A single server Markovian queuing system with limited buffer and reverse balking
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صندلی اداریAbstract
The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.
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References
Awasthi, B. (2018). Performance Analysis of M / M / 1 / K Finite Capacity Queueing Model with Reverse Balking and Reverse Reneging. Journal of Computer and Mathematical Sciences, 9, 850–855.
Choudhury, A., & Medhi, P. (2011A). Balking and reneging in multi-server Markovian queuing system. International Journal of Mathematics in Operation Research, 3(4), 377-394.
Choudhury, A., & Medhi, P. (2011B). A simple analysis of impatience in multi-server queues. International Journal of Applied Management Science, 3, 294-315.
Choudhury, A., & Medhi, P. (2011C). Some aspects of balking and reneging in finite buffer queue. RAIRO-Operations Research, 45(3), 223-240.
Choudhury, A., & Medhi, P. (2012). A few words on M/Ek/1/1 queuing model with reneging customers. International Journal of Research in Applied Natural and Statistical Sciences, 1(1), 1-7
Haghighi, A. M., Medhi, J., & Mohanty, S. G. (1986). On a multi-server Markovian queuing system with balking and reneging. Computer and Operational Research, 13(4), 421–425.
Haight, F. A. (1957). Queuing with balking. Biometrika, 44(3/4), 360–369.
Haight, F. A. (1959). Queuing with reneging. Metrika, 2(1), 186–197.
Jain, N. K., Kumar, R., & Som, B. K. (2014). An M/M/1/N queuing system with reverse balking. American Journal of Operational Research, 2(2), 17-20.
Kumar, R., Som, B. K., & Jain, S. (2015). An M/M/1/N feedback queuing system with reverse balking. Journal of Reliability and Statistical Studies, 8(1), 31-38.
Sasikala, S., & Thaigaranjan, M. (2016). The M/M/1/N interdependent queuing model with controllable arrival rates and reverse balking. International Journal of Current Research, 8(1), 311-316.
Som, B. K., & Kumar, R. (2012). An M/M/1/N queuing model with retention of reneged customers and balking. American Journal of Operational Research, 2(1), 1-5.
Som, B. K., & Kumar, R. (2017). A heterogeneous queuing system with reverse balking and reneging. Journal of Industrial and Production Engineering, 2(2), 1-5.
Sharma, J. K.(2013). Operation research theory and applications, 5 ed, Macmillan publishers India Ltd, Chennai.
Swarup, K., Gupta, P. K., & Mohan, M. (2014). An introduction to management science operation research, 16 ed, Sultan Chand & Sons educational publishers, New Delhi.