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.