Kuyruğa Dahil Olmama ve Kuyruğu Terk Etme İle Budanmış Gelişlerarası Erlang Kuyruk Modeli ER/M/C/K nın Analitik Çözümü

Abstract

Bu makalede kuyruğa dahil olmama ve kuyruğu terk etme ile budanmış gelişlerarası Erlang kuyruk modeli Er, /M/c/k nin r,c ve k nın genel değerleri için analitik çözüm ele alınmıştır. Çalışmada dikkate alınmış olan kuyruk disiplini ilk gelen ilk hizmet alınır (FIFO) şeklindedir. Daha evvelce yayınlanmış sonuçları, mevcut çalışmanın özel durumları olduğu da ayrıca gösterilmiştir.

Keywords

• Budanmış Gelişlerarası Erlang Kuyruk Modeli
• Durağan Durum Olasılığı
• Kuyruğa Dahil Olmama
• Kuyruğu Terk Etme

Analytical Solution of the Truncated Interarrival Erlangian Queue: ER/M/C/K With Balking and Reneging

Abstract

This paper aimed to treat the analytical solution of the truncated interarrival Erlangian queue: E/M/c/k with balking and reneging for general values of r, c and k. The discipline considered here is FIFO. Some previously published results are shown to be special cases of the present results.

Keywords

• Balking
• Reneging
• Steady-State Probability
• Truncated Interarrival Erlangian Queue

References

1. AL-SEEDY, R.O. and AL-BRAHEEM, F. M., "An Interarrival Hyperexponential Machine Interference with Balking, Reneging, State-Dependent, Spares and an Additional Server for Longer Queues". IJMMS, 27, 737-747, 2001.
2. BUNDAY, B. D., "An Introduction to Queueing Theory". John Wiley, New York, 1996.
3. GROSS, D. and HARRIS, C. M., "Fundamentals of Queueing Theory". John Wiley, New York, 1974.
4. GUPTA, S. K., “Queues with Hyper - Poisson input and Exponential Service Time Distribution with State Dependent Arrival and Service Rates". Oper. Res., 15, 847-856, 1967.
5. JAIN, M. and RAKHEE, S. M., "N-Policy for a Machine Repair System with Spares and Reneging". Appl. Math. Modelling, 28, 513-531, 2004.
6. KLEINROCK, L., "Queueing Systems". Vol. 1, John Wiley, New York, 1975.
7. MEDHI, J., "Stochastic Models in Queueing Theory". Academic Press, New York, 1991.
8. MORSE, P. M., “Queues, Inventories and Maintenance”. John Wiley, New York, 1958.

9. PEARN, W. L. and CHANG, Y. C., "Optimal Management of the N-policy M/EK/1 Queueing system with a Removable Service Station: A Sensitivity Investigation": Comp. Oper. Res., 31, 1001-1015, 2004.
10. SADLAM, V. and TORUM, H., "On Optimization of Stochastic Service System with two Heterogeneous Channels" Inter. J. Appl. Math, 16, 131-137, 2004.
11. SHAWKY, A. I., "The Single-Server Machine Interference Model with Balking, Reneging and an Additional Server for Longer Queues". Microelectron. Reliab., 37, 355-357, 1997.
12. SHAWKY, A. I., "The Machine Interference model M/M/C/K/N with Balking, Reneging and Spares" Opsearch, 37, 25-35, 2000.
13. SHAWKY, A. I., "An Interarrival Hyperexponential Machine Interference Model: Hr/M/c/k/N with Balking and Reneging". Comm. Korean Math. Soc., 16, 659-666, 2001.
14. SHAWKY, A. I., "The Service Erlangian Machine Interference Model: M/Er/1/k/N with Balking and Reneging". J. Appl. Math.& Computing, 18, 431-439, 2005.
15. SHAWKY, A. I. and EL - PAOUMY, M. S., "The Interarrival Hyperexponential Queues: Hk/M/c/N with Balking and Reneging". Stochastics and Stochastics Reports, 69, 67-76, 2000.
16. SHAWKY, A. I. and EL - PAOUMY, M.S., "The Truncated Hyper-Poisson Queues: Hk/M/2/N with Balking, Reneging and Heterogeneous Servers". O. R. Transactions, 4, 66-75, 2000.
17. SHAWKY, A. I., and EL - PAOUMY. M. S., "The Truncated Hyperexponential Service Queues: M/Hk/1/N with Balking and Reneging". Far East J. Theo. Stat., 16, 73-80, 2002.
18. WHITE, J. A., SCHMIDT, J. W. and Bennett, G. K., "Analysis of Queueing Systems". Academic Press, New York, 1975.