Heavy-Traffic Limits of Queueing Networks with Polling Stations: Brownian Motion in a Wedge

Published Online:https://doi.org/10.1287/moor.1070.0273

References

  • Andradóttir S., Ayhan H., Down D. G. Dynamic server allocation for queueing networks with flexible servers. Management Sci. (2003) 51:952–968Google Scholar
  • Bertsimas D., Niño-Mora J. Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part II, the multi-station case. Math. Oper. Res. (1999) 24:331–361LinkGoogle Scholar
  • Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(Wiley, New York) CrossrefGoogle Scholar
  • Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems: Theory Appl. (1998) 30:89–148CrossrefGoogle Scholar
  • Bramson M., Dai J. G. Heavy traffic limits for some queueing networks. Ann. Appl. Probab. (2001) 11:49–90CrossrefGoogle 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):681–719CrossrefGoogle Scholar
  • Coffman E. G., Puhalskii A. A., Reiman M. I. Polling systems in heavy traffic: A Bessel process limit. Math. Oper. Res. (1998) 23:257–303LinkGoogle Scholar
  • Dai J. G., Jennings O. B. Stabilizing queueing networks with setups. Math. Oper. Res. (2004) 29:891–922LinkGoogle Scholar
  • Harrison J. M. The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. (1978) 10:886–905CrossrefGoogle Scholar
  • Iglehart D. L., Whitt W. Multiple channel queues in heavy traffic II: Sequences, networks, and batches. Adv. Appl. Probab. (1970) 2:355–369CrossrefGoogle Scholar
  • Jacod J., Shiryaev A. N.Limit Theorems for Stochastic Processes (2003) 2nd ed.(Springer, Berlin) CrossrefGoogle Scholar
  • Jennings O. B. Heavy-traffic limits of queueing networks with polling stations: A workload averaging principle. (2008) . Working paper, Duke University, Durham, NCGoogle 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
  • Kumar P. R., Seidman T. I. Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automatic Control (1990) AC-35:289–298CrossrefGoogle Scholar
  • Kumar S. Two-server closed networks in heavy traffic: Diffusion limits and asymptotic optimality. Ann. Appl. Probab. (2000) 10:930–961CrossrefGoogle Scholar
  • Kushner H. H.Heavy Traffic Analysis of Controlled Queueing and Communication Networks (2001) (Springer Verlag, New York) CrossrefGoogle Scholar
  • Lan W.-M., Olsen T. L. Multi-product systems with both setup times and costs: Fluid bounds and schedules. Oper. Res.54(3):505–522LinkGoogle Scholar
  • Markovitz D., Wein L. M. Heavy traffic analysis of dynamic cyclic policies: A unified treatment of the single machine scheduling problem. Oper. Res. (2001) 49:246–270LinkGoogle Scholar
  • Markovitz D., Reiman M. I., Wein L. M. The stochastic economic lot scheduling problem: Heavy traffic analysis of dynamic cyclic policies. Oper. Res. (2000) 48:136–154LinkGoogle Scholar
  • Peterson W. P. A heavy traffic limit theorem for networks of queues with multiple customer types. Math. Oper. Res. (1991) 16:90–118LinkGoogle Scholar
  • Reiman M. I., Baccelli F., Fayolle G. Some diffusion approximations with state space collapse. Modeling and Performance Evaluation Methodology (1984) (Springer, Berlin) 209–240CrossrefGoogle Scholar
  • Reiman M. I., Wein L. Heavy traffic analysis of polling systems in tandem. Oper. Res. (1999) 47:524–534LinkGoogle Scholar
  • Resing J. A. C. Polling systems and multitype branching processes. Queueing Systems: Theory Appl. (1993) 13(4):409–426CrossrefGoogle Scholar
  • Takagi H.Analysis of Polling Systems (1986) (MIT Press, Cambridge, MA) Google Scholar
  • Takagi H., Takagi H. Queueing analysis of polling systems. Stochastic Analysis of Computer and Communication Systems (1990) (North-Holland, Amsterdam) 267–318Google Scholar
  • Van der Mei R. D., Levy H. Polling systems in heavy traffic: Exhaustiveness of service policies. Queueing Systems: Theory Appl. (1997) 27(2):227–250CrossrefGoogle Scholar
  • Van der Mei R. D., Olsen T. L. Polling systems with periodic server routing in heavy-traffic: Distribution of the delay. J. Appl. Probab. (2003) 40(2):305–326CrossrefGoogle Scholar
  • Varadhan S. R. S., Williams R. J. Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. (1985) 38:405–443CrossrefGoogle Scholar
  • Whitt W. Weak convergence theorems for priority queues: Preemptive-resume discipline. J. Appl. Probab. (1971) 8:74–94CrossrefGoogle Scholar
  • Williams R. J. Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems: Theory Appl. (1998a) 30:27–88CrossrefGoogle Scholar
  • Williams R. J. An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems: Theory Appl. (1998b) 30:5–25CrossrefGoogle Scholar
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