/G/1 production system. Int J Prod Res 29(10):2135–2149 Google Scholar
  43. Cox DR (1955) The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Math Proc Camb Philos Soc 51:433–441 Google Scholar
  44. 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 Google Scholar
  45. 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 Google Scholar
  46. Doshi BT (1986) Queueing systems with vacations—a survey. Queueing Syst, Theory Appl 1(1):29–66 Google Scholar
  47. Dragalin VP, Mishkoy GK (1984) Servicing with mixed priority and orientation. Eng Cybern 22(5):9–15 Google Scholar
  48. Drekic S (2003) A preemptive resume queue with an expiry time for retained service. Perform Eval 54(1):59–74 Google Scholar
  49. 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 Google Scholar
  50. Efrosinin D, Semenova O (2009) Queueing model with non-reliable server and threshold-based recovery. In: Conference proceedings, MMR2009, Moscow, pp 546–550 Google Scholar
  51. El-Taha M (2003) Allocation of service time in a two-server system. Comput Oper Res 30(5):683–693 Google Scholar
  52. El-Taha M, Maddah B (2006) Allocation of service time in a multiserver system. Manag Sci 52(4):623–637 Google Scholar
  53. Federgruen A, Green L (1986) Queueing systems with service interruptions. Oper Res 34:752–768 Google Scholar
  54. Federgruen A, Green L (1988) Queueing systems with service interruptions II. Nav Res Logist Q 35:345–358 Google Scholar
  55. 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 Google Scholar
  56. 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 Google Scholar
  57. 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 Google Scholar
  58. Fiems D, Steyaert B, Bruneel H (2002) Randomly interrupted GI-G-1 queues: service strategies and stability issues. Ann Oper Res 112:171–183 Google Scholar
  59. 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 Google Scholar
  60. 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 Google Scholar
  61. Fiems D, Maertens T, Brunee H (2008) Queueing systems with different types of interruptions. Eur J Oper Res 188(3):838–845 Google Scholar
  62. Fischer MJ (1977) An approximation to queueing systems with interruptions. Manag Sci 24:338–344 Google Scholar
  63. Gaver DP (1962) A waiting line with interrupted service including priority. J Rl Stat Soc B 24:73–90 Google Scholar
  64. Gaver DP (1968) Diffusion approximation and models for certain congestion problems. J Appl Probab 5:607–623 Google Scholar
  65. 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 Google Scholar
  66. Gelenbe E, Derochette D (1978) Performance of rollback recovery systems under intermittent failures. Commun ACM 21(6):493–499 Google Scholar
  67. Georganas ND (1976) Buffer behavior with poisson arrivals and bulk geometric service. IEEE Trans Commun Technol 24:938–940 Google Scholar
  68. 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 Google Scholar
  69. 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 Google Scholar
  70. 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 Google Scholar
  71. Gray WJ, Wang PP, Scott M (2004) A queueing model with multiple types of server breakdowns. Qual Technol Quant Manag 1(2):245–255 Google Scholar
  72. Greenberg AG, Srikant R, Whitt W (1999) Resource sharing for book-ahead and instantaneous-request calls. IEEE/ACM Trans Netw 7(1):10–22 Google Scholar
  73. Gupta SM, Kavusturucu A (2000) Production systems with interruptions, arbitrary topology and finite buffers. Ann Oper Res 93:145–176 Google Scholar
  74. 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 Google Scholar
  75. Heines TS (1979) Buffer behavior in computer communication systems. IEEE Trans Comput 28:573–576 Google Scholar
  76. Hsieh Y-C, Andersland MS (1995) Repairable single server systems with multiple breakdowns modes. Microelectron Reliab 35:309–318 Google Scholar
  77. Hsu J (1974) Buffer behavior with Poisson arrival and geometric output processes. IEEE Trans Commun Technol 22:1940–1941 Google Scholar
  78. Ibe OC, Trivedi KS (1990) Two queues with alternating service and server breakdowns. Queueing Syst 7(3–4):253–268 Google Scholar
  79. Ishizaki F (2004) Decomposition property in a discrete-time queue with multiple input streams and service interruptions. J Appl Probab 41(2):524–534 Google Scholar
