Invariance of workload in queueing systems

In multi-server systems, invariance of workload is a key step in establishing conservation and strong conservation laws. Although several articles have dealt with the issue, invariance of workload has been either assumed, asserted without proof, or the proof given is unsatisfactory, except when service times are exponential. In this article we consider a multi-server queueing system with a work-conserving, non-preemptive, and non-anticipative scheduling rule and give a proof for the invariance of the workload in queue and in system for all such rules. We also show that invariance of workload holds for a subclass of strict priority rules.

[1]  M. Dacre,et al.  The achievable region approach to the optimal control of stochastic systems , 1999 .

[2]  Dimitris Bertsimas,et al.  The achievable region method in the optimal control of queueing systems; formulations, bounds and policies , 1995, Queueing Syst. Theory Appl..

[3]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[4]  Jr. Shaler Stidham.  Optimal Design of Queueing Systems , 2009 .

[5]  Gunter Bolch,et al.  A conservation law for G/G/m queueing systems , 2004, Acta Informatica.

[6]  Awi Federgruen,et al.  Characterization and Optimization of Achievable Performance in General Queueing Systems , 1988, Oper. Res..

[7]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[8]  Shaler Stidham,et al.  Sample-path conservation laws, with applications to scheduling queues and fluid systems , 2000, Queueing Syst. Theory Appl..

[9]  Erol Gelenbe,et al.  Analysis and Synthesis of Computer Systems , 1980 .

[10]  David D. Yao,et al.  Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control , 1992, Oper. Res..

[11]  A. Federgruen,et al.  M / G / c queueing systems with multiple customer classes: characterization and control of achievable performance under nonpreemptive priority rules , 1988 .

[12]  Comparison of servicing strategies in multichannel queueing systems , 1981 .

[13]  S. Stidham,et al.  Sample-Path Analysis of Queueing Systems , 1998 .

[14]  Daniel P. Heyman,et al.  Stochastic models in operations research , 1982 .