Entropy maximization and NT vacation M/G/1 model with a startup and unreliable server: comparative analysis on the first two moments of system size

References

• Alfa , A. S. and Frigui , I. 1996 . Discrete NT-policy single serverqueue with Markovian arrival process and phase type service . Eur. J. Oper. Res. , 88 : 599 – 613 .
   Web of Science ®Google Scholar
• Alfa , A. S. and Li , W. 2000 . Optimal (N,T)-policy for M/G/1 system with cost structures . Perform. Eval. , 42 : 265 – 277 .
   Google Scholar
• Arizono , I. , Cui , Y. and Ohta , H. 1991 . An analysis of M/M/S queueing systems based on the maximum entropy principle . J. Oper. Res. Soc. , 42 : 69 – 73 .
   Web of Science ®Google Scholar
• Artalejo , J. R. and Lopez-Herrero , M. J. 2004 . Entropy maximization and the busy period of some single-server vacation models . RAIRO Oper. Res. , 38 : 195 – 213 .
   Google Scholar
• Baker , K. R. 1973 . A note on operating policies for the queue M/M/1 with exponential startup . INFOR , 11 : 71 – 72 .
   Google Scholar
• Borthakur , A. and Medhi , J. 1987 . Poisson input queueing system with startup time and under control-operating policy . Comput. Oper. Res. , 14 : 33 – 40 .
   Web of Science ®Google Scholar
• Borthakur , A. , Medhi , J. and Gohain , R. 1987 . Poisson input queueing systems with startup time and under control operating policy . Comput. Oper. Res. , 14 : 33 – 40 .
   Web of Science ®Google Scholar
• Burden , R. L. and Faires , J. D. 1989 . Numerical Analysis , 4 , Thomson : Information/Publishing Group .
   Google Scholar
• Doganata , Y. N. 1990 . “ NT-vacation policy for M/G/1 queue with starter ” . In Communication, Control, and Signal Processing , Edited by: Arikan , E. 663 – 1669 . Amsterdam : Elsevier Science .
   Google Scholar
• Doshi , B. T. 1986 . Queueing systems with vacations – a survey . Queueing Syst. , 1 : 29 – 66 .
   Google Scholar
• El-Affendi , M. A. and Kouvatsos , D. D. 1983 . A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium . Acta Inform. , 19 : 339 – 355 .
   Web of Science ®Google Scholar
• Gakis , K. G. , Rhee , H. K. and Sivazlian , B. D. 1995 . Distributions and first moments of the busy and idle periods in controllable M/G/1 queueing models with simple and dyadic policies . Stoch. Anal. Appl. , 13 ( 1 ) : 47 – 81 .
   Web of Science ®Google Scholar
• Gaver , D. P. 1962 . A waiting line with interrupted service, including priorities . J. Roy. Stat. Soc. Ser. B , 24 : 73 – 96 .
   Google Scholar
• Guiasu , S. 1986 . Maximum entropy condition in queueing theory . J. Opl. Res. Soc. , 37 : 293 – 301 .
   Web of Science ®Google Scholar
• Hur , S. and Paik , S. J. 1999 . The effect of different arrival rates on the N-policy of M/G/1 with server setup . Appl. Math. Model. , 23 : 289 – 299 .
   Web of Science ®Google Scholar
• Hur , S. , Kim , J. and Kang , C. 2003 . An analysis of the M/G/1 system with N and T policy . Appl. Math. Model. , 27 : 665 – 675 .
   Google Scholar
• Ke , J. C. 2003 . The analysis of a general input queue with N policy and exponential vacations . Queueing Syst. , 45 : 135 – 160 .
   Web of Science ®Google Scholar
• Ke , J. C. 2004 . Bi-level control for batch arrival queues with an early startup and un-reliable server . Appl. Math. Model. , 28 : 469 – 485 .
