Techniques

Analytical and Stochastic Modeling Techniques and by Chesoong Kim, Olga Dudina, Alexander Dudin, Sergey Dudin

By Chesoong Kim, Olga Dudina, Alexander Dudin, Sergey Dudin (auth.), Khalid Al-Begain, Dieter Fiems, Jean-Marc Vincent (eds.)

This booklet constitutes the refereed court cases of the nineteenth foreign convention on Analytical and Stochastic Modelling suggestions and functions, ASMTA 2012, held in Grenoble, France, in June 2012. The 20 revised complete papers awarded have been rigorously reviewed and chosen from a number of submissions. The papers are equipped in topical sections on queueing structures; networking purposes; Markov chains; stochastic modelling.

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Extra info for Analytical and Stochastic Modeling Techniques and Applications: 19th International Conference, ASMTA 2012, Grenoble, France, June 4-6, 2012. Proceedings

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Computers & Operations Research 35(8), 2497–2519 (2008) 13. : Performance comparison of several priority schemes with priority jumps. Annals of Operations Research 180(3), 1168–1185 (2008) 14. : Approximation for a two-class weighted fair queueing discipline. Performance Evaluation 67(10), 946–958 (2010) 15. : Calculation of output characteristics of a priority queue through a busy period analysis. European Journal of Operational Research 198(3), 891–898 (2009) 16. : Power series approximations for two-class generalized processor sharing systems.

In our model, there are a number of free parameters such as λ, μ, ν1 , ν2 and α. Thus, the optimization formulation presented above is only one of several options. However, aiming for the optimization of α is natural in the call center context, as it can be controlled by the operator (directly), or by the ACD (automatically). In Fig. 1, the cost model is evaluated for varying α, under the parameter setting specified in Table 1. For the setting considered in Fig. 1a, cost evaluation yields a non-trivial optimal value for α when C1 ∈ {300, 500}.

4 Factorial Moments Next, we derive explicit expressions for the partial factorial moments Mki , (i, k) ∈ {0, 1, 2} × Z+ , which relate to the coefficients of z k in the series Πi (1 + z) as follows, ∞ Mki k Πi (1 + z) = z , i ∈ {0, 1, 2} . (22) k! k=0 For k = 0, (13) already provides the answer, since M0i = Πi (1). π0,0 1 Cz1 1 Cz2 Mk2 = + , k ≥ 1. π0,0 Together with (13) (with Πi (1) = M0i ), this provides explicit expressions for all Mki , k ∈ Z+ , i ∈ {0, 1, 2}. 4, explicit expressions are given for the stationary distribution and the partial factorial moments.

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