A two-phase quorum queueing system with Bernoulli vacation schedule, setup, and N-policy for an unreliable server with delaying repair

We present in this paper a thorough classified review of queueing system with unreliable server. We then consider a queueing system where service is rendered to groups of customers of fixed quorum size. Service consists of two consecutive phases. The server needs a setup following an idle period, and may take a vacation following the second phase of service. The idle period ends only when at least N customers are in the queue. While providing service, the server may breakdown and a delay period precedes the repair period. This model generalises many of the models available in the literature. For this model, we obtain the steady state system size distributions and discuss the optimal management policy. Illustrative numerical examples are provided.

[1]  Jeffrey P. Kharoufeh,et al.  An M/M/1 retrial queue with unreliable server , 2006, Oper. Res. Lett..

[2]  Jau-Chuan Ke,et al.  Bi-level control for batch arrival queues with an early startup and un-reliable server , 2004 .

[3]  Gautam Choudhury,et al.  An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism , 2009, Appl. Math. Comput..

[4]  Jau-Chuan Ke,et al.  Batch arrival queues under vacation policies with server breakdowns and startup/closedown times , 2007 .

[5]  Chuen-Horng Lin,et al.  Fuzzy analysis of queueing systems with an unreliable server: A nonlinear programming approach , 2006, Appl. Math. Comput..

[6]  Quan-Lin Li,et al.  Reliability approximation of a Markov queueing system with server breakdown and repair , 1997 .

[7]  R. Nadarajan,et al.  A general bulk service queue with arrival rate dependent on server breakdowns , 1994 .

[8]  Peng Zhang,et al.  A discrete-time retrial queue with negative customers and unreliable server , 2009, Comput. Ind. Eng..

[9]  Wen Lea Pearn,et al.  The randomized vacation policy for a batch arrival queue , 2010 .

[10]  Hsing Kenneth Cheng.  Pricing and capacity decisions of clustered twin-computer systems subject to breakdowns , 1999, Decis. Support Syst..

[11]  Che Soong Kim,et al.  Erlang loss queueing system with batch arrivals operating in a random environment , 2009, Comput. Oper. Res..

[12]  Che Soong Kim,et al.  The BMAP/PH/N retrial queue with Markovian flow of breakdowns , 2008, Eur. J. Oper. Res..

[13]  Faouzi Kamoun,et al.  Performance analysis of a non-preemptive priority queuing system subjected to a correlated Markovian interruption process , 2008, Comput. Oper. Res..

[14]  Inderjit Singh,et al.  Three-server bulk service queue with service interruptions and exponential repairs , 1991 .

[15]  Qing Zhao,et al.  A discrete-time Geo/G/1 retrial queue with starting failures and second optional service , 2007, Comput. Math. Appl..

[16]  Ioannis Dimitriou,et al.  A repairable queueing model with two-phase service, start-up times and retrial customers , 2010, Comput. Oper. Res..

[17]  Jau-Chuan Ke,et al.  Optimal NT policies for M/G/1 system with a startup and unreliable server , 2006, Comput. Ind. Eng..

[18]  Herwig Bruneel,et al.  System delay versus system content for discrete-time queueing systems subject to server interruptions , 2006, Eur. J. Oper. Res..

[19]  Rakshit Negi,et al.  Determining satisfaction through customer-perceived service quality and value: evidence from Ethiopian Telecommunications , 2010 .

[20]  Genqi Xu,et al.  The well-posedness of an M/G/1 queue with second optional service and server breakdown , 2009, Comput. Math. Appl..

[21]  Anamika Jain,et al.  Working vacations queueing model with multiple types of server breakdowns , 2010 .

[22]  Jau-Chuan Ke,et al.  The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns , 2003 .

[23]  Qiang Lu,et al.  Service failure, recovery and improvement: the case of a Chinese restaurant. , 2008 .

[24]  Chuen-Horng Lin,et al.  Maximum entropy solutions for batch arrival queue with an un-reliable server and delaying vacations , 2006, Appl. Math. Comput..

[25]  P. Patrick Wang,et al.  Quality-related measures of unreliable machines with preventive maintenance , 1996, Comput. Oper. Res..

