9 Strong Stability of Queueing Systems and Networks: a Survey and Perspectives
9.1. Introduction
9.2. Preliminary and notations
9.3. Strong stability of queueing systems
9.4. Conclusion and further directions
9.5. References
14 10 Time-varying Queues: a Two-time-scale Approach 10.1. Introduction 10.2. Time-varying queues 10.3. Main results 10.4. Concluding remarks 10.5. References
16 Index
List of Illustrations
1 Chapter 2Figure 2.1. A classical busy periodFigure 2.2. A period under level xFigure 2.3. A busy period with lossesFigure 2.4. A period of level greater than z
2 Chapter 4Figure 4.1.
3 Chapter 5Figure 5.1. Cor(Λ(t), X1 (t)) for μ1 = 1, γ = 2 and DΛ = 2. For a color version ...Figure 5.2. Estimated distribution of Xi for several phases i, with Λ ~ U (0, 6)...Figure 5.3.Histogram estimating the distribution of X, with Λ ~ U (0, 6) and γ =...Figure 5.4. Estimated distribution of X for different values of γ, with Λ ~ U(0,...Figure 5.5.Cor(X,Λ) for DΛ = 1 andγ = 0.5. For a color version of this figure, s...
4 Chapter 6Figure 6.1. A matrix determining the base vectors of some subspace
5 Chapter 8Figure 8.1. Retrial queuing system of type M/GI/1//N with collisions of the cust...Figure 8.2. Density function of the gamma distribution. For a color version of t...Figure 8.3. Bimodal probability distribution of the number of customers in the s...Figure 8.4. Steady-state distributions. For a color version of this figure, see ...Figure 8.5. vs λ∕N,
6 Chapter 10Figure 10.1. Function H(y) = H(y,t)
List of Tables
1 Chapter 1Table 1.1. Mean number in system for the three casesTable 1.2. Complementary Cumulative distributions of interarrival times
2 Chapter 6Table 6.1. n = 50, k = 2, q = 25 , ε = 1%Table 6.2. n = 50, ω= 2, q = 25 ,ε = 1%Table 6.3. n = 50, k = 10, q = 25, ε = 1%Table 6.4. Estimates of the number of “good” permutations by the fast simulation...Table 6.5. Estimates for the parameters α(s) and β (s)Table 6.6. Comparison of exact values with statistical estimates
3 Chapter 8Table 8.1. Mean sojourn time E(TS) of the customer under service at various valu...Table 8.2. Mean number of retrials for various values of λ and α = βTable 8.3. Numerical values of model parametersTable 8.4. Kolmogorov distance between prelimit distribution P(i) and the asympt...Table 8.5. Kolmogorov distance between prelimit distribution P(i) and the asympt...Table 8.6. Kolmogorov distance between distribution Ps(i) and approximation of t...Table 8.7. Mean number of retrials in prelimiting and limiting situations for va...Table 8.8. Numerical values of model parametersTable 8.9. Simulation resultsTable 8.10. Numerical values of parameters of gamma distributed interarrival tim...Table 8.11. Simulation resultsTable 8.12. Numerical values of parameters of gamma distributed retrial timesTable 8.13. Simulation resultsTable 8.14. Numerical values of model parametersTable