  80. 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 Google Scholar
  81. Ishizaki F, Takine T, Takahashi Y, Hasegawa T (1994) A generalized SBBP/G/1 queue and its applications. Perform Eval 21:163–181 Google Scholar
  82. 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 Google Scholar
  83. Jain M, Bhargava C (2008) Bulk arrival retrial queue with unreliable server and priority subscribers. Int J Oper Res 5(4):242–259 Google Scholar
  84. Jain M, Jain A (2010) Working vacations queueing model with multiple types of server breakdowns. Appl Math Model 34:1–13 Google Scholar
  85. Jaiswal NK (1961) Preemptive resume priority queue. Oper Res, 9:732–742 Google Scholar
  86. Jayawardene AK, Kella O (1996) M/G/∞ with alternating renewal breakdowns. Queueing Syst 22:79–95 Google Scholar
  87. 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 Google Scholar
  88. 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 Google Scholar
  89. Kamoun F (2009) Performance evaluation of a queuing system with correlated packet-trains and server interruption. Telecommun Syst 41(4):267–277 Google Scholar
  90. Karlin S, Taylor HE (1975) A first course in stochastic processes, 2nd edn. Academic Press, San Diego Google Scholar
  91. Ke JC (2004) Bi-level control for batch arrival queues with an early startup and un-reliable server. Appl Math Model 28:469–485 Google Scholar
  92. 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 Google Scholar
  93. 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 Google Scholar
  94. Ke JC (2006b) On M/G/1 system under N-T policies with breakdowns, startup and closedown. Appl Math Model 30:49–66 Google Scholar
  95. Ke JC (2007) Batch arrival queues under vacation policies with server breakdowns and startup/closedown times. Appl Math Model 31(7):1282–1292 Google Scholar
  96. 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 Google Scholar
  97. Keilson J (1962) Queues subject to service interruptions. Ann Math Stat 33(4):1314–1322 Google Scholar
  98. 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 Google Scholar
  99. 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 Google Scholar
  100. Kernane T (2009) A single server retrial queue with different types of server interruptions. E-prints, February 2009 Google Scholar
  101. 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 Google Scholar
  102. 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 Google Scholar
  103. Koba EV (2001) On a queueing system with repetition and pushing calls out. J Autom Inf Sci 33(3):48–51 Google Scholar
  104. 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 Google Scholar
  105. Krishnamoorthy A, Pramod PK (2010) On a discrete time queue with interruptions and repeat or resumption of service. Submitted for publication Google Scholar
  106. 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 Google Scholar
  107. 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 Google Scholar
  108. 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 Google Scholar
  109. 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 Google Scholar
  110. 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 Google Scholar
  111. Kroese DP, Nicola VF (1999) Efficient estimation of overflow probabilities in queues with breakdowns. Perform Eval 36–37:471–484 Google Scholar
  112. Kulkarni VG, Choi BD (1990) Retrial queues with server subject to breakdowns and reairs. Queueing Syst, Theory Appl 7(2):191–208 Google Scholar
  113. 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 Google Scholar
  114. Kulkarni VG, Nicola NF, Trivedi KS (1987) The completion time of a job in multimode systems. Adv Appl Probab 19:932–954 Google Scholar
  115. Laevens K, Bruneel H (1995) Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers. Eur J Oper Res 85:161–177 Google Scholar
  116. Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modelling. ASA-SIAM, Philadelphia Google Scholar
  117. Lee DS (1997) Analysis of a single server queue with semi-Markovian service interruption. Queueing Syst 27:153–178 Google Scholar
  118. 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 Google Scholar
  119. 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 Google Scholar
