Abstract
The optimal F-policy can be used to control the admission of customers in queueing scenarios having limited waiting space. According to F-policy, as soon as the capacity of the system becomes full, the arriving customers are restricted to join the system until there is a drop in the number of customers in the system to a threshold level ‘F’ due to departure of the served customers. In spite of enormous applications of F-policy models in several queueing systems, a limited number of papers has appeared in the queueing literature. The main objective of this article is to provide a state-of-the-art and survey of literature on the state dependent queueing models operating under F-policy. In this article, we describe the mathematical formulation of queueing models operating under F-policy in two categories namely, finite capacity and finite population models. The methodological aspect of non-Markov models with F-policy is presented. The exhaustive list of work done on F-policy is also provided in tabular form.
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References
Artalejo JR, Gómez-Corral A (2008) Retrial queueing systems. Springer, Berlin
Balachandran KR (1973) Control policies for a single server system. Manage Sci 19:1013–1018. https://doi.org/10.1287/mnsc.19.9.1013
Bose SK (2002) An introduction to queueing systems, 1st edn. Springer US, Boston
Brugno A, Dudin AN, Manzo R (2018) Analysis of a strategy of adaptive group admission of customers to single server retrial system. J Ambient Intell Humaniz Comput 9:123–135. https://doi.org/10.1007/s12652-016-0419-7
Chang C-J, Ke J-C (2015) Randomized controlling arrival for a queueing system with subject to server breakdowns. Optimization 64:941–955. https://doi.org/10.1080/02331934.2013.804076
Chang C-J, Ke J-C, Huang H-I (2011) The optimal management of a queueing system with controlling arrivals. J Chin Inst Ind Eng 28:226–236. https://doi.org/10.1080/10170669.2011.552922
Chang F-M, Ke J-C, Liou C-H (2013) Controlling arrival for the machine repair problem with switching failure. J Phys Conf Ser 410:012116. https://doi.org/10.1088/1742-6596/410/1/012116
Chang C-J, Chang F-M, Ke J-C (2014) Economic application in a Bernoulli F-policy queueing system with server breakdown. Int J Prod Res 52:743–756. https://doi.org/10.1080/00207543.2013.835882
Clerc M (2006) Particle swarm optimization. ISTE, London
Cox DR (1955) The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Math Proc Cambridge Philos Soc 51:433–441. https://doi.org/10.1017/S0305004100030437
D’Arienzo MP, Dudin AN, Dudin SA, Manzo R (2019) Analysis of a retrial queue with group service of impatient customers. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-019-01318-x
Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York
Geem ZW (2009) Music-inspired harmony search algorithm. Springer, Berlin
Goswami V (2016) Relationship between randomized F-policy and randomized N-policy in discrete-time queues. OPSEARCH 53:131–150. https://doi.org/10.1007/s12597-015-0220-y
Gross D, Shortie JF, Thompson JM, Harris CM (2008) Fundamentals of queueing theory, 4th edn. Wiley, New Jersey
Gupta SM (1995) Interrelationship between controlling arrival and service in queueing systems. Comput Oper Res 22:1005–1014
Hassin R, Haviv M (2003) To queue or not to queue: equilibrium behavior in queueing systems. Springer Science & Business Media, Boston
Heyman D (1977) The T-policy for the M/G/1 queue. Manage Sci 23:775–778
Huang H-I, Hsu P-C, Ke J-C (2011) Controlling arrival and service of a two-removable-server system using genetic algorithm. Expert Syst Appl 38:10054–10059. https://doi.org/10.1016/j.eswa.2011.02.011
Jain M, Bhagat A (2014) F-policy retrial queue with unreliable server: a computational approach. In: International conference on emerging trends in global management practices—an interdisciplinary approach, pp 741–759