   Web of Science ®Google Scholar
• Ke , J.-C. 2006 . On M/G/1 system under NT policies with breakdowns, startup and closedown . Appl. Math. Model. , 30 : 49 – 66 .
   Web of Science ®Google Scholar
• Ke , J.-C. and Lin , C. H. 2006 . Maximum entropy solutions for batch arrival queue with an un-reliable server and delaying vacations . Appl. Math. Comput. , 183 : 1328 – 1340 .
   Web of Science ®Google Scholar
• Ke , J.-C. and Wang , K. H. 2003 . Analysis of operating characteristics for the heterogeneous batch arrivals queue with server startup and breakdowns . RAIRO-Oper. Res. , 37 : 157 – 177 .
   Google Scholar
• Kouvatsos , D. D. 1986 . Maximum entropy and the G/G/1/N queue . Acta Inform. , 23 : 545 – 565 .
   Web of Science ®Google Scholar
• Lee , H. W. and Park , J. O. 1997 . Optimal strategy in N-policy production system with early set-up . J. Oper. Res. Soc. , 48 : 306 – 313 .
   Web of Science ®Google Scholar
• Li , W. and Alfa , A. S. 2000 . Optimal policies for M/M/m queue with two different kinds of (N,T)-policies . Naval Res. Logist. , 47 : 240 – 258 .
   Web of Science ®Google Scholar
• Li , W. , Shi , D. and Chao , X. 1997 . Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations . J. Appl. Prob. , 34 : 546 – 555 .
   Web of Science ®Google Scholar
• Medhi , J. and Templeton , J. G.C. 1992 . A Poisson input queue under N-policy and with a general start up time . Comput. Oper. Res. , 19 ( 1 ) : 35 – 41 .
   Web of Science ®Google Scholar
• Minh , D. L. 1988 . Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations . Eur. J. Oper. Res. , 36 : 197 – 201 .
   Web of Science ®Google Scholar
• Pearn , W. L. , Ke , J.-C. and Chang , Y. C. 2004 . Sensitivity analysis of the optimal management policy for a queueing system with a removable and non-reliable server . Comput. Ind. Eng. , 46 : 87 – 99 .
   Web of Science ®Google Scholar
• Sengupta , B. 1990 . A queue with service interruptions in an alternating random environment . Oper. Res. , 38 : 308 – 318 .
   Web of Science ®Google Scholar
• Shore , J. E. Derivation of equilibrium and time-dependent solutions to M/M/∞/N and M/M/∞ queueing systems using entropy maximization . Proceedings of National Computer Conference . pp. 483 – 487 . AFIPS .
   Google Scholar
• Shore , J. E. 1982 . Information theoretic approximations for M/G/1 and G/G/1 queueing systems . Acta Inform. , 17 : 43 – 61 .
   Web of Science ®Google Scholar
• Takagi , H. 1993 . M/G/1/K queues with N-policy and setup times . Queueing Syst. , 14 : 79 – 98 .
   Google Scholar
• Tang , Y. H. 1997 . A single-server M/G/1 queueing system subject to breakdowns – some reliability and queueing problem . Microelectronics Reliab. , 37 : 315 – 321 .
   Web of Science ®Google Scholar
• Wang , K.-H. , Shuang , S. L. and Pearn , W. L. 2002 . Maximum entropy analysis to the N policy M/G/1 queueing system with a removable server . Appl. Math. Model. , 26 : 1151 – 1162 .
   Google Scholar
• Wang , K.-H. , Wang , T. Y. and Pearn , W. L. 2005 . Maximum entropy analysis to the N policy M/G/1 queueing system with server breakdowns and general startup times . Appl. Math. Comput. , 165 : 45 – 61 .
   Web of Science ®Google Scholar
• Wang , K.-H. 2005 . Comparative analysis for the N policy M/G/1 queueing system with a removable and unreliable server . Math. Meth. Oper. Res. , 61 : 505 – 520 .
   Google Scholar