  120. 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 Google Scholar
  121. 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 Google Scholar
  122. Lucatoni D (1991) New results on the single server queue with a batch Markovian arrival process. Stoch Models 7:1–46 Google Scholar
  123. 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 Google Scholar
  124. 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 Google Scholar
  125. Madan KC (1973) A priority queueing system with service interruptions. Stat Neerl 27:115–123 Google Scholar
  126. Madan KC (1976) Interrupted service queueing with arrivals and departures in batches of variable size. Math Operforsch Stat 7(1):139–149 Google Scholar
  127. Madan KC (1989) A single channel queue with bulk service subject to interruptions. Microelectron Reliab 29:813–818 Google Scholar
  128. Madan KC (1992) A bulk queueing system with random failures and two phase repairs. Microelectron Reliab 32:669–677 Google Scholar
  129. Madan KC (2000) An M/G/1 queue with second optional service. Queueing Syst, Theory Appl 31(1):37–46 Google Scholar
  130. 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 Google Scholar
  131. Medhi J (2002) A single server Poisson input queue with a second optional channel. Queueing Syst 42(1):239–242 Google Scholar
  132. 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 Google Scholar
  133. Milovanova TA (2007a) BMAP/G/1/r System with last come first served probabilistic priority. In: Inform protsessy, pp 153–167 Google Scholar
  134. 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 Google Scholar
  135. Milovanova TA (2009) BMAP/G/1/∞ System with last come first served probabilistic priority. Autom Remote Control 70:885–896 Google Scholar
  136. Mitrani LL, Avi-Itzhak B (1968) A many server queue with service interruptions. Oper Res 16:628–638 Google Scholar
  137. Mohebbi E (2003) Supply interruptions in a lost-sales inventory system with random lead time. Comput Oper Res 30(3):411–426 Google Scholar
  138. Nain P (1983) Queueing systems with service interruptions: an approximation model. Perform Eval 3:123–129 Google Scholar
  139. Neuts MF (1979) A versatile Markovian point process. J Appl Probab 16:764–779 Google Scholar
  140. Neuts MF (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore [1994 version is Dover Edition] Google Scholar
  141. Neuts MF (1989) Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York Google Scholar
  142. Neuts MF, Lucatoni D (1979) A Markovian queue with N servers subject to breakdowns and repairs. Manag Sci 25:849–861 Google Scholar
  143. Nicola VF (1986) A single server queue with mixed types of interruptions. Acta Inf 23:465–486 Google Scholar
  144. 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 Google Scholar
  145. Nunez-Queija R (2000) Sojourn times in a processor sharing queue with service interruptions. Queueing Syst 34:351–386 Google Scholar
  146. Pang G, Whitt W (2009) Heavy-traffic limits for many-server queues with service interruptions. Queueing Syst 61:167–202 Google Scholar
  147. 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 Google Scholar
  148. 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 Google Scholar
  149. 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 Google Scholar
  150. Pramod PK (2010) GEO/G/1 queue with service interruption. Bull Kerala Math Assoc 6(1):9–16 Google Scholar
  151. Pyke R (1961) Markov renewal processes: Definitions and preliminary properties. Ann Math Stat 32:1231–1242 Google Scholar
  152. Ramaswami V (1980) The N/G/1 queue and its detailed analysis. Adv Appl Probab 12:222–261 Google Scholar
  153. 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 Google Scholar
  154. Samira T, Aissani A (2010) Unreliable M/G/1 retrial queue: monotonicity and comparability. Queueing Syst 64:227–252 Google Scholar
  155. Sandhu D, Posner MJM (1989) A priority M/G/1 queue with to voice/data communication. Eur J Oper Res 40:99–108 Google Scholar
  156. Sengupta B (1990) Queue with service interruptions in an alternating random environment. Oper Res 38(2):308–318 Google Scholar
  157. Sherman NP, Kharoufeh JP (2006) An M/M/1 retrial queue with unreliable server. Oper Res Lett 34(6):697–705 Google Scholar
  158. 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 Google Scholar
