
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,028 |
تعداد مشاهده مقاله | 67,082,893 |
تعداد دریافت فایل اصل مقاله | 7,656,362 |
On fluctuation analysis of different kinds of n-policy queues with single vacation | ||
International Journal of Nonlinear Analysis and Applications | ||
دوره 12، شماره 2، بهمن 2021، صفحه 2029-2040 اصل مقاله (419.39 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5340 | ||
نویسندگان | ||
Hind Saad Kazem* ؛ Ali Hussein Mahmood Al-Obaidi | ||
Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq | ||
تاریخ دریافت: 14 اسفند 1399، تاریخ بازنگری: 26 اردیبهشت 1400، تاریخ پذیرش: 11 تیر 1400 | ||
چکیده | ||
In this paper, we debate queueing systems with N-policy and single vacation. We consider these systems when the vacation times have Erlang distribution. Moreover, we adapted the input by studying two different kinds: first, an ordinary Poisson input, and second, type 2 geometric batch input. We derive the probability generating function of the number of units in the system in two cases by using fluctuation analysis. | ||
کلیدواژهها | ||
N-policy؛ single vacation؛ fluctuation theory؛ input batches؛ bulk input؛ marked delayed renewal process؛ delayed renewal process؛ point process؛ marked point process؛ random walk | ||
مراجع | ||
[1] L. Abolnikov and A. Dukhovny, Markov chains with transition delta-matrix: ergodicity conditions, invariant probability measures and applications, J. Appl. Math. Stoch. Anal. 4 (1991) 333-355. [2] L. Abolnikov, J.H. Dshalalow and A. Treerattrakoon, On a dual hybrid queueing system, Nonlinear Anal. Hybrid Syst. 2 (2008) 96–109. [3] R.P. Agarwal and J.H. Dshalalow, New fluctuation analysis of D-policy bulk queues with multiple vacations, Math. Comput. Model. 41 (2005) 253–269. [4] Y. Baba, On the MX/G/1 queue with vacation time, Operat. Res. Let. 5 (1986) 93–98. [5] J.B. Bacot and J.H. Dshalalow, A bulk input queueing system with batch gated service and multiple vacation policy, Math. Comput. Model. 34 (2001) 873–886. [6] K.C. Chae and H.W. Lee, MX/G/1 vacation models with N-policy: heuristic interpretation of the mean waiting time, J. Operat. Res. Soc. 46 (1995) 258-264. [7] G. Choudhury, A batch arrival queue with a vacation time under single vacation policy, Comput. Operat. Res. 29 (2002) 1941–1955. [8] G. Choudhury, An MX/G/1 queueing system with a setup period and a vacation period, Que. Syst. 36 (2000) 23-38. [9] G. Choudhury and H.K. Baruah, Analysis of a Poisson queue with a threshold policy and a grand vacation process: an analytic approach, Sankhy¯a: Indian J. Stat. Ser. B (2000) 303–316. [10] G. Choudhury and M. Paul, A batch arrival queue with an additional service channel under N-policy, Appl. Math. Comput. 156 (2004) 115–130. [11] J.H. Dshalalow, A note on D-policy bulk queueing systems, J. Appl. Prob. 38 (2001) 280–283. [12] J. H. Dshalalow and A. Merie, Fluctuation analysis in queues with several operational modes and priority customers, Top 26 (2018) 309–333. [13] J. H. Dshalalow and J. Yellen, Bulk input queues with quorum and multiple vacations, Math. Prob. Engin. 2 (1996) 95–106. [14] J.H. Dshalalow and L. Tadj, A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time, Int. J. Math. Math. Sci. 15 (1992) 189–194. [15] J.H. Dshalalow and R.T. White, Current Trends in Random Walks on Random Lattices, Math. 9 (2021) 11–48. [16] J. H. Dshalalow, Queueing processes in bulk systems under the D-policy, J. Appl. Prob. 34 (1998) 976–989. [17] S. Kalita and G. Choudhury, Some aspects of a batch arrival Poisson queue with N-policy, Stoch. Model. Appl. 5 (2002) 21–32. [18] H. W. Lee, S. L. Soon and C. C. Kyung, Operating characteristics of MX/G/1 queue with N-policy, Que. Syst. 15 (1994) 387–399.[19] H.W. Lee and M.M. Srinivasan, Control policies for the MX/G/1 queueing system, Manag. Sci. 35 (1989) 708–721. [20] H. W. Lee, S. S. Lee, J.O. Park and K.C. Chae, Analysis of the M x/G/1 queue by N-policy and multiple vacations, J. Appl. Prob. 31 (1994) 476–496. [21] S.S. Lee, H. W. Lee, S.H. Yoon and K.C. Chae, Batch arrival queue with N-policy and single vacation, Comput. Operat. Res. 22 (1995) 173–189. [22] K. C. Madan and W. Abu–Dayyeh, Restricted admissibility of batches into an M/G/1 type bulk queue with modified Bernoulli schedule server vacations, ESAIM: Prob. Stat. 6 (2002) 113–125. [23] J. Medhi, Single server queueing system with Poisson input: a review of some recent developments, Adv. Combin. Meth. Appl. Prob. Stat. 5 (1997) 317–338. [24] E. Rosenberg and U. Yechiali, The Mx/G/1 queue with single and multiple vacations under the LIFO service regime, Operat. Res. Let. 14 (1993) 171–179. [25] J. Teghem, Control of the service process in a queueing system, Euro. J. Operat. Res. 23 (1986) 141–158. [26] J. Teghem, On a decomposition result for a class of vacation queueing systems, J. Appl. Prob.27 (1990) 227–231. | ||
آمار تعداد مشاهده مقاله: 15,562 تعداد دریافت فایل اصل مقاله: 391 |