# Introduction to MAP Queueing Networks

MAP Queueing Networks (QNs) are a superset of product-form queueing
networks and queueing networks with high service variability. MAP QNs
can
both model traditional service time distributions (exponential,
hyper-exponential, Erlang), which do not have memory of the past
sampled values, as well as service processes with temporal dependence
(burstiness, correlations) between consecutive service times. This is
made possible by describing service time processes with Markovian
Arrival Processes (MAPs), see our KPC-fitting
section for further
information on MAP processes and how to fit a service
time trace into a MAP.

This Web page provides scripts to define and analyze a MAP Queueing
Network. We have collected in the MAPQN
Toolbox MATLAB scripts for generating the state space of a MAP
Queueing Network and compute its exact performance by numerically
solving the underlying Markov chain. The toolbox also includes basic
functions for manipulating and fitting small MAPs with two sates. The LR Bounds, instead, are useful for the
approximate evaluation of a MAP Queueing Network performance. By the LR
bounds we can compute upper and lower limit on the main performance
indexes of a queueing network, such as utilization, throughputs (which
also give response times by Little's Law), mean queue-lengths, and
higher-order moments of the queue-lengths.

You can find in the Examples
section how to define some simple queueing networks. For a
technical overview of these models with point to references in Publications and Presentations.