abstract: This dissertation studies the scheduling in two stochastic networks, a co-located wireless network and an outpatient healthcare network, both of which have a cyclic planning horizon and a deadline-related performance metric. For the co-located wireless network, a time-slotted system is considered. A cycle of planning horizon is called a frame, which consists of a fixed number of time slots. The size of the frame is determined by the upper-layer applications. Packets with deadlines arrive at the beginning of each frame and will be discarded if missing their deadlines, which are in the same frame. Each link of the network is associated with a quality of service constraint and an average transmit power constraint. For this system, a MaxWeight-type problem for which the solutions achieve the throughput optimality is formulated. Since the computational complexity of solving the MaxWeight-type problem with exhaustive search is exponential even for a single-link system, a greedy algorithm with complexity O(nlog(n)) is proposed, which is also throughput optimal. The outpatient healthcare network is modeled as a discrete-time queueing network, in which patients receive diagnosis and treatment planning that involves collaboration between multiple service stations. For each patient, only the root (first) appointment can be scheduled as the following appointments evolve stochastically. The cyclic planing horizon is a week. The root appointment is optimized to maximize the proportion of patients that can complete their care by a class-dependent deadline. In the optimization algorithm, the sojourn time of patients in the healthcare network is approximated with a doubly-stochastic phase-type distribution. To address the computational intractability, a mean-field model with convergence guarantees is proposed. A linear programming-based policy improvement framework is developed, which can approximately solve the original large-scale stochastic optimization in queueing networks of realistic sizes. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

Cellular automata (CA) are fully discrete dynamical systems. Space is represented by a regular lattice while time proceeds in finite steps. Each cell of the lattice is assigned a state, chosen from a finite set of "values". The states of the cells are updated synchronously according to a local interaction rule, whereby each cell obeys the same rule. Formal definitions of deterministic, probabilistic and lattice-gas CA are presented. With the so-called mean-field approximation any CA model can be transformed into a deterministic model with continuous state space. CA rules, which characterise movement, single-component growth and many-component interactions are designed and explored. It is demonstrated that lattice-gas CA offer a suitable tool for modelling such processes and for analysing them by means of the corresponding mean-field approximation. In particular two types of many-component interactions in lattice-gas CA models are introduced and studied. The first CA captures in abstract form the essential ideas of activator-inhibitor interactions of biological systems. Despite of the automaton´s simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed (Turing pattern). In the second CA, rules are designed to mimick the dynamics of excitable systems. Spatial patterns produced by this automaton are the self-organised formation of spiral waves and target patterns. Properties of both pattern formation processes can be well captured by a linear stability analysis of the corresponding nonlinear mean-field (Boltzmann) equations.