Polling systems with periodic server routing in heavy traffic: renewal arrivals

This paper considers heavy-traffic limit theorems for polling models with periodic server routing with general renewal arrivals and mixtures of gated and exhaustive service policies. We provide a strong conjecture for the limiting waiting-time distribution in a general parameter setting when the load tends to 1, under proper heavy-traffic scalings.

[1]  Lawrence M. Wein,et al.  Heavy Traffic Analysis of Polling Systems in Tandem , 2011, Oper. Res..

[2]  R. D. van der Mei Polling systems with periodic server routing in heavy traffic , 1999 .

[3]  Hideaki Takagi,et al.  Application of Polling Models to Computer Networks , 1991, Comput. Networks ISDN Syst..

[4]  Jac Jacques Resing,et al.  Polling systems with regularly varying service and/or switchover times , 1999 .

[5]  Lawrence M. Wein,et al.  Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem , 2015, Oper. Res..

[6]  Jacques Resing,et al.  Polling systems and multitype branching processes , 1993, Queueing Syst. Theory Appl..

[7]  T. Olsen,et al.  Periodic polling systems in heavy-traffic: distribution of the delay , 2003 .

[8]  Lawrence M. Wein,et al.  Dynamic Scheduling of a Two-Class Queue with Setups , 2011, Oper. Res..

[9]  Izhak Rubin,et al.  Polling with a General-Service Order Table , 1987, IEEE Trans. Commun..

[10]  Onno Boxma,et al.  The single server queue : heavy tails and heavy traffic , 2000 .

[11]  Edward G. Coffman,et al.  Polling Systems in Heavy Traffic: A Bessel Process Limit , 1998, Math. Oper. Res..

[12]  Moshe Sidi,et al.  Polling systems: applications, modeling, and optimization , 1990, IEEE Trans. Commun..

[13]  Lawrence M. Wein,et al.  The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies , 2015, Oper. Res..

[14]  Lawrence M. Wein,et al.  Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem , 2015, Transp. Sci..

[15]  Feng Cheng,et al.  A Practical Scheduling Method for Multiclass Production Systems with Setups , 1999 .

[16]  M. Reiman,et al.  Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle , 1995 .

[17]  Christine Fricker,et al.  Monotonicity and stability of periodic polling models , 1994, Queueing Syst. Theory Appl..

[18]  François Baccelli,et al.  Elements Of Queueing Theory , 1994 .

[19]  Walter Willinger,et al.  Self-Similar Network Traffic and Performance Evaluation , 2000 .

[20]  Robert D. van der Mei,et al.  Polling systems in heavy traffic: Exhaustiveness of service policies , 1997, Queueing Syst. Theory Appl..

[21]  Ruth J. Williams,et al.  Brownian models of multiclass queueing networks , 1990, 29th IEEE Conference on Decision and Control.

[22]  Tava Lennon Olsen,et al.  Approximations for the waiting time distribution in polling models with and without state-dependent setups , 2001, Oper. Res. Lett..

[23]  J. Michael Harrison,et al.  Brownian models of multiclass queueing networks: Current status and open problems , 1993, Queueing Syst. Theory Appl..