Jain M, Bhagat A (2015a) Analysis of bulk retrial queue using maximum entropy principle. Int J Oper Res 23:477–496. https://doi.org/10.1504/IJOR.2015.070146
Jain M, Bhagat A (2015b) Transient analysis of finite F-policy retrial queues with delayed repair and threshold recovery. Natl Acad Sci Lett 38:257–261. https://doi.org/10.1007/s40009-014-0337-1
Jain M, Meena RK (2017) Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy. Cogent Math 4:1–17. https://doi.org/10.1080/23311835.2017.1306961
Jain M, Sanga SS (2017a) Performance modeling and ANFIS computing for finite buffer retrial queue under F-policy. In: Proceedings of sixth international conference on soft computing for problem solving. Patiala, India, pp 248–258
Jain M, Sanga SS (2017b) Control F-policy for fault tolerance machining system with general retrial attempts. Natl Acad Sci Lett 40:359–364. https://doi.org/10.1007/s40009-017-0573-2
Jain M, Sanga SS (2019a) F-Policy for M/M/1/K retrial queueing model with state-dependent rates. In: Performance prediction and analytics of fuzzy, reliability and queuing models. Asset analytics (Performance and Safety Management). pp 127–138
Jain M, Sanga SS (2019b) Admission control for finite capacity queueing model with general retrial times and state-dependent rates. J Ind Manag Optim. https://doi.org/10.3934/jimo.2019073
Jain M, Sanga SS (2019c) Optimal control F-policy for M/M/R/K queue with an additional server and balking. Int J Appl Comput Math. https://doi.org/10.1007/s40819-019-0747-3
Jain M, Sanga SS (2020) Fuzzy cost optimization and admission control for machine interference problem with general retrial. J Test Eval. https://doi.org/10.1520/jte20180882
Jain M, Sharma GC, Sharma R (2012) Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up. Int J Math Oper Res 4:152–174. https://doi.org/10.1504/IJMOR.2012.046375
Jain M, Sanga SS, Meena RK (2016a) Control F-policy for Markovian retrial queue with server breakdowns. In: 1st International conference on power electronics, intelligent control and energy systems (ICPEICES). New Delhi, India, pp 1–5
Jain M, Shekhar C, Shukla S (2016b) Queueing analysis of machine repair problem with controlled rates and working vacation under F-Policy. Proc Natl Acad Sci India Sect A Phys Sci 86:21–31. https://doi.org/10.1007/s40010-015-0233-1
Jain M, Shekhar C, Meena RK (2017) Admission control policy of maintenance for unreliable server machining system with working vacation. Arab J Sci Eng 42:2993–3005. https://doi.org/10.1007/s13369-017-2488-0
Jain M, Shekhar C, Meena RK (2019) Performance analysis and control F-policy for fault-tolerant system with working vacation. OPSEARCH 56:409–431. https://doi.org/10.1007/s12597-019-00369-0
Jayaraman R, Matis TI (2011) Finite population models-single station queues. Wiley encyclopedia of operations research and management science. Wiley, Hoboken, pp 1–6
Karaesmen F, Gupta S (1997) Duality relations for queues with arrival and service control. Comput Oper Res 24:529–538. https://doi.org/10.1016/S0305-0548(96)00072-X
Ke J-C, Chang F-M, Chang C-J (2010) Controlling arrivals for a Markovian queueing system with a second optional service. Int J Ind Eng Theory Appl Pract 17:48–57
Ke J-C, Chang C-J, Chang F-M (2014) A standby redundant system with F-policy. In: Proceedings of the 2014 international conference on industrial engineering and operations management Bali, Indonesia, January 7–9
Kosten L (1967) The Custodian Problem. In: Cruon OR (ed) Queueing theory, recent developments and applications. English University Press, Oxford, pp 65–70
Kumar K, Jain M (2013) Threshold F-policy and N-policy for multi-component machining system with warm standbys. J Ind Eng Int 9:9–28. https://doi.org/10.1186/2251-712X-9-28
