Dynamic Server Allocation for Queueing Networks with Flexible Servers

References

• Andradóttir S., Ayhan H., Down D. G. Server assignment policies for maximizing the steady-state throughput of finite queueing systems. Management Sci. (2001) 47:1421–1439Link, Google Scholar
• Armony M., Bambos N. Queueing networks with interacting service resources. Proc. 37th Annual Allerton Conf. Comm., Control, Comput. (1999) (Monticello, IL)42–51Google Scholar
• Avram F., Bertsimas D., Ricard M., Kelly F., Williams R. J. Fluid models of sequencing problems in open queueing networks: An optimal control approach. The IMA Volumes in Mathematics and Its Applications (1995) 71(Springer-Verlag, New York) 199–237Crossref, Google Scholar
• Bell S. L., Williams R. J. Dynamic scheduling of a system with two parallel servers in heavy traffic with complete resource pooling: Asymptotic optimality of a continuous review threshold policy. Ann. Appl. Probab. (2001) 11:608–649Crossref, Google Scholar
• Bramson M. Instability of FIFO queueing networks. Ann. Appl. Probab. (1994) 4:414–431Crossref, Google Scholar
• Bramson M. Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Systems: Theory Appl. (1997) 23:1–26Crossref, Google Scholar
• Bramson M., Williams R. J. On dynamic scheduling of stochastic networks in heavy traffic and some new results for the workload process. Proc. 39th IEEE Conf. Decision Control. (2000) (Sydney, Australia)516–521Crossref, Google Scholar
• Chen H. Fluid approximations and stability of multiclass queueing networks I: Work-conserving disciplines. Ann. Appl. Probab. (1995) 5:637–665Crossref, Google Scholar
• Dai J. G. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. (1995) 5:49–77Crossref, Google Scholar
• Dai J. G.Stability of Fluid and Stochastic Processing Networks (1999) . Publication No. 9 Centre for Mathematical Physics and Stochastics. http://http://www.maphysto.dk/Google Scholar
• Dai J. G., Meyn S. P. Stability and convergence of moments for multiclass queueing networks via fluid models. IEEE Trans. Automatic Control (1995) 40:1889–1904Crossref, Google Scholar
• Davis M. H. A. Piecewise deterministic Markov processes: A general class of diffusion stochastic models. J. Royal Statist. Soc. Series B (1984) 46:353–388Google Scholar
• Harrison J. M. Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. (2000) 10:75–103Crossref, Google Scholar
• Harrison J. M., LÓpez M. J. Heavy traffic resource pooling in parallel-server systems. Queueing Systems: Theory Appl. (1999) 33:339–368Crossref, Google Scholar
• Harrison J. M., Van Mieghem J. A. Dynamic control of Brownian networks: State space collapse and equivalent workload formulations. Ann. Appl. Probab. (1997) 7:747–771Crossref, Google Scholar
• Hillier F. S., So K. C. On the simultaneous optimization of server and work allocations in production line systems with variable processing times. Oper. Res. (1996) 44:435–443Link, Google Scholar
• Humes C. A regulator stabilization technique: Kumar-Seidman revisited. IEEE Trans. Automatic Control (1994) 39:191–196Crossref, 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, Atlanta, GAGoogle 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) 35:289–298Crossref, Google Scholar
• Laws C. N. Resource pooling in queueing networks with dynamic routing. Adv. Appl. Probab. (1992) 24:699–726Crossref, Google Scholar
• Maglaras C. Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimality. Ann. Appl. Probab. (2000) 10:897–929Crossref, Google Scholar
• Mandelbaum A., Stolyar A. L. Scheduling flexible servers with convex delay costs: Heavy traffic optimality of the generalized cμ rule. Oper. Res. (2003) . ForthcomingGoogle Scholar
• Meyn S. P., Down D. Stability of generalized Jackson networks. Ann. Appl. Probab. (1994) 4:124–148Crossref, Google Scholar
• Rybko A. N., Stolyar A. L. Ergodicity of stochastic processes describing the operation of open queueing networks. Problems Inform. Transmission (1992) 28:199–220Google Scholar
• Sigman K. The stability of open queueing networks. Stochastic Processes and Their Appl. (1990) 35:11–25Crossref, Google Scholar
• Squillante M. S., Xia C. H., Yao D. D., Zhang L. Threshold-based priority policies for parallel-server systems with affinity scheduling. Proc. 2001 American Control Conf. (2001) (Arlington, VA)2992–2999Crossref, Google Scholar
• Williams R. J., McDonald D. R., Turner S. R. E. On dynamic scheduling of a parallel server system with complete resource pooling. Analysis of Communication Networks: Call Centres, Traffic and Performance (2000) 28(American Mathematical Society, Providence, RI) 49–71Fields Institute CommunicationsCrossref, Google Scholar