The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

QMLE: a methodology for statistical inference of service demands from queueing data

Estimating the demands placed by services on physical resources is an essential step for the definition of performance models. For example, scalability analysis relies on these parameters to predict queueing delays under increasing loads. In this paper, we investigate maximum likelihood (ML) estimators for demands at load-independent and load-dependent resources in systems with parallelism constraints. We define a likelihood function based on state measurements and derive necessary conditions for its maximization. We then obtain novel estimators that accurately and inexpensively obtain service demands using only aggregate state data. With our approach, and also thanks to approximation methods for computing marginal and joint distributions for the load-dependent case, confidence intervals can be rigorously derived, explicitly taking into account both topology and concurrency levels of the services. Our estimators and their confidence intervals are validated against simulations and real system measurements for two multi-tier applications, showing high accuracy also in the presence of load-dependent resources

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