Telecommunications engineers and operations researchers aim to manage complex and fluctuating traffic flows through extended networks. Among other techniques, they have exploited results from the theory of large deviations to estimate the likelihood that a demand in service will overflow the available resources. A key concept in such analyses is the so-called effective bandwidth, reflected in a function Λ(s) defined for positive real numbers s. This function helps define a useful criterion to decide whether a desired quality of service can be upheld over long times, despite the threat of disruptive rare events.
In a recent paper, LML External Fellow Rosemary Harris and colleague Massimo Cavallaro review the concept of the effective bandwidth and show that the function Λ(s) plays a role analogous to the Helmholtz free energy of statistical physics. To model traffic flow, they focus on models from two classes of non-Markovian arrival processes and show how the service request statistics influence the effective bandwidth. To gain insight into more complex and realistic processes, the researchers explore how a so-called “cloning method” adapted from statistical physics – a technique especially useful for exploring rare large deviations via simulations – can be used to efficiently compute the effective bandwidth numerically. Cloning simulations with on-off models show that having more regular on and off periods lowers the effective bandwidth, leaving resources available for other requests.
The authors believe the methods developed could find use in practical applications and the validation of traffic management protocols in a wide variety of settings.
The paper, which has been accepted in the Journal of Statistical Mechanics, is available as a pre-print at https://arxiv.org/abs/1902.00477.