Optimal routing in queueing networks

The paper:

Optimal Routing in General Finite Multi-Server Queueing Networks

is accepted for publication in the PLOS ONE. This paper has also been lying around for quite some time, but now we managed to finish it up and get it published.

The design of general finite multi-server queueing networks is a challenging problem that arises in many real-life situations, including in computer networks, manufacturing systems, and telecommunication networks. In this paper with Frederico Cruz, we examine the optimal routing problem in arbitrary configured acyclic queueing networks.

The design of networks with random arrivals, random service times, multiple servers, and a finite number of buffer spaces is a challenging problem that arises in many real-life situations, e.g. in manufacturing systems, computer networks, public services, call centers, pedestrian and vehicular traffic, among other situations. The problem is challenging firstly because finite queueing networks are notoriously difficult to analyze analytically, and closed form expressions are not easily constructed for the performance measures of such systems, and secondly because the underlying network design problems involved are usually very hard to solve.

The overall objective in this paper is to maximize the system’s throughput by optimizing the routing probabilities through the queueing network, that is, the focus is specifically to solve the Optimal Routing Problem. We presented numerical results showing the merits of the approach. Approximations for the routing probability vector are also presented and evaluated. This latter is interesting for managerial decision making as well.

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