Volume 7, Issue 2, April 2018, Page: 31-39
An Analytical Solution for Queue: M/D/1 with Balking
Kotb Abdel Hamid Kotb, Department of Mathematics and Statistics, Faculty of Science, Tanta University, Tanta, Egypt
Moamer Akhdar, Department of Mathematics and Statistics, Faculty of Science, Tanta University, Tanta, Egypt
Received: Jan. 17, 2018;       Accepted: Jan. 31, 2018;       Published: Feb. 27, 2018
DOI: 10.11648/j.acm.20180702.11      View  456      Downloads  40
In this paper we examine the how to of deriving analytical solution in steady-state for non-truncated single-server queueing and service time are fixed (deterministic) with addition the concept balking, using iterative method and the probability generating function. Some measures of effecting of queuing system are obtained using a smooth and logical manner also some special cases of this system. Finality, some numerical values are given showily the effect of correlation between the (p0, pn, L, Wq) and the additional concepts.
Deterministic, Queueing System, Measures of Effectiveness, Generating Function
To cite this article
Kotb Abdel Hamid Kotb, Moamer Akhdar, An Analytical Solution for Queue: M/D/1 with Balking, Applied and Computational Mathematics. Vol. 7, No. 2, 2018, pp. 31-39. doi: 10.11648/j.acm.20180702.11
Copyright © 2018 Authors retain the copyright of this article.
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M. R. Oliver, Table of the waiting time distribution for the constant service queue (M/D/1), International journal computers mathematical, 2 (1968), 35–56.
V. B. Iversen, Exact calculation of waiting time distributions in queueing systems with constant holding times, NTS-4, Fourth Nordic teletraffic Seminar, Helsinki (1982).
V. B. Iversen and L. Staalhagen, Waiting time distribution in M/D/1 queueing systems, Electronics Letters, 35 (1999), 2184–2185.
O. Brun and J. Garcia, Analytical solution of finite capacity M/D/1 queues, Journal of applied probability, 4 (2000), 1092-1098.
E. V. Koba, Stability condition for M/D/1 retrial queuing system with a limited waiting time, Cybernetics and systems analysis, 2 (2000), 184-186.
E. V. Koba, An M/D/1 queuing system with partial synchronization of its incoming flow and demands repeating at constant intervals, Cybernetics and systems analysis, 6 (2000), 177-180.
Kenji Nakagawa, On the series expansion for the stationary probabilities of an M/D/1 queue, Journal of the operations research society of Japan, 2 (2005), 111-122.
V. B. Iversen, Teletraffic engineering and network planning, Technical university of Denmark, (2007).
D. Groos and C. M. Harris, Fundamentals of queueing theory, New York, John wiley and sons, 4th edition, (2008).
K. L. Prasad and B. Usha, A comparison between M/M/1 and M/D/1 queuing models to vehicular traffic at Kannyakumari district, Journal of mathematics, 1 (2015), 13-15.
M. I. Hussain, B. Ahmed and R. Ali, A discrete event simulation for the analytical modeling of M/D/1 queues: Output buffer of an ATM multiplexer, Innovative Computing Technology (INTECH), (2016).
B. Kim, J. Kim, Explicit solution for the stationary distribution of a discrete-time finite buffer queue, Journal of Industrial and Management Optimization, 12 (2016), 1121-1133.
J. W. Baek, H. W. Lee, S. Ahn and Y. H. Bae, Exact time-dependent solutions for the M/D/1 queue, Operations Research Letters, 44 (2016), 692–695.
Kotobi and Bilén, Spectrum sharing via hybrid cognitive players evaluated by an M/D/1 queuing model, Journal on wireless communications and networking, 85 (2017), 1-11.
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