The Unreliable M/M/1 Retrial Queue in a Random Environment

REFERENCES

• Abramson , M.A. MATLAB implementation of NOMADm Optimization Software, 2011. http://www.gerad.ca/NOMAD/Abramson/NOMADm.html.
   Google Scholar
• Abramson , M.A. ; Audet , C. Convergence of mesh adaptive direct search to second-order stationary points . SIAM Journal on Optimization 2006 , 17 ( 2 ), 606 – 619 .
   Web of Science ®Google Scholar
• Aissani , A. On the M/G/1/1 queueing system with repeated orders and unreliable server. Journal of Technology 1988, 6, 98–123, (in French).
   Google Scholar
• Aissani , A. Unreliable queuing with repeated orders . Microelectronics and Reliability 1993 , 33 ( 14 ), 2093 – 2106 .
   Web of Science ®Google Scholar
• Aissani , A. A retrial queue with redundancy and unreliable server . Queueing Systems: Theory and Applications 1994 , 17 ( 3–4 ), 431 – 449 .
   Web of Science ®Google Scholar
• Artalejo , J.R. Analysis of an M/G/1 queue with constant repeated attempts and server vacations . Computers & Operations Research 2007 , 24 ( 6 ), 493 – 504 .
   Google Scholar
• Artalejo , J.R. New results in retrial queueing systems with breakdown of the servers. Statistica Neerlandica 1994 48 (1), 23–36.
   Google Scholar
• Artalejo , J.R. ; Gómez-Corral , A. Retrial Queueing Systems: A Computational Approach ; Springer : Berlin, Germany , 2008.
   Google Scholar
• Audet , C. Convergence results for pattern search algorithms are tight. Technical Report 98-24, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1998.
   Google Scholar
• Audet , C. ; Dennis , J.E. Pattern search algorithms for mixed variable programming . SIAM Journal on Optimization 2000 , 11 , 573 – 594 .
   Web of Science ®Google Scholar
• Audet , C. ; Dennis , J.E. Analysis of generalized pattern searches . SIAM Journal on Optimization 2003 , 13 , 889 – 903 .
   Web of Science ®Google Scholar
• Audet , C. ; Dennis , J.E. Mesh adaptive direct search algorithms for constrained optimization . SIAM Journal on Optimization 2006 , 17 ( 1 ), 188 – 217 .
   Web of Science ®Google Scholar
• Audet , C. ; Orban , D. Finding optimal algorithmic parameters using derivative-free optimization . SIAM Journal on Optimization 2006 , 17 ( 3 ), 642 – 664 .
   Web of Science ®Google Scholar
• Bright , L. ; Taylor , P.G. Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes . Communications in Statistics: Stochastic Models 1995 , 11 ( 3 ), 497 – 525 .
   Google Scholar
• Bright , L.W. ; Taylor , P.G. Equilibrium distributions for level-dependent quasi-birth-and-death processes . In Matrix Analytic Methods in Stochastic Models: Proceedings of the 1st International Conference ; Chakravarthy , S.R. , Alfa , A.S. , Eds.; Marcel, Dekker : New York , 1997 ; 359 – 375 .
   Google Scholar
• Coope , I.E. ; Price , C.J. On the convergence of grid-based methods for unconstrained optimization . SIAM Journal on Optimization 2001 , 11 , 859 – 869 .
   Web of Science ®Google Scholar
• Falin , G.I. The M/M/1 retrial queue with retrials due to server failures . Queueing Systems: Theory and Applications 2008 , 58 , 155 – 160 .
   Web of Science ®Google Scholar
• Falin , G.I. An M/G/1 retrial queue with an unreliable server and general repair times . Performance Evaluation 2010 , 67 , 569 – 582 .
   Web of Science ®Google Scholar
• Falin , G.I. ; Templeton , J.G.C. Retrial Queues ; Chapman & Hall : New York, NY , 1997 .
   Google Scholar
• Gómez-Corral , A. A bibliographical guide to the analysis of retrial queues through matrix analytic techniques . Annals of Operations Research 2006 , 141 , 163 – 191 .
   Web of Science ®Google Scholar
• Kharoufeh , J.P. Level-dependent quasi-birth-and-death processes. In Wiley Encyclopedia of Operations Research and Management Science, Cochran, J., Cox, A., Keskinocak, P., Kharoufeh, J.P., Smith, J.C., Eds.; John Wiley & Sons, Inc.: Hoboken, NJ, 2011.
   Google Scholar
• Kim , C.S. ; Klimenok , V. ; Lee , S.C. ; Dudin , A. The BMAP/PH/1 retrial queueing system operating in random environment . Journal of Statistical Planning and Inference 2007 , 137 , 3904 – 3916 .
