QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements

AbstractWorkload measurements in enterprise systems often lead to observe a dependence between the number of requests running at a resource and their mean service requirements. However, multiclass performance models that feature these dependences are challenging to analyze, a fact that discourages practitioners from characterizing workload dependences. We here focus on closed multiclass queueing networks and introduce QD-AMVA, the first approximate mean-value analysis (AMVA) algorithm that can efficiently and robustly analyze queue-dependent service times in a multiclass setting. A key feature of QD-AMVA is that it operates on mean values, avoiding the computation of state probabilities. This property is an innovative result for state-dependent models, which increases the computational efficiency and numerical robustness of their evaluation. Extensive validation on random examples, a cloud load-balancing case study and comparison with a fluid method and an existing AMVA approximation prove that QD-AMVA is efficient, robust and easy to apply, thus enhancing the tractability of queue-dependent models

Queueing Networks With Blocking.

The area of classical (product form) queueing networks is briefly discussed. The principal results for classical queueing networks are summarized. The transfer, service and rejection blocking policies are defined, and their use in queueing network models are presented. An overview of the literature in the area of queueing networks with blocking is given, and the relations between the three blocking policies is discussed in general. Duality theorems for open and closed queueing networks with rejection blocking and a single job class are proved. Using a duality theorem, an exact solution is found for closed blocking networks which contain so many jobs that if one station is empty all other stations are full. Algorithms to compute performance measures, in particular throughputs, follow from the way the solution is obtained. It is then proved that for open, mixed and closed networks with rejection blocking, multiple job classes, general service time distributions and reversible routing the equilibrium state probabilities have product form. The reversed process for these networks is examined, and it is proved that it represents a network of the same type. Formulas for throughputs are derived, and algorithms to compute performance measures are outlined. Finally, closed central server models with state-dependent routing, multiple job classes and rejection blocking are investigated. The equilibrium state probabilities have a modified product form, and the reversed process is a network of the same type. Formulas for performance measures are derived for this model and algorithms to compute them are outlined