Volume 20 | Number 1 | Year 2015 | Article Id. IJMTT-V20P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V20P502
Queueing Systems [1] is one of the real life application technique between a customer and server who is approaching for a service facility. Numerical applications is one of the way to find a solution to any queueing model. Our review covers only general methods that can be applied for a wide range of time dependent queues. In this paper we try to investigate the potential and limitations of numerical methods to evaluate the service quality of time-dependent single facility delay systems.
[1] Gross, Donald, Carl M. Harris, 1998. Fundamental of Queueing Theory, 3rd edition John Wiley & Sons, New York.
[2] Gross, Donald, Douglas R. Miller, 1984. The Randomization technique as a modeling tool and solution procedure for Transient Markov Processes. Operations Research 32(2): 343-361.
[3] Dormand Jr, Pj Prince 1980. A family of embedded Runge-kutta formulae Journal of Computational and Applied Mathematics, 6: 19-26.
[4] Ingolfsson, Armann, Elvira, Akhmetshina, Susan Budge, Yongyueli, Xudong Wu. 2007. A survey and experimental comparison of service level- Approximation methods for Non-stationary M(t) / M / S(t) Queueing systems. INFORMS journal on computing 19(2): 201-214.
[5] Grassmann W.K. 1977. Transient solutions in Markovian Queueing Systems Computers and Operations Research 4(1): 47-53.
[6] Brahimi M.D.J., Worthington, 1991. The finite capacity multi-server queue with inhomogeneous arrival rate and discrete service time distribution and its application to continuous service time problems. European Journal of Operational Research, 50(3): 310-324.
[7] Worthington, Dave A. Wall. 1999. Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems. Journal of the Operational Research Society, 50(8): 777-788.
[8] Massey, William, A. Ward Whitt, 1996. Stationary process approximations for the non stationary Erlang loss model. Operations Research, 44(6): 976.
[9] Reibman, A., K. Trivedi, 1988. Numerical transient analysis of Markov models. Computers and Operations Research, 15: 19-36.
[10] Taaffe, M.R. 1982. Approximately non stationary queueing models. Ph.D. dissertation. The Ohio State University.
[11] Navid Izady, 2010. On Queues with Time Varying Demand Ph.D. dissertation Lancaster University, Management School.
A. Nellai Murugan, S. Vijayakumari Saradha, "Queueing Systems – A Numerical Approach," International Journal of Mathematics Trends and Technology (IJMTT), vol. 20, no. 1, pp. 7-10, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V20P502