References
- L. Afanasjeva, On periodic distribution of waiting-time process. In: Stability problems for stochastic models (Uzhgorod, 1984), Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1155 (1985) 1–20.
- G. Arsenishvili, Diffusion approximation of virtual waiting time of the M/M/1 system (the ]mar tingale approach), Kibernetika 1 (1991), pp. 90–93, 135 (in Russian).
- S. Belousova, The waiting time under heavy traffic for priority systems with semi-Markov servicing, Ukrain. Math. Zh. 37(4) (1985), pp. 411–417, 542 (in Russian).
- P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
- A. Borovkov, Stochastic Processes in Queueing Theory, Nauka, Moscow, 1972 (in Russian).
- A. Borovkov, Asymptotic Methods in Theory of Queues, Nauka, Moscow, 1980 (in Russian).
- O. Boxma, On a tandem queueing model with identical service times at both counters. I, II, Adv. Appl. Prob. 11(3) (1979), pp. 616–643, 644–659.
- J. Cohen, Asymptotic relations in queueing theory, Stochastic Process. Appl. 1 (1973), pp. 107–124.
- M. Csörgo, P. Deheuvels and L. Horváth, An approximation of stopped sums with applications in queueing theory, Adv. Appl. Prob. 19(3) (1987), pp. 674–690.
- Y. Guo and Y. Liu, A law of iterated logarithm for multiclass queues with preemptive priority service discipline, Queueing Syst. 79(3) (2015), pp. 251–291.
- Y. Guo, Asymptotic variability analysis for multi-Server generalized Jackson network in overloaded, Acta Mathematicae Applicatae Sinica, English Series 32(3) (2016), pp. 713–730.
- Y. Guo and Z. Li, Asymptotic variability analysis for a two-stage tandem queue, part I: the functional law of the iterated logarithm, J. Math. Anal. Appl. 450(2) (2017), pp. 1479–1509.
- Y. Guo and Z. Li, Asymptotic variability analysis for a two-stage tandem queue, part II: the law of the iterated logarithm, J. Math. Anal. Appl. 450(2) (2017), pp. 1510–1534.
- G. Falin, Periodic queues in heavy traffic, Adv. Appl. Prob. 21(2) (1989), pp. 485–487.
- J. Harrison and V. Nguyen, Brownian models of multiclass queueing networks: current status and open problems, Queueing Syst.: Theory Appl. 13 (1993), pp. 5–40.
- J. Hooke and N. Prabhu, Priority queues in heavy traffic, Oper.Res. 8(5) (1971), pp. 1–9.
- D. Iglehart, Multiple channel queues in heavy traffic. IV. law of the iterated logarithm, Zeitschrift Für Wahrscheinlicht-Keitstheorie Und Verwandte Gebiete 17 (1971), pp. 168–180.
- D. Iglehart, Weak convergence in queueing theory, Adv. Appl. Prob. 5 (1973), pp. 570–594.
- D. Iglehart and W. Whitt, Multiple channel queues in heavy traffic. I, Adv. Appl. Prob. 2 (1970a), pp. 150–177.
- D. Iglehart and W. Whitt, Multiple channel queues in heavy traffic. II: sequences, networks and batches, Ad. Appl. Prob. 2 (1970b), pp. 355–369.
- F. Karpelevich and A. Kreinin, Heavy Traffic Limits for Multiphase Queues, American Mathematical Society, Providence, Rhode Island, 1994.
- J. Kingman, On queues in heavy traffic, J. R. Statist. Soc. 24 (1962a), pp. 383–392.
- J. Kingman, The single server queue in heavy traffic, Proc. Camb. Phil. Soc. 57 (1962b), pp. 902–904.
- E. Kyprianou, The virtual waiting time of the GI/G/1 queue in heavy traffic, Adv. Appl. Prob. 3 (1971a), pp. 249–268.
- E. Kyprianou, On the quasi-stationary distribution of the virtual waiting time in queues with poisson arrivals, J. Appl. Prob. 8 (1971b), pp. 494–507.
- E. Kyprianou, On the quasi-stationary distributions of GI/M/1 queue, J. Appl. Prob. 9 (1972a), pp. 117–128.
- E. Kyprianou, The quasi-stationary distributions of queues in heavy traffic, J. Appl. Prob. 9 (1972b), pp. 821–831.
- H. Kobyashi, Application of the diffusion approximation to queueing networks, J. ACM 21 (1974), pp. 316–328.
- S. Minkevičius, On the law of the iterated logarithm in multiphase queueing systems, Lithuanian Math. J. 35(3) (1995), pp. 360–366.
- S. Minkevičius, On the law of the iterated logarithm in multiphase queueing systems. II, Informatica 8(3) (1997), pp. 367–376.
- S. Minkevičius, Complex transient processes in multiphase queuing systems. II, Lietuvos Matematikos Rinkinys 39(3) (1999), pp. 343–356 (in Russian).
- S. Minkevičius, On the law of the iterated logarithm for extreme values in multiphase queueing systems, Lithuanian Math. J. 42 (2002), pp. 470–486 (in Russian).
- S. Minkevičius, On the law of the iterated logarithm in multiserver open queueing networks, Stochastics 86(1) (2014), pp. 46–59.
- A. Pečinkin and H. Aripov, The limit distribution of the virtual waiting time in the system GI/M/1, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. 1 (1975), pp. 27–32, 104 (in Russian).
- Y. Prohorov, Transient phenomena in queues, Lietuvos Matematikos Rinkinys 3 (1963), pp. 199–206 (in Russian).
- A. Puhalskii, Moderate deviations for queues in critical loading, Queueing Syst.: Theory Appl. 31(3–4) (1999), pp. 359–392.
- Z.H. Qin and X.G. Hui, Strong approximations for the open queueing network in heavy traffic, Sci. China Ser. A 35(5) (1992), pp. 521–535.
- M. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984), pp. 441–459.
- L. Sakalauskas and S. Minkevičius, On the law of the iterated logarithm in open queueing networks, Eur. J. Oper. Res. 120 (2000), pp. 632–640.
- R. Schassberger, Warteschlangen, Springer-Verlag, Vienna–New York, 1973.
- V. Strassen, An invariance principle for the law of the iterated logarithm, Zeitschrift Für Wahrscheinlicht-Keitstheorie Und Verwandte Gebiete 3 (1964), pp. 211–226.
- W. Szczotka, An invariance principle for queues in heavy traffic, Math. Oper. Forsch. Statist. Ser. Optim. 8(4) (1977), pp. 591–631.
- W. Szczotka and K. Topolski, Conditioned limit theorem for the pair of waiting time and queue line processes, Queueing Syst.: Theory Appl. 5(4) (1989), pp. 393–400.
- O. Teunis, Some more results for the stable M/G/1 queue in heavy traffic, J. Appl. Prob. 16(1) (1979), pp. 187–197.
- W. Whitt, Heavy traffic limit theorems for queues: a survey, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin–Heidelberg–New York, 98 (1974), 307–350.
- W. Whitt, An interpolation approximation for the mean workload in a GI/G/1 queue, Oper. Res. 37(6) (1989), pp. 936–952.