[26]  Ivan Atencia,et al.  An M[X]/G/1 retrial queue with server breakdowns and constant rate of repeated attempts , 2007, Ann. Oper. Res..

[27]  Madhu Jain,et al.  Optimal policy for bulk queue with multiple types of server breakdown , 2009 .

[28]  Hamed Nassar,et al.  Performance Analysis of an ATM Buffered Switch Transmitting Two-Class Traffic over Unreliable Channels , 2003 .

[29]  Jinting Wang,et al.  An M/G/1 queue with second optional service and server breakdowns , 2004 .

[30]  Wen Lea Pearn,et al.  Maximum entropy analysis to the N policy M/G/1 queueing system with server breakdowns and general startup times , 2005, Appl. Math. Comput..

[31]  Gautam Choudhury,et al.  A batch arrival retrial queueing system with two phases of service and service interruption , 2010, Comput. Math. Appl..

[32]  R. Nadarajan,et al.  Series queue with general bulk service, random breakdown and vacation , 1991 .

[33]  Kuo-Hsiung Wang,et al.  A maximum entropy approach for the (p,N)-policy M/G/1 queue with a removable and unreliable server , 2009 .

[34]  Jau-Chuan Ke,et al.  On M/G/1 system under NT policies with breakdowns, startup and closedown , 2006 .

[35]  Madhu Jain,et al.  Optimal repairable M x /G/1 queue with multi-optional services and Bernoulli vacation , 2010 .

[36]  Dong-Yuh Yang,et al.  Controlling arrivals for a queueing system with an unreliable server: Newton-Quasi method , 2009, Appl. Math. Comput..

[37]  Kailash C. Madan,et al.  A single channel queue with bulk service subject to interruptions , 1989 .

[38]  János Sztrik,et al.  Reliability Investigations of Heterogeneous Terminal Systems Using MOSEL , 2004 .

[39]  Wen Lea Pearn,et al.  Optimal management for infinite capacity N-policy M/G/1 queue with a removable service station , 2011, Int. J. Syst. Sci..

[40]  Uri Yechiali,et al.  Polling systems with breakdowns and repairs , 2003, Eur. J. Oper. Res..

[41]  Attahiru Sule Alfa,et al.  A class of multi-server queueing system with server failures , 2009, Comput. Ind. Eng..

[42]  Qing Zhao,et al.  Discrete-time Geo/G/1 retrial queue with general retrial times and starting failures , 2007, Math. Comput. Model..

[43]  Antonis Economou,et al.  Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs , 2008, Oper. Res. Lett..

[44]  Yinghui Tang,et al.  Discrete-time GeoX/G/1 queue with unreliable server and multiple adaptive delayed vacations , 2008 .

[45]  Kyung Chul Chae,et al.  Maintenance of deteriorating single server queues with random shocks , 2009, Comput. Ind. Eng..

[46]  Zhe George Zhang,et al.  Optimal (d, c) vacation policy for a finite buffer M/M/c queue with unreliable servers and repairs , 2009 .

[47]  Mark A. Abramson,et al.  AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS , 2009, Probability in the Engineering and Informational Sciences.

[48]  David Perry,et al.  A correlated M/G/1-type queue with randomized server repair and maintenance modes , 2000, Oper. Res. Lett..

[49]  Nawel Gharbi,et al.  GSPN analysis of retrial systems with servers breakdowns and repairs , 2006, Appl. Math. Comput..

[50]  Bin Liu,et al.  Transient analysis of an M , 2008, Eur. J. Oper. Res..

[51]  Gautam Choudhury,et al.  An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair , 2008, Perform. Evaluation.

[52]  Ivan Atencia,et al.  A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times , 2009, Comput. Ind. Eng..

[53]  Gang Yang,et al.  An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs , 2009, Comput. Math. Appl..

[54]  Pu Patrick Wang,et al.  A vacation queueing model with service breakdowns , 2000 .

[55]  Peter G. Harrison,et al.  Reliability modelling using G-queues , 2000, Eur. J. Oper. Res..

[56]  Gennadi Falin.  An M/G/1 retrial queue with an unreliable server and general repair times , 2010, Perform. Evaluation.