   Web of Science ®Google Scholar
• Kim , C.S. ; Klimenok , V. ; Mushko , V. ; Dudin , A. The BMAP/PH/N retrial queueing system operating in Markovian random environment . Computers and Operations Research, 2010 , 37 , 1228 – 1237 .
   Web of Science ®Google Scholar
• Klimenok , V. A BMAP/SM/1 queueing system with hybrid operation mechanism . Automation & Remote Control 2005 , 66 ( 5 ), 779 – 790 .
   Web of Science ®Google Scholar
• Klimenok , V. ; Dudin , A. Multi-dimensional asymptotically quasi-toeplitz markov chains and their application in queueing theory . Queueing Systems: Theory and Applications 2006 , 54 , 245 – 259 .
   Web of Science ®Google Scholar
• Kulkarni , V.G. ; Choi , B.D. Retrial queues with server subject to breakdowns and repairs . Queueing Systems: Theory and Applications 1990 , 7 ( 2 ), 191 – 208 .
   Google Scholar
• Latouche , G. ; Ramaswami , V. A logarithmic reduction algorithm for quasi-birth-and-death processes . Journal of Applied Probability 1993 , 30 , 650 – 674 .
   Web of Science ®Google Scholar
• Latouche , G. ; Ramaswami , V. Introduction to Matrix-Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability. American Statistical Association and the Society for Industrial and Applied Mathematics, Alexandria, VA and Philadelphia, PA, 1999.
   Google Scholar
• Lewis , R.M. ; Torczon , V. Pattern search algorithms for bound constrained minimization . SIAM Journal on Optimization 1999 , 9 , 1082 – 1099 .
   Web of Science ®Google Scholar
• Lewis , R.M. ; Torczon , V. Pattern search algorithms for linearly constrained minimization . SIAM Journal on Optimization 2000 , 10 , 917 – 941 .
   Web of Science ®Google Scholar
• Li , H. ; Zhao , Y.Q. A retrial queue with a constant retrial rate, server break downs and impatient customers . Stochastic Models 2005 , 21 ( 2–3 ), 531 – 550 .
   Web of Science ®Google Scholar
• Moutzoukis , E. ; Langaris , C. Non-preemptive priorities and vacations in a multiclass retrial queueing system . Communications in Statistics: Stochastic Models 1996 , 12 ( 3 ), 455 – 472 .
   Google Scholar
• Neuts , M.F. Further results on the M/M/1 queue with randomly varying rates . OPSEARCH 1978 , 15 , 158 – 168 .
   Google Scholar
• Neuts , M.F. The M/M/1 queue with randomly varying arrival and service rates. OPSEARCH 1978, 15, 139–157.
   Google Scholar
• Neuts , M.F. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach ; Dover Publications , Inc. : New York , 1999 .
   Google Scholar
• Roszik , J. ; Sztrik , J. Performance analysis of finite-source retrial queues operating in random environments . International Journal of Operational Research 2007 , 2 ( 3 ), 254 – 268 .
   Google Scholar
• Sherman , N.P. ; Kharoufeh , J.P. An M/M/1 retrial queue with unreliable server . Operations Research Letters 2006 , 34 ( 6 ), 697 – 705 .
   Web of Science ®Google Scholar
• Sherman , N.P. ; Kharoufeh , J.P. Optimal Bernoulli routing in an unreliable M/G/1 retrial queue . Probability in the Engineering and Informational Sciences 2011 , 25 ( 1 ), 1 – 20 .
   Web of Science ®Google Scholar
• Sherman , N.P. ; Kharoufeh , J.P. ; Abramson , M.A. An M/G/1 retrial queue with unreliable server for streaming multimedia applications . Probability in the Engineering and Informational Sciences 2009 , 23 ( 2 ), 281 – 304 .
   Web of Science ®Google Scholar
• Torczon , V. On the convergence of pattern search algorithms . SIAM Journal on Optimization 1997 , 7 ( 1 ), 1 – 25 .
   Web of Science ®Google Scholar
• Tweedie , R.L. Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. In Mathematical Proceedings of the Cambridge Philosophical Society; 1975, Vol. 78, pp. 125–136.
   Google Scholar
• Wang , J. ; Cao , J. ; Li , Q. Reliability analysis of the retrial queue with server breakdowns and repairs . Queueing Systems: Theory and Applications 2001 , 38 ( 4 ), 363 – 380 .
   Web of Science ®Google Scholar
• Wu , J. ; Liu , Z. ; Yang , G. Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment . Applied Mathematical Modeling 2011 , 35 , 1184 – 1193 .
   Web of Science ®Google Scholar