This handbook aims to highlight fundamental, methodological and
computational aspects of networks of queues to provide insights and
to unify results that can be applied in a more general manner. The
handbook is organized into five parts:
Part 1 considers exact analytical results such as of product
form type. Topics include characterization of product forms by
physical balance concepts and simple traffic flow equations,
classes of service and queue disciplines that allow a product form,
a unified description of product forms for discrete time queueing
networks, insights for insensitivity, and aggregation and
decomposition results that allow sub networks to be aggregated into
single nodes to reduce computational burden.
""
Part 2 looks at monotonicity and comparison results such as for
computational simplification by either of two approaches:
stochastic monotonicity and ordering results based on the ordering
of the process generators, and comparison results and explicit
error bounds based on an underlying Markov reward structure leading
to ordering of expectations of performance measures.
""
Part 3 presents diffusion and fluid results. It specifically
looks at the fluid regime and the diffusion regime. Both of these
are illustrated through fluid limits for the analysis of system
stability, diffusion approximations for multi-server systems, and a
system fed by Gaussian traffic.
Part 4 illustrates computational and approximate results through
the classical MVA (mean value analysis) and QNA (queueing network
analyzer) for computing mean and variance of performance measures
such as queue lengths and sojourn times; numerical approximation of
response time distributions; and approximate decomposition results
for large open queueing networks.
""
Part 5 enlightens selected applications as loss networks
originating from circuit switched telecommunications applications,
capacity sharing originating from packet switching in data
networks, and a hospital application that is of growing present day
interest.
The book shows that the intertwined progress of theory and
practice will remain to be most intriguing and will continue to be
the basis of further developments in queueing networks."
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