Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

References

• Albin , S. 1984 . Approximating a point process by a renewal process, II: superposition arrival processes to queues . Operations Research , 32 ( 5 ) : 1133 – 1162 .
   Web of Science ®Google Scholar
• Altíok , T. 1997 . Performance Analysis of Manufacturing Systems , New York, NY : Springer-Verlag .
   Google Scholar
• Altíok , T. and Melamed , B. 2001 . The case for modeling correlation in manufacturing Systems . IIE Transactions , 33 : 779 – 791 .
   Web of Science ®Google Scholar
• Avi-Itzhak , B. and Naor , P. 1963 . Some queueing problems with the service station subject to breakdown . Operations Research , 11 : 303 – 320 .
   Web of Science ®Google Scholar
• Balcío[gtilde]lu , B. , Jagerman , D. L. and Altíok , T. 2005 . Merging and splitting autocorrelated arrival processes and impact on queueing performance. Technical report TR-2005-020, Department of Industrial & Systems Engineering, Rutgers University, Piscataway, NJ 08854
   Google Scholar
• Dallery , Y. and Gershwin , S. B. 1992 . Manufacturing flow line systems: a review of models and analytical results . Queueing Systems , 12 : 3 – 94 .
   Google Scholar
• Davis , P. J. and Rabinowitz , P. 1967 . Numerical Integration , Waltham, MA : Blaisdell .
   Google Scholar
• Federgruen , A. and Green , L. 1986 . Queueing systems with service interruptions . Operations Research , 34 : 752 – 768 .
   Web of Science ®Google Scholar
• Federgruen , A. and Green , L. 1988 . Queueing systems with service interruptions II . Naval Research Logistics , 35 : 345 – 358 .
   Web of Science ®Google Scholar
• Fendick , K. W. , Saksena , V. R. and Whitt , W. 1989 . Dependence in packet queues . IEEE Transactions on Communications , 37 : 1173 – 1183 .
   Web of Science ®Google Scholar
• Fischer , W. and Meier-Hellstern , K. 1992 . The Markov-modulated Poisson process (MMPP) cookbook . Performance Evaluation , 18 : 149 – 171 .
   Web of Science ®Google Scholar
• Gaver , D. P. 1962 . A waiting line with interrupted service including priorities . Journal of the Royal Statistical Society , B24 : 73 – 90 .
   Google Scholar
• Gray , W. J. , Wang , P. P. and Scott , M. 2004 . A queueing model with multiple types of server breakdowns . Quality Technology & Quantitative Management , 1 ( 2 ) : 245 – 255 .
   Google Scholar
• Jagerman , D. L. 1982 . An inversion technique for the Laplace transform . Bell System Technical Journal , 61 ( 8 ) : 1995 – 2002 .
   Google Scholar
• Jagerman , D. L. , Balcío[gtilde]lu , B. , Altíok , T. and Melamed , B. 2004 . Mean waiting time approximations in the G/G/1 Queue . Queueing Systems , 46 ( 3 ) : 481 – 506 .
   Web of Science ®Google Scholar
• Jagerman , D. L. and Melamed , B. 1992a . The transition and autocorrelation structure of TES processes part I: general theory . Stochastic Models , 8 ( 2 ) : 193 – 219 .
   Google Scholar
• Jagerman , D. L. and Melamed , B. 1992b . The transition and autocorrelation structure of TES processes part II: special cases . Stochastic Models , 8 ( 3 ) : 499 – 527 .
   Google Scholar
• Jardine , A. K.S. and Tsang , A. H.C. 2006 . Maintenance, Replacement and Reliability , Boca Raton, FL : Taylor & Francis .
   Google Scholar
• Kleinrock , L. 1975 . Queueing Systems, Vol. I: Theory , New York, NY : Wiley .
   Google Scholar
• Li , W. , Shi , D. and Chao , X. 1997 . Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations . Journal of Applied Probability , 34 ( 2 ) : 546 – 555 .
   Web of Science ®Google Scholar
• Livny , M. , Melamed , B. and Tsiolis , A. K. 1993 . The impact of autocorrelation on queuing systems . Management Science , 39 ( 3 ) : 322 – 339 .
   Web of Science ®Google Scholar
• Melamed , B. 1991 . TES: a class of methods for generating autocorrelated uniform variates . ORSA Journal on Computing , 3 : 317 – 329 .
   Google Scholar
• Melamed , B. 1993 . “ An overview of TES processes and modeling methodology ” . In Performance Evaluation of Computer and Communication Systems , Edited by: Donatiello , L. and Nelson , R. 359 – 393 . London, , UK : Springer-Verlag .
   Google Scholar
• Mitrany , I. L. and Avi-Itzhak , B. 1968 . A many-server queue with service interruptions . Operations Research , 16 : 628 – 638 .
   Web of Science ®Google Scholar
• Neuts , M. and Lucantoni , D. 1979 . A Markovian queue with N servers subject to breakdowns and repairs . Management Science , 25 ( 9 ) : 849 – 861 .
   Web of Science ®Google Scholar
• Riordan , J. 1962 . Stochastic Service Systems , New York, NY : Wiley .
   Google Scholar
• Shantikumar , J. G. and Buzacott , J. A. 1980 . On the approximation to the single server queue . International Journal of Production Research , 18 ( 6 ) : 761 – 773 .
   Web of Science ®Google Scholar
• Sherman , N. P. and Kharoufeh , J. P. 2006 . An M/M/1 retrial queue with unreliable server . Operations Research Letters , 34 ( 6 ) : 697 – 705 .
   Web of Science ®Google Scholar
• Sztrik , J. and Gál , T. 1990 . A recursive solution of a queueing model for a multi-terminal system subject to breakdowns . Performance Evaluation , 11 ( 1 ) : 1 – 7 .
   Web of Science ®Google Scholar
• Tang , Y. H. 1997 . A single-server M/G/1 queueing system subject to breakdowns-some reliability and queueing problems . Microelectronics and Reliability , 37 ( 2 ) : 315 – 321 .
   Web of Science ®Google Scholar
• Thiruvengadam , K. 1963 . Queueing with breakdowns . Operations Research , 11 : 62 – 71 .
   Web of Science ®Google Scholar
• Wang , J. , Cao , J. and Li , Q. 2001 . Reliability analysis of the retrial queue with server breakdowns and repairs . Queueing Systems , 38 ( 4 ) : 363 – 380 .
   Web of Science ®Google Scholar
• White , H. and Christie , L. S. 1958 . Queueing with preemptive priorities or with breakdowns . Operations Research , 6 : 79 – 95 .
   Web of Science ®Google Scholar
• Whitt , W. 1983 . The queueing network analyzer . Bell System Technical Journal , 62 ( 9 ) : 2779 – 2815 .
   Google Scholar
• Xueming , Y. and Li , W. 2003 . Availability analysis of the queueing system GI/PH/1 with server breakdowns . Journal of Systems Science and Complexity , 16 ( 2 ) : 177 – 183 .
   Google Scholar