Performance analysis of queueing networks with blocking (original) (raw)

Analysis of Queueing Networks with Blocking

International Series in Operations Research & Management Science, 2001

Queueing network models have been widely applied for performance modeling and analysis of computer networks. Queueing network models with finite capacity queues and blocking (QNB) allow representing and analyzing systems with finite resources and population constraints. Different protocols can be defined to deal with finite capacity resources and they can be modeled in queueing networks with blocking by various blocking types or mechanisms. Modeling heterogeneous networks having different blocking protocols leads to heterogeneous QNB where the service centers may have different blocking types. QNB are difficult to analyze, except for the special class of product-form networks. Most of the analytical methods proposed in literature provide an approximate solution with a limited computational cost. This tutorial introduces queueing network models with finite capacity queues and various types of blocking. We discuss the main solution techniques for their exact and approximate analysis to derive network performance indices. We present and compare the solution methods for open and closed networks to identify the criteria for the appropriate selection of a solution method. We provide some application examples of this class of models to computer and communication networks.

Queueing Networks with Blocking: Analysis, Solution Algorithms and Properties

Lecture Notes in Computer Science, 2011

Queueing network models with finite capacity queues and blocking are used for modeling and performance evaluation of systems with finite resources and population constraints, such as communication and computer systems, traffic, production and manufacturing systems. Various blocking types can be defined to represent different system behaviors, network protocols and technologies. Queueing networks with blocking are difficult to analyze, except for the special class of product-form networks. Most of the analytical methods proposed in literature provide an approximate solution with a limited computational cost. This tutorial introduces queueing networks with finite capacity queues and blocking, the main solution techniques for their analysis and some network properties. We introduce exact and approximate algorithms for quantitative evaluation of open and closed networks with blocking. We present the conditions under which exact solutions can be derived and some criteria for the appropriate selection of approximate solution method. We present some equivalence properties that relate different types of blocking types that ca be applied for model analysis of heterogeneous networks. We provide some application examples of this class of models to communication networks and distributed computer systems.

Properties and analysis of queueing network models with finite capacities

Lecture Notes in Computer Science, 1993

Queueing network models with finite capacity queues and blocking are used to represent systems with finite capacity resources and with resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in literature to represent the various behaviours of real systems with limited resources. Queueing networks with finite capacity queues and blocking, their properties and the

Queueing networks with blocking

Performance Evaluation, 2003

The area o f 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 o jeueing network models are presented. An overview of the literature in the area o f 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 rejec tion blocking, multiple job classes, general service time distributions and reversible routing the equili brium state probabilities have product form. The reversed process for these netwoiks is examined, and it is proved that it represents a network o f 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.

Closed Queueing Networks With Finite Capacity Queues: Approximate Analysis

Queueing networks with finite capacity queues and blocking are applied to model systems with finite resources and population constraints, such as computer and communication systems, as well as traffic, production and manufacturing systems. Various blocking types can be defined to represent different system behaviors. When a customer attempts to enter a full capacity queue blocking occurs. The analysis of queueing networks with finite capacity queues is often based on approximate methods and simulation, since exact analytical techniques cannot be applied because of the synchronization constraint, except for a few special cases. Various approximate analytical methods have been proposed in literature and provide a solution in terms of average performance indices such as throughput and mean response time. These methods have different characteristics including model assumptions and constraints, type of blocking, algorithm accuracy and efficiency. We present a comparison of some significant approximate methods to analyze closed queueing networks with finite capacity queues. By experimental results we identify the condition under which one can appropriately select a given solution method. Experimental comparisons have been performed by the Queueing Networks with Blocking Analyzer (QNBA), a software tool developed for modelling and analysis of queueing network models with finite capacity queues and blocking.

A survey of product form queueing networks with blocking and their equivalences

Annals of Operations Research, 1994

Queueing network models have been extensively used to represent and analyze resource sharing systems, such as production, communication and information systems. Queueing networks with blocking are used to represent systems with finite capacity resources and with resource constraints. Different blocking mechanisms have been defined and analyzed in the literature to represent distinct behaviors of real systems with limited resources. Exact product form solutions of queueing networks with blocking have been derived, under special constraints, for different blocking mechanisms. In this paper we present a survey of product form solutions of queueing networks with blocking and equivalence properties among different blocking network models. By using such equivalences we can extend product form solution to queueing network models with different blocking mechanisms. The equivalence properties include relationships between open and closed product form queueing networks with different blocking mechanisms.

Parametric Analysis of Queueing Networks with Blocking

1988

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