Phân Tích Biến Động cho Mạng Xếp Hàng Hai Trạm Trong Giao Thông Nặng Với Các Quy Trình Đến Bị Điều Khiển Bởi Các Hàng Đợi

Caramellino, L. Strassen’s law of the iterated logarithm for diffusion processes for small time. Stochastic Processes and their Applications, 74(1): 1–19 (1998) Chen, H., Mandelbaum, A. Discrete flow networks: bottleneck analysis and fluid approximations. Mathematics of Operations Research, 16(2): 408–446 (1991) Chen, H., Mandelbaum, A. Stochastic discrete flow networks: diffusion approximations and bottlenecks. Annals of Probability, 19(4): 1463–1519 (1991) Chen, H., Mandelbaum, A. Hierarchical modelling of stochastic networks, Part I: fluid models, Stochastic Modeling and Analysis of Manufacturing Systems, edited by D.D. Yao, Springer-Verlag, 1994, 47–105 Chen, H., Mandelbaum, A. Hierarchical modelling of stochastic networks, Part II: strong approximations. Stochastic Modeling and Analysis of Manufacturing Systems, edited by D.D. Yao, Springer-Verlag, 1994, 107–131 Chen, H., Shanthikumar, J.G. Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic. Disctete Event Dynamic Systems, 4: 269–291 (1994) Chen, H., Shen, X. Strong approximations for multiclass feedforward queueing networks. Annals of Applied Probability, 10: 828–876 (2000) Chen, H., Yao, D.D. Fundamentals of Queueing Networks. Springer-Verlag, New York, 2001 Csörgő, M., Révész, P. Strong Approximations in Probability and Statistics, Academic Press, New York, 1981 Csörgő, M., Horváth, L. Weighted Approximations in Probability and Statistics. Wiley, New York, 1993 Daduna, H. Cycle times in two-stage closed queueing networks: applications to multiprogrammed computer systems with virtual memory. Operations Research, 34(2): 281–288 (1986) Dai, J.G. On the positive Harris recurrence for multiclass queueing networks. Annals of Applied Probability, 5: 49–77 (1995) Gamarnik, D., Zeevi, A. Validity of heavy traffic steady-state approximations in generalized Jackson networks. Annals of Applied Probability, 16(1): 56–90 (2006) Guo, Y. Asymptotic variability analysis for multi-server generalized Jackson network in overloaded. Acta Mathematicae Applicatae Sinica, English Series, 32(3): 713–730 (2016) Guo, Y., Hou, X. Strong approximation method and the (functional) law of iterated logarithm for GI/G/1 queue. Journal of Systems Science and Complexity, 30(5): 1097–1106 (2017) Guo, Y., Hou, X. Functional law of the iterated logarithm for multiclass queues with preemptive priority service discipline: the overloaded case. Stochastic Models in Reliability, Network Security and System Safety Essays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday, edited by Li Q., Wang J. and Yu H., Springer, 2019, 315–343 Guo, Y., Hou, X. Functional law of the iterated logarithm for multiclass queues with preemptive priority service discipline: the underloaded and critically loaded case. Stochastic Models in Reliability, Network Security and System Safety Essays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday, edited by Li Q., Wang J. and Yu H., Springer, 2019, 344–360 Guo, Y., Hou, X., Liu, Y. A functional law of the iterated logarithm for multi-class queues with batch arrivals. Annals of Operations Research, 300: 51–77 (2021) Guo, Y., Li, Z. Asymptotic variability analysis for a two-stage tandem queue, part I: The functional law of the iterated logarithm. Journal of Mathematical Analysis and Applications, 450(2): 1479–1509 (2017) Guo, Y., Li, Z. Asymptotic variability analysis for a two-stage tandem queue, part II: The law of the iterated logarithm. Journal of Mathematical Analysis and Applications, 450(2): 1510–1534 (2017) Guo, Y., Liu, Y. A law of iterated logarithm for multiclass queues with preemptive priority service discipline. Queueing Systems, 79(3): 251–291 (2015) Guo, Y., Liu, Y., Pei, R. Functional law of iterated logarithm for multi-server queues with batch arrivals and customer feedback. Annals of Operations Research, 264: 157–191 (2018) Guo, Y., Song, Y. The (functional) law of the iterated logarithm of the sojourn time for a multiclass queue. Journal of Industrial and Management Optimization, 16(3): 1049–1076 (2020) Horváth, L. Strong approximations of open queueing network. Mathematics of Operations Research, 17: 487–508 (1990) Iglehart, G.L. Multiple channel queues in heavy traffic: IV. Law of the iterated logarithm. Z.Wahrscheinlichkeitstheorie verw. Geb., 1971, 17: 168–180 (1971) Harrison, J.M., Williams, R.J. Brownian models of open queueing networks with homogeneous customer populations. Stochastics, 22: 77–115 (1987) Horváth, L. Strong approximations of renewal processes and their applications. Acta Mathematica Hungarica, 47(1–2): 13–27 (1986) Horváth, L. Strong approximations of open queueing network. Mathematics of Operations Research, 17: 487–508 (1990) Jackson, J.R. Networks of waiting lines. Operations Research, 5: 518–521 (1957) Jackson, J.R. Jobshop-like queueing systems. Management Science, 10: 131–142 (1963) Jin, W.J. A link queue model of network traffic flow. Transportation Science, 55(2): 436–455 (2021) Kleinrock, L. Creating a mathematical theory of computer networks. Operations Research, 50(1): 125–131 (2002) Lee, T. (Yew Sing) Models for design and control of single server polling computer and communication systems. Operations Research, 46(4): 515–531 (1998) Lévy, P. Théorie de l’addition des variables aléatories. Gauthier-Villars, Paris, 1937 Lévy, P. Procesus stochastique et mouvement Brownien. Gauthier-Villars, Paris, 1948 Minkevičius, S., Steišūnas, S. A law of the iterated logarithm for global values of waiting time in multiphase queues. Statistics and Probability Letters, 61(4): 359–371 (2003) Minkevičius, S. On the law of the iterated logarithm in multiserver open queueing networks. Stochastics, 86(1): 46–59 (2014) Sakalauskas, L.L., Minkevičius, S. On the law of the iterated logarithm in open queueing networks. European Journal of Operational Research, 120(3): 632–640 (2000) Reiman, M.I. Open queueing networks in heavy traffic. Mathematics of Operations Research, 9: 441–458 (2000) Strassen, V. An invariance principle for the law of the iterated logarith. Z. Wahrscheinlichkeitstheorie verw Gebiete, 3(3): 211–226 (1964) Tsai, T.H. Empirical law of the iterated logarithm for Markov chains with a countable state space. Stochastic Processes and their Applications, 89(2): 175–191 (2000) Zhang, H., Hsu, G. Strong approximations for priority queues: Head-of-the-line-first discipline. Queueing Systems, 10: 213–233 (1992) Zhang, H., Hsu, G., Wang, R. Strong approximitions for multiple channel queues in heavy traffic. Journal of Applied Probability, 28: 658–670 (1990) Zhang, H. Strong approximations for irreducible closed queueing networks. Advances in Applied Probability, 29: 498–522 (1997)