Expected delay analysis of polling systems in heavy traffic

We study the expected delay in a cyclic polling model with mixtures of exhaustive and gated service in heavy traffic. We obtain closed-form expressions for the mean delay under standard heavy-traffic scalings, providing new insights into the behaviour of polling systems in heavy traffic. The results lead to excellent approximations of the expected waiting times in practical heavy-load scenarios and moreover, lead to new results for optimizing the system performance with respect to the service disciplines.

[1]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[2]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[3]  Onno Boxma,et al.  Pseudo-conservation laws in cyclic-service systems , 1986 .

[4]  高木 英明,et al.  Analysis of polling systems , 1986 .

[5]  W. P. Groenendijk.  WAITING-TIME APPROXIMATIONS FOR CYCLIC-SERVICE SYSTEMS WITH MIXED SERVICE STRATEGIES , 1988 .

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

[7]  Moshe Sidi,et al.  Dominance relations in polling systems , 1990, Queueing Syst. Theory Appl..

[8]  Kin K. Leung,et al.  Cyclic-Service Systems with Probabilistically-Limited Service , 1991, IEEE J. Sel. Areas Commun..

[9]  J. P. C. Blanc.  Performance evaluation of polling systems by means of the power-series algorithm , 1992, Ann. Oper. Res..

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

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

[12]  Mandyam M. Srinivasan,et al.  Descendant set: an efficient approach for the analysis of polling systems , 1994, IEEE Trans. Commun..

[13]  Hideaki Takagi,et al.  Queueing analysis of polling models: progress in 1990-1994 , 1998 .

[14]  Ward Whitt,et al.  Computing transient and steady-state distributions in polling models by numerical transform inversion , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[15]  Robert D. van der Mei,et al.  Optimization of Polling Systems with Bernoulli Schedules , 1995, Perform. Evaluation.

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

[17]  Ward Whitt,et al.  Computing Distributions and Moments in Polling Models by Numerical Transform Inversion , 1996, Perform. Evaluation.

[18]  Mandyam M. Srinivasan,et al.  The individual station technique for the analysis of cyclic polling systems , 1996 .

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

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

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

[22]  Robert D. van der Mei,et al.  Polling systems in heavy traffic: Higher moments of the delay , 1999, Queueing Syst. Theory Appl..