A Mathematical Measure for Flexibility in Communication Networks

Abstract

For communication networks research, flexibility of network design and networking solutions is considered a competitive advantage. However, this advantage is typically only claimed on an argumentative level and neither formally supported nor thoroughly investigated. To support the claim of flexibility and to make the flexibility of different solutions comparable, its degree must be quantified and thus made measurable. In this work, we propose a mathematical basis to quantify a degree of flexibility achieved by communication networks. We motivate that flexibility can be cast to the "size" of a set of achievable demand changes. Consequently, we propose the use of mathematical measure theory to quantify achieved networking flexibility. We derive several implications on the basic structure of flexibility, extend the insights towards a utility of flexibility and develop systematic approaches for both analytical and empirical measurement of flexibility. We apply the insights to several use-cases, showing that flexibility is in fact not as straight-forward to argue as it seems at first glance.

Optimizing the Flexibility of SDN Control Plane

“…For example, in DC traffic engineering, the authors in [24] consider it as the additional throughput performance for increasing traffic, in comparison to a proportional behavior. In [8], we propose a general measure of flexibility that is abstracted from different use cases. We interpret flexibility of a network as its ability to adapt its state to changing requirements promptly and with little effort in order to satisfy specific requests.…”

“…We interpret flexibility of a network as its ability to adapt its state to changing requirements promptly and with little effort in order to satisfy specific requests. Formally, we have the following definition: Flexibility is the ratio of the number of requests that can be satisfied (adapted) over the total number of requests, under predefined time and cost constraint [8].…”

“…The definition of cost constraint, on the other hand, is broader and use case-specific. It can reflect the induced cost of adaptation, which is the extra mechanism to enable the adaption, the overhead to implement the adaptation, and even a function of the system's performance after and/or before the adaptation [8]. For a flexible system, we would expect both constraints as small as possible.…”

“…Moreover, there is no existing metric that evaluates the DC placement as a design choice for distributed control plane. We advocate in our previous work [1], [8], [9] that a measure of flexibility would be beneficial when comparing different design choices of a network. Such a measure is derived from the definition of flexibility as a system's ability to satisfy external changing requirements in a timely and cost-efficient manner.…”

“…That is, in addition to the ability to dynamically adapt, the adaptation time (i.e., how fast the adaptation can take) and cost (e.g., the induced extra latency and bandwidth) matter when evaluating flexibility. With the flexibility measurement framework [8] in mind, we proceed with optimizing the flexibility of our network, which in a nutshell involves deciding the network's design parameters, e.g., the number of DCs and their locations, to deliver the highest possible flexibility value.…”