  159. Singh IP, Ram C (1991) Three-server bulk service queue with service interruptions and exponential repairs. Microelectron Reliab 31:257–259 Google Scholar
  160. Sondhi MM, Gopinath B, Mitra D (1974) Formulas on queues in burst processes – 2. Bell Syst Tech J 53(3):425–448 Google Scholar
  161. Tadj L, Choudhary G (2005) Optimal design and control of queues. TOP 13(2):359–412 Google Scholar
  162. Tadj L, Choudhary G (2009) A quorum queueing system with an unreliable server. Appl Math Lett 22:1710–1714 Google Scholar
  163. Takagi H (1991) Queueing analysis: a foundation of performance evaluation, vol. 1: Vacation and priority systems, Part 1. Amsterdam, Elsevier Google Scholar
  164. Takagi H (1993) Queueing analysis, vol 3: Discrete-time systems. Amsterdam, Elsevier Google Scholar
  165. Takine T, Sengupta B (1997) A single server queue with service interruptions. Queueing Syst 26:285–300 Google Scholar
  166. 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 Google Scholar
  167. Tatashev AG (1995) An inverse service discipline in a queuing system with batch input. Autom. Control Comput. Sci. 29(1):39–43 Google Scholar
  168. Tatashev AG (1999) Priority-service discipline in an M n/G n/1/1 system. Cybern Syst Anal 35(5):841–843 Google Scholar
  169. Tatashev AG (2000) A single-channel system with inverse service discipline and heterogeneous demands. Cybern Syst Anal 36(3):459–462 Google Scholar
  170. Tatashev AG (2001a) The \(\mathit{MAP}/G_{N_{1}}/1\) queueing system with two special service disciplines. Autom Remote Control 62(12):1958–1963 Google Scholar
  171. Tatashev AG (2001b) A queueing system M N|G N|1|1 with loss of interrupted requests. Cybern Syst Anal 37(4):615–617 Google Scholar
  172. 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 Google Scholar
  173. 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 Google Scholar
  174. Tatashev AG (2003b) A queueing system with inverse discipline, two types of customers and Markov input flow. Autom Remote Control 64(11):1755–1759 Google Scholar
  175. Thirurengadan K (1963) Queueing with breakdowns. Oper Res 11:62–71 Google Scholar
  176. Tian N, Zhang ZG (2006) Vacation queueing models–theory and applications. Springer international series. Springer, Berlin Google Scholar
  177. Towsley D (1980) The analysis of a statistical multiplexer with nonindependent arrivals and errors. IEEE Trans Commun COM-28:65–72 Google Scholar
  178. 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 Google Scholar
  179. Uluscu OS, Ozbas B, Altiok T, Or I, Almaz AO (2009) Transit vessel scheduling in the Strait of Istanbul. J Navig 62:59–77 Google Scholar
  180. 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 Google Scholar
  181. Varghese J, Chakravarthy SR, Krishnamoorthy A (2012) On a customer induced interruption in a service system. To appear in J Stoch Anal Appl Google Scholar
  182. 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 Google Scholar
  183. Walraevens J, Steyaert B, Bruneel H (2006) A preemptive repeat priority queue with resampling: performance analysis. Ann Oper Res 146:189–202 Google Scholar
  184. Wang J (2004) An M/G/1 queue with second optional service and service breakdowns. Comput Math Appl 47:1713–1723 Google Scholar
  185. Wang J, Cao J (2001) Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Syst, Theory Appl 38(4):363–380 Google Scholar
  186. 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 Google Scholar
  187. White H, Christie LS (1958) Queueing with preemptive priorities or with breakdowns. Oper Res 6:79–95 Google Scholar
  188. Yang OWW, Mark JW (1990) Performance analysis of integrated services on a single server system. Perform Eval 11:79–92 Google Scholar
  189. 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 Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2012

Authors and Affiliations

  • A. Krishnamoorthy
    • 1
  • P. K. Pramod
    • 2
  • S. R. Chakravarthy
    • 3
    Email author
  1. 1.Department of MathematicsCochin University of Science and TechnologyCochinIndia
  2. 2.Department of MathematicsCollege of EngineeringKidangoorIndia
  3. 3.Department of Industrial and Manufacturing EngineeringKettering UniversityFlintUSA

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