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The Journal of Statistics and Management Systems (JSMS) is a world leading journal publishing high quality, rigorously peer-reviewed original research on theoretical and applied statistics and management systems since 1998. The scope is intentionally broad, but papers must make a novel contribution to the field to be considered for publication. Topics include, but are not limited to, the following: • Statistics • Applied Statistics • Industrial Statistics • Statistical Inference • Interdisciplinary role of Statistics • Actuarial Sciences • Decision Sciences • Managerial Aspects • Management Sciences • Management Information Systems

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Open Access Research Article

On the queueing theory : Problems and applications

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* Corresponding author · click or hover a name for details

pp. 913–919Vol. 28Issue 5July 2025DOI: 10.47974/JSMS-1399XML
Received:
09 Apr 2024
Published Online:
05 Jun 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1399
Pages:
913–919

Abstract

In this paper, the queueing theory and its applications are considered. Some basic concepts and results are presented, and some important queue disciplines and mass service systems are considered. 

Keywords

Subject Classifications

90B2268M2060K2560K30

References

[1] F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, “Open, closed, and mixed networks of queues with different classes of customers”, Journal of the ACM, vol. 22, no. 2, pp. 248-260 (1975). 
[2] A. Bobbio, M. Gribaudo, and M. Telek, “Analysis of large scale interacting systems by mean field method”, 2008 Fifth International Conference on Quantitative Evaluation of Systems, pp. 215-224 (2008). 
[3] S. K. Bose, An Introduction to Queueing Systems, Kluwer Academic Publishers/Plenum Publishers, Dordrecht-Boston-London (2001). 
[4] M. Bramson, “A stable queueing network with unstable fluid model”, The Annals of Applied Probability, vol. 9, no. 3, pp. 818-853 (1999). 
[5] J. P. Buzen, “Computational algorithms for closed queueing networks with exponential servers”, Communications of the ACM, vol. 16, no. 9, pp. 527-531 (1973). 
[6] H. Chen, and W. Whitt, “Diffusion approximatioms for open queueing networks with service interruptions”, Queueing Systems, vol. 13, no. 4, pp. 335-359 (1993). 
[7] E. Gelenbe, “G-networks with triggered customer movement”, Journal of Applied Probability, vol. 30, no. 3, pp. 742-748 (1993). 
[8] W. J. Gordon, and G. F. Newell, “Closed queueing systems with exponential servers”, Operations Research, vol. 15, no. 2, pp. 254-265 (1967). 
[9] J. F. Shortle, J. M. Thompson, D. Gross, and C. M. Harris, Fundamentals of Queueing Theory, 5th ed., Wiley Series in Probability and Statistics, John Wiley & Sons, New York (2018). 
[10] F. P. Kelly, “Networks of queues with customers of different types”, Journal of Applied Probability, vol. 12, no. 3, pp. 542-554 (1975). 
[11] L. R. Lipsky, Queueing Theory: A Linear Algebraic Approach, Macmillan, New York (1992). 
[12] S. M. Stefanov, “On the implementation of stochastic quasigradient methods to some facility location problems”, Yugoslav Journal of Operations Research, vol. 10, no. 2, pp. 235-256 (2000). 
[13] S. M. Stefanov, “Convex separable minimization subject to bounded variables”, Computational Optimization and Applications. An International Journal, vol. 18, no. 1, pp. 27-48 (2001). 
[14] S. M. Stefanov, Separable Programming: Theory and Methods, Applied Optimization, vol. 53, Kluwer Academic Publishers, Dordrecht-Boston-London (2001). 
[15] S. M. Stefanov, “Convex quadratic minimization subject to a linear constraint and box constraints”, Applied Mathematics Research Express AMRX, vol. 2004, no. 1, pp. 17-42 (2004). 
[16] S. M. Stefanov, “Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints”, Journal of Interdisciplinary Mathematics, vol. 12, no. 5, pp. 647-673 (2009). 
[17] S. M. Stefanov, “Solution of some convex separable resource allocation and production planning problems with bounds on the variables”, Journal of Interdisciplinary Mathematics, vol. 13, no. 5, pp. 541-569 (2010). 
[18] S. M. Stefanov, “On the solution of multidimensional convex separable continuous knapsack problem with bounded variables”, European Journal of Operational Research, vol. 247, no. 2, pp. 366-369 (2015). 
[19] S. M. Stefanov, “Strictly convex separable optimization with linear equality constraints and bounded variables”, Journal of Statistics and Management Systems, vol. 21, no. 2, pp. 261-272 (2018). 
[20] S. M. Stefanov, “Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems”, Journal of Information and Optimization Sciences, vol. 42, no. 1, pp. 1-16 (2021). 
[21] S. M. Stefanov, “On the numerical solution of separable stochastic inventory control problems”, Journal of Information and Optimization Sciences, vol. 42, no. 3, pp. 533-561 (2021). 
[22] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer Optimization and Its Applications, vol. 177, Springer, Cham (2021). 
[23] S. M. Stefanov, “On the solution of quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 44, no. 2, pp. 243-253 (2023). 
[24] S. M. Stefanov, “Continuous linear knapsack problems revisited”, Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[25] S. M. Stefanov, “Numerical solution of box constrained separable convex quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 45, no. 1, pp. 57-71 (2024). 
[26] S. M. Stefanov, “Linear programming problems and matrix games”, Journal of Interdisciplinary Mathematics, vol. 27, no. 1, pp. 57-65 (2024). 
[27] S. M. Stefanov, “Scheduling theory and applications revisited”, Journal of Interdisciplinary Mathematics, to appear. 
[28] M. Tanner, Practical Queueing Analysis, McGraw-Hill, New York (1995). 
[29] W. Whitt, “The queueing network analyzer”, The Bell System Techical Journal, vol. 62, no. 9, pp. 2779-2815 (1983). 
[30] W. Whitt, Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer Series in Operations Research, Springer-Verlag, New York-Berlin-Heidelberg (2002). 
[31] K. Yamada, “Diffusion approximation for open state-dependent queueing networks in the heavy traffic situation”, The Annals of Applied Probability, vol. 5, no. 4, pp. 958-982 (1995).

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