Queueing Systems

, Volume 60, Issue 3, pp 193-202

First online:

A note on stable flow-equivalent aggregation in closed networks

  • Giuliano CasaleAffiliated withComputer Science Department, College of William and Mary Email author 

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We introduce the Conditional Mean Value Analysis (CMVA) algorithm, an exact solution method for product-form load-dependent closed queueing networks that provides a numerically stable solution of models where the load-dependent Mean Value Analysis (MVA) is numerically unstable. Similarly to the MVA algorithm for constant-rate queues, CMVA performs operations in terms of mean quantities only, i.e., queue-lengths, throughput, response times. Numerical stability derives from a new version of the MVA arrival theorem for load-dependent models which is expressed in terms of mean queue-lengths instead of marginal probabilities. The formula is obtained by the analysis of the conditional state spaces which describe network equilibrium as seen by jobs during their residence times at queues. We also provide a generalization of CMVA to multiclass models that preserves the numerical stability property.


Queueing networks Flow-equivalent aggregation Product-form Numerical stability

Mathematics Subject Classification (2000)

60K25 68M20