Markovian working vacation queue with imperfect service, balking and retrial

Markovian queue with working vacation, retrial and impatient customers has been investigated by including the feature of imperfect service during working vacation. If the server is occupied, an incoming customer may either decide to balk from the system or join the retrial orbit following the classical retrial policy. When there is no customer in the system, the server switches over to a working vacation (WV) mode. The customers who enter into the system during working vacation are also served at a slower speed. The probability generating functions (PGFs) are derived for evaluating the distributions of the number of customers in the system and orbit, which are further utilized to derive several performance metrics in closed form. The sensitivity analysis has been done to explore the sensitiveness of various descriptors on the system performance measures. Finally, a cost function is constructed and minimized using quasi-Newton method (QNM) and genetic algorithm (GA).

[1]  Sudeep Singh Sanga,et al.  Admission control for finite capacity queueing model with general retrial times and state-dependent rates , 2020, Journal of Industrial & Management Optimization.

[2]  Jau-Chuan Ke,et al.  Modified vacation policy for M/G/1 retrial queue with balking and feedback , 2009, Comput. Ind. Eng..

[3]  S. Ammar.  Transient solution of an M/M/1 vacation queue with a waiting server and impatient customers , 2017 .

[4]  Feng Zhang,et al.  Strategic joining in M/M/1 retrial queues , 2013, Eur. J. Oper. Res..

[5]  Naishuo Tian,et al.  The M/M/1 queue with working vacations and vacation interruptions , 2007 .

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

[8]  Jau-Chuan Ke,et al.  On an unreliable-server retrial queue with customer feedback and impatience , 2018 .

[9]  Kaili Li,et al.  Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions , 2016, RAIRO Oper. Res..

[10]  Shunfu Jin,et al.  An imperfect sensing-based channel reservation strategy in CRNs and its performance evaluation , 2020 .

[11]  Shan Gao,et al.  M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy , 2014, J. Appl. Math..

[12]  Sherif I. Ammar.  Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations , 2015, Appl. Math. Comput..

[13]  Xiu-li Xu,et al.  Fluid Model Modulated by an M/M/1 Working Vacation Queue with Negative Customer , 2018 .

[14]  Leslie D. Servi,et al.  M/M/1 queues with working vacations (M/M/1/WV) , 2002, Perform. Evaluation.

[15]  Alexander S. Rumyantsev,et al.  Performance analysis and stability of multiclass orbit queue with constant retrial rates and balking , 2019, Perform. Evaluation.

[16]  Madhu Jain,et al.  Admission Control Policy of Maintenance for Unreliable Server Machining System with Working Vacation , 2017 .

[17]  Onno J. Boxma,et al.  Analysis and optimization of vacation and polling models with retrials , 2015, Perform. Evaluation.

[18]  Pikkala Vijaya Laxmi,et al.  Analysis of variant working vacations queue with customer impatience , 2017 .

[19]  Sherif I. Ammar,et al.  The busy period of an M/M/1 queue with balking and reneging , 2013 .

[20]  Madhu Jain,et al.  State dependent M/M/1/WV queueing system with inspection, controlled arrival rates and delayed repair , 2014 .

[21]  Naishuo Tian,et al.  Stochastic decompositions in the M/M/1 queue with working vacations , 2007, Oper. Res. Lett..

[22]  P. Vijaya Laxmi,et al.  Analysis of a working vacations queue with impatient customers operating under a triadic policy , 2014 .

[23]  Ragab Omarah Al-Seedy,et al.  Transient solution of the M/M/c queue with balking and reneging , 2009, Comput. Math. Appl..

[24]  Madhu Jain,et al.  Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement , 2019, Appl. Math. Comput..

[25]  S. Dharmaraja,et al.  Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers' impatience , 2017, RAIRO Oper. Res..

[26]  Mian Zhang,et al.  M/G/1 queue with single working vacation , 2012 .

[27]  K. V. Vijayashree,et al.  Transient Analysis of an M/M/c Queue Subject to Multiple Exponential Vacation , 2015 .

[28]  N. Selvaraju,et al.  Impatient customers in an M/M/1 queue with single and multiple working vacations , 2013, Comput. Ind. Eng..