Kumar K, Jain M, Shekhar C (2019) Machine repair system with F-policy, two unreliable servers, and warm standbys. J Test Eval 47:361–383. https://doi.org/10.1520/JTE20160595
Kuo C-C, Wang K-H, Pearn W (2011) The interrelationship between N-policy M/G/1/K and F-policy G/M/1/K queues with startup time. Qual Technol Quant Manag 8:237–251
Mitchell M (1998) An introduction to genetic algorithms, 5th edn. MIT Press Cambridge, Cambridge
Rao SS (2009) Engineering optimization. Wiley, Hoboken
Sanga SS, Jain M (2019a) Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement. Appl Math Comput 363:124624. https://doi.org/10.1016/j.amc.2019.124624
Sanga SS, Jain M (2019b) FM/FM/1 double orbit retrial queue with customers’ joining strategy: a parametric nonlinear programing approach. Appl Math Comput 362:124542. https://doi.org/10.1016/j.amc.2019.06.056
Schwarz JA, Selinka G, Stolletz R (2016) Performance analysis of time-dependent queueing systems: survey and classification. Omega 63:170–189. https://doi.org/10.1016/j.omega.2015.10.013
Shekhar C, Jain M, Raina AA, Iqbal J (2017) Optimal (N, F) policy for queue- dependent and time-sharing machining redundant system. Int J Qual Reliab Manag 34:798–816. https://doi.org/10.1108/IJQRM-07-2016-0105
Tadj L, Choudhury G (2005) Optimal design and control of queues. Top 13:359–412. https://doi.org/10.1007/BF02579061
Tian N, Zhang ZG (2006) Vacation queueing models theory and applications. Springer US, Boston
Wang K-H, Yang D-Y (2009) Controlling arrivals for a queueing system with an unreliable server: Newton-Quasi method. Appl Math Comput 213:92–101. https://doi.org/10.1016/j.amc.2009.03.002
Wang KH, Kuo CC, Pearn WL (2007) Optimal control of an M/G/1/K queueing system with combined F policy and startup time. J Optim Theory Appl 135:285–299. https://doi.org/10.1007/s10957-007-9253-6
Wang K-H, Kuo C-C, Pearn WL (2008) A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time. Appl Math Model 32:958–970. https://doi.org/10.1016/j.apm.2007.02.023
Wu D-A, Takagi H (2006) M/G/1 queue with multiple working vacations. Perform Eval 63:654–681. https://doi.org/10.1016/j.peva.2005.05.005
Yadin M, Naor P (1963) Queueing systems with a removable service station. J Oper Res Soc 14:393–405. https://doi.org/10.1057/jors.1963.63
Yang D-Y, Chang P-K (2015) A parametric programming solution to the F-policy queue with fuzzy parameters. Int J Syst Sci 46:590–598. https://doi.org/10.1080/00207721.2013.792975
Yang DY, Ke JC (2014) Cost optimization of a repairable M/G/1 queue with a randomized policy and single vacation. Appl Math Model 38:5113–5125. https://doi.org/10.1016/j.apm.2014.03.012
Yang D-Y, Wang K-H (2013) Interrelationship between randomized F-policy and randomized N-policy queues. J Ind Prod Eng 30:30–43. https://doi.org/10.1080/10170669.2012.761286
Yang DY, Yang NC (2018) Performance and cost analysis of a finite capacity queue with two heterogeneous servers under F-policy. Int J Serv Oper Informatics 9:101–115. https://doi.org/10.1504/IJSOI.2018.092578
Yang D-Y, Wang K-H, Wu C-H (2010) Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation. J Comput Appl Math 234:545–556. https://doi.org/10.1016/j.cam.2009.12.046
Yeh C, Lee Y-T, Chang C-J, Chang F-M (2017) Analysis of a two-phase queue system with < p, F > -policy. Qual Technol Quant Manag 14:178–194. https://doi.org/10.1080/16843703.2016.1208489
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Jain, M., Sanga, S.S. State dependent queueing models under admission control F-policy: a survey. J Ambient Intell Human Comput 11, 3873–3891 (2020). https://doi.org/10.1007/s12652-019-01638-y
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DOI: https://doi.org/10.1007/s12652-019-01638-y