[57]  Wen Lea Pearn,et al.  (Applied Mathematical Modelling,31(10):2199-2212)Optimal Control of the N Policy M/G/1 Queueing System with Server Breakdowns and General Startup Times , 2007 .

[58]  Gautam Choudhury,et al.  The N-policy for an unreliable server with delaying repair and two phases of service , 2009, J. Comput. Appl. Math..

[59]  Wen Lea Pearn,et al.  (Engineering Computations: International Journal for Computer-Aided Engineering and Software,25(8):783-800)Optimal Randomized Control Policy of an Unreliable Server System with Second Optional Service and Startup , 2008 .

[60]  János Sztrik,et al.  Performance Modelling of Nonhomogeneous Unreliable Multiserver Systems Using MOSEL , 2003 .

[61]  Dirk P. Kroese,et al.  Efficient Estimation of Overflow Probabilities in Queues with Breakdowns , 1998, Perform. Evaluation.

[62]  Wen Lea Pearn,et al.  Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup , 2010, J. Comput. Appl. Math..

[63]  Kailash C. Madan,et al.  A bulk queueing system with random failures and two phase repairs , 1992 .

[64]  Barış Tan.  A three-station merge system with unreliable stations and a shared buffer , 2001 .

[65]  S. R. Devadasan,et al.  Design and development of modified service failure mode and effects analysis model , 2007 .

[66]  Sungsoo Kim,et al.  A capacity planning model of unreliable multimedia service systems , 2002, J. Syst. Softw..

[67]  M. Haridass,et al.  Analysis of a Bulk Queue with Unreliable Server and Single Vacation , 2008 .

[68]  Jau-Chuan Ke,et al.  Modified T vacation policy for an M/G/1 queueing system with an unreliable server and startup , 2005, Math. Comput. Model..

[69]  R. Nadarajan,et al.  Two units connected in series with general bulk service and random breakdown in unit 2 , 1989 .

[70]  János Sztrik,et al.  Homogeneous finite-source retrial queues with server subject to breakdowns and repairs , 2005, Math. Comput. Model..

[71]  Yinghui Tang,et al.  An M/Ek/1 queueing system with no damage service interruptions , 2011, Math. Comput. Model..

[72]  Chuen-Horng Lin,et al.  Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation , 2008 .

[73]  Stefan Van Gulck,et al.  Note on the article: Maximum entropy analysis of the M[x]/M/1 queueing system with multiple vacations and server breakdowns , 2008, Comput. Ind. Eng..

[74]  Jinting Wang,et al.  Unreliable production-inventory systems with hyper-exponential renewal demand processes , 2005, Appl. Math. Comput..

[75]  Gautam Choudhury,et al.  An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair , 2009 .

[76]  Hans Daduna,et al.  On the behavior of stable subnetworks in non-ergodic networks with unreliable nodes , 2009, Comput. Networks.

[77]  X. Zhang,et al.  A performance analysis of a discrete-time queueing system with server interruption for modeling wireless ATM multiplexer , 2003, Perform. Evaluation.

[78]  Wen Lea Pearn,et al.  Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup , 2010 .

[79]  Pieter Wartenhorst,et al.  N parallel queueing systems with server breakdown and repair , 1995 .

[80]  Kuo-Hsiung Wang,et al.  Maximum entropy analysis of the M[x]/M/1 queueing system with multiple vacations and server breakdowns , 2007, Comput. Ind. Eng..

[81]  Gautam Choudhury,et al.  A quorum queueing system with an unreliable server , 2009, Appl. Math. Lett..

[82]  Shunsuke Ihara,et al.  Maximum Entropy Analysis , 1993 .

[83]  B Vinod,et al.  Performance models for unreliable flexible manufacturing systems , 1984 .

[84]  Antonis Economou,et al.  Synchronized abandonments in a single server unreliable queue , 2010, Eur. J. Oper. Res..

[85]  Wen Lea Pearn,et al.  (Journal of Computational and Applied Mathematics,228(1):274-278)Optimization of the T Policy M/G/1 Queue with Server Breakdowns and General Startup Times , 2009 .