Averaging Principles for a Diffusion-Scaled, Heavy-Traffic Polling Station with K Job Classes

References

• Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(Wiley, New York) Crossref, Google Scholar
• Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems: Theory Appl. (1998) 30:89–148Crossref, Google Scholar
• Çinlar E.Introduction to Stochastic Processes (1975) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Coffman E. G. Polling systems in heavy traffic: A Bessel process limit. Math. Oper. Res. (1998) 23:257–303Link, Google Scholar
• Coffman E. G., Puhalskii A. A., Reiman M. I. Polling systems with zero switchover times: A heavy traffic averaging principle. Ann. Appl. Probab. (1995) 5(3):681–719Crossref, Google Scholar
• Jacod J., Shiryaev A. N.Limit Theorems for Stochastic Processes (2003) 2nd ed.(Springer, Berlin) Crossref, Google Scholar
• Jennings O. B. Multiclass queueing networks with setup delays: Stability analysis and heavy traffic approximation. (2000) . Ph.D. thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology, AtlantaGoogle Scholar
• Jennings O. B. Heavy-traffic limits of queueing networks with polling stations: Brownian motion in a wedge. Math. Oper. Res. (2008) 33(1):12–35Link, Google Scholar
• Lennon-Olsen T. Approximations for the waiting time distribution in polling models with and without state-dependent setups. Oper. Res. Lett. (2001) 28(3):113–123Crossref, Google Scholar
• Lennon-Olsen T., Van der Mei R. D. Polling systems with periodic server routing in heavy-traffic: Distribution of the delay. J. Appl. Probab. (2003) 40(2):305–326Crossref, Google Scholar
• Mann H. B., Wald A. On stochastic limit and order relationships. Ann. Math. Statist. (1943) 14:217–226Crossref, Google Scholar
• Van der Mei R. D., Levy H. Polling systems in heavy traffic: Exhaustiveness of service policies. Queueing Systems: Theory Appl. (1997) 27(3–4):227–250Crossref, Google Scholar
• Williams R. J. An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems: Theory Appl. (1998) 30:5–25Crossref, Google Scholar
• Williams R. J. Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems: Theory Appl. (1998) 30:27–88Crossref, Google Scholar