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http://dx.doi.org/10.9723/jksiis.2018.23.1.053

Waiting Time Analysis of Discrete-Time BMAP/G/1 Queue Under D-policy  

Lee, Se Won (부경대학교 경영학부)
Publication Information
Journal of Korea Society of Industrial Information Systems / v.23, no.1, 2018 , pp. 53-63 More about this Journal
Abstract
In this paper, we analyze the waiting time of a queueing system with D-BMAP (discrete-time batch Markovian arrival process) and D-policy. Customer group or packets arrives at the system according to discrete-time Markovian arrival process, and an idle single server becomes busy when the total service time of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state waiting time distribution is derived in the form of a generating function. Mean waiting time is derived as a performance measure. Simulation is also performed for the purpose of verification and validation. Two simple numerical examples are shown.
Keywords
Discrete-Time Batch Markovian Arrival Process(D-BMAP); D-policy; Server Control Policy; Waiting Time;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 Takagi, H., "Queueing Analysis: Vol III, Discrete-time Systems," North-Holland, 1993.
2 Bruneel, H. and Kim, B.G., "Discrete-Time Models for Communication Systems Including ATM," Kluwer Academic Publishers, 1993.
3 Paxson, V. and Floyd, S., “Wide Area Traffic: The Failure of Poisson Modeling,” IEEE/ACM Transactions on Networking, Vol. 3, No. 3, pp. 226-244, 1995.   DOI
4 Lucantoni, D.M., "New Results for the Single Server Queue with a Batch Markovian Arrival Process," Stochastic Models, Vol. 7, No. 1, pp. 1-46, 1991.   DOI
5 Latouche, G. and Ramaswami, V., "A Unified Stochastic Model for the Packet Stream from Periodic Sources," Performance Evaluation, Vol 14, No. 12, pp. 103-121, 1992.   DOI
6 Ramaswami, V. and Latouche, G., Modeling Packet Arrivals from Asynchronous Input Lines, in "Teletraffic Science for New Cost-Effective Systems, Networks and Services," ITC-12, M. Bonatti Ed., North-Holland, Amsterdam, pp. 721-727, 1989.
7 Wang, S. S. and Silvester, J.A., "A Discrete-Time Performance Model for Integrated Service ATM Multiplexers," Proceeding of IEEE COLBECOM, pp. 757-761, 1993.
8 Lee, H.W., "Queueing Theory," Sigma Press, 2006 (in Korean).
9 Balachandran, K.R., “Control Policies for a Single Server System,” Management Science, Vol. 19, No. 9, pp. 1013-1018, 1973.   DOI
10 Bachandran, K.R. and Tijms, H., “On the D-policy for the M/G/1 Queue,” Management Science, Vol. 21, No. 9, pp. 1073-1076, 1975.
11 Liu, R. and Deng, Z., "The Steady-State System Size Distribution for a Modified D-policy Geo/G/1 Queueing System," Mathematical Problems in Engineering, Vol. 2014, Article ID 345129, 2014.
12 Li, J. and Niu, S.C., “The Waiting Time Distribution for the GI/G/1 Queue under the D-policy,” Probability in the Engineering and Informational Sciences, Vol. 6, No. 3, pp. 287-308, 1992.   DOI
13 Lee, H.W., Cheon, S.H. and Seo, W.J., “Queue Length and Waiting Time of the M/G/1 Queue under the D-policy and Multiple Vacations,” Queueing Systems, Vol. 54, No. 4, pp. 261-280, 2006.   DOI
14 Baek, J.W. and Lee, H.W., "Waiting Time Analysis of a Batch Arrival Queue under a Workload Control," International Journal of Industrial Engineering Vol. 14, No. 3, pp. 298-306, 2007.
15 Lee, S.W., Lee, H.W., and Baek, J.W., "Analysis of Discrete-Time Geo/G/1 Queue under the D-policy," 6th International Conference on Queueing Theory and Network Analysis, 2011, Seoul, Korea, QTNA2011.
16 Lee, S.W., Lee, H.W., and Baek, J.W., “Analysis of Discrete-Time MAP/G/1 Queue under Workload Control,” Performance Evaluation, Vol. 69, No. 2, pp. 71-85, 2012.   DOI
17 Lan, S. and Tang, Y., "Analysis of a Discrete-Time $Geo^{{\lambda}_1,{\lambda}_2}/G/1$ Queue with N-policy and D-policy," Journal of Applied Mathematics and Computing, Vol. 53, No. 1-2, pp. 657-681, 2017.   DOI
18 Lee, S.W., "Workload Analysis of Discrete-Time BMAP/G/1 Queue under D-policy," Journal of the Korea Industrial Information Systems Research, Vol. 21, No. 6, pp. 1-12, 2016.   DOI
19 Kim, N.K., Chang, S.H. and Chae, K.C., "On the Relationships among Queue Lengths at Arrival, Departure, and Random Epochs on the Discrete-time Queue with D-BMAP Arrivals," Operations Research, Vol. 30, pp. 25-32, 2002.
20 Lee, S.W., “A Unified Approach for the Analysis of Discrete-time MAP/G/1 Queue: by Workload Analysis,” Journal of the Korea Industrial Information Systems Research, Vol. 22, No. 1, pp. 23-32, 2017.   DOI
21 Lee, K.-G., Choi, S. and Ryu, S.-W., "Development of Simulation System for Evaluating Performance of the Flat Display Manufacturing Line with Repetitive Process," The Journal of Information Systems, Vol. 17, No. 4, pp. 301-319, 2008.   DOI
22 Lee, H.W., Kim, S.A., Lee, S.W., “Analysis and Cost Optimization of the M/G/1 Queue under the D-policy and LCFS discipline,” Stochastic Analysis and Applications, Vol. 26, No. 1, pp. 39-59, 2008.   DOI