Jaron Sanders

Scaled control in the QED regime

We develop many-server asymptotics in the Quality-and-Efficiency-Driven (QED) regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also derive corrected QED approximations, generalizing earlier results for the Erlang B, C and A models. These results are useful for the dimensioning of large systems equipped with an active control policy. In particular, the corrected approximations can be leveraged to establish the optimality gaps related to square-root staffing and asymptotic dimensioning with admission control.

Wireless network control of interacting Rydberg atoms

We identify a relation between the dynamics of ultracold Rydberg gases in which atoms experience a strong dipole blockade and spontaneous emission, and a stochastic process that models certain wireless random-access networks. We then transfer insights and techniques initially developed for these wireless networks to the realm of Rydberg gases, and explain how the Rydberg gas can be driven into crystal formations using our understanding of wireless networks. Finally, we propose a method to determine Rabi frequencies (laser intensities) such that particles in the Rydberg gas are excited with specified target excitation probabilities, providing control over mixed-state populations.

Achievable performance in product-form networks

We characterize the achievable range of performance measures in product-form networks where one or more system parameters can be freely set by a network operator. Given a product-form network and a set of configurable parameters, we identify which performance measures can be controlled and which target values can be attained. We also discuss an online optimization algorithm, which allows a network operator to set the system parameters so as to achieve target performance metrics. In some cases, the algorithm can be implemented in a distributed fashion, of which we give several examples. Finally, we give conditions that guarantee convergence of the algorithm, under the assumption that the target performance metrics are within the achievable range.

Optimality gaps in asymptotic dimensioning of many-server systems

The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving asymptotic dimensioning problems that trade off revenue, costs and service quality. We derive bounds for the optimality gaps that capture the differences between the true optimum and the asymptotic optimum based on the QED approximations. Our bounds generalize earlier results for classical many-server systems. We also apply our bounds to a many-server system with threshold control.

Online Network Optimization Using Product-Form Markov Processes

We develop a gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the prohibitive computational burden of calculating the gradient in terms of the stationary probabilities. The proposed approach instead relies on measuring empirical frequencies of the various states through simulation or online operation so as to obtain estimates for the gradient. Besides the reduction in computational effort, a further benefit of the online operation lies in the natural adaptation to slow variations in ambient parameters as commonly occurring in dynamic environments. On the downside, the measurements result in inherently noisy and biased estimates. We exploit mixing time results in order to overcome the impact of the bias and establish sufficient conditions for convergence to a globally optimal solution. We discuss our algorithm in the context of different systems, including queueing networks, loss networks, and wireless networks. We also illustrate how the algorithm can be used in such systems to optimize a service/cost trade-off, to map parameter regions that lead to systems meeting specified constraints, and to achieve target performance measures. For the latter application, we first identify which performance measures can be controlled depending on the set of configurable parameters. We then characterize the achievable region of performance measures in product-form networks, and finally we describe how our algorithm can be used to achieve the target performance in an online, distributed fashion, depending on the application context.