Stochastic modeling and optimization of large-scale and resource-constrained systems

QC 20261008

Abstract

This thesis investigates how large-scale systems can make effective use of limited communication, computing, and observation resources when operating under uncertainty, incomplete information, or evolving conditions. Across the problems considered, a common conclusion emerges: reliable and efficient performance does not necessarily require continuously updated information or simply increasing capacity and computational power; instead, it depends on identifying the stochastic structure of the system and using it to determine when information is needed and where resources are most valuable. To this end, this thesis develops stochastic models, analytical methods, and optimization frameworks for three problems in edge intelligence and smart microscopy.

The first contribution considers load balancing in distributed computing systems in which users independently select servers without access to a continuously updated global system state. Instead, users construct local estimates from their own routing decisions and from occasional status updates broadcast by the servers. The analysis establishes conditions under which such decentralized operation remains stable despite sparse information, communication losses, and heterogeneous server capacities. Increasing the relative update rate generally reduces the stationary backlog and brings the distributed policy closer to the centralized benchmark. However, for sparse update rates, the backlog can be non-monotonic in the update reception probability: moderate communication losses diversify user beliefs and can mitigate synchronized routing based on outdated server states, whereas at higher relative update rates, more reliable reception improves performance.

The second contribution addresses the joint dimensioning of wireless and computing resources in multi-cellular edge-intelligent networks. Wireless access, spatially distributed traffic, edge-server queueing, and AI inference are modeled as a coupled stochastic system subject to statistical requirements on latency, coverage, server load, and inference accuracy. Stochastic geometry is used to characterize the spatial properties of the cellular network and to derive tractable uplink-capacity expressions. These results are integrated with queueing models and empirically characterized inference workloads to formulate an end-to-end resource-dimensioning problem for bandwidth and computing capacity. The resulting analysis exposes trade-offs that cannot be identified when communication and computation are designed independently. In noise-limited systems, denser infrastructure improves wireless conditions but reduces statistical multiplexing at the servers, creating an opposing computing cost. In interference-limited systems, densification with fixed frequency reuse may provide little benefit because increased interference offsets shorter transmission distances; when frequency reuse is adapted with network density, densification can again reduce both communication and computing requirements.

The third contribution considers adaptive observation in automated microscopy, where many asynchronously evolving regions of interest compete for a limited imaging budget. The biological dynamics are modeled as large ensembles of independent Markov processes, for which exact and asymptotic characterizations enable a scalable representation of their aggregate temporal evolution. Building on this structure, the observation problem is formulated as a restless multi-process multi-armed bandit under partial observability, and a computationally efficient Whittle-index policy is derived. Numerical results show that the policy is particularly effective when temporal persistence makes past observations informative about future activity. Experiments on biological microscopy data further show that the proposed policy captures 93% more biologically relevant events than fixed cyclic scanning.

Taken together, these contributions show that reliable operation in resource-constrained stochastic systems does not necessarily require complete information, continuous coordination, or ever-increasing infrastructure.  Instead, the key is to identify which aspects of uncertainty and system history are relevant to decision-making, and to allocate communication, computation, and observation resources accordingly. The thesis provides analytical and algorithmic tools for determining when information is sufficient for distributed coordination, how communication and computation should be provisioned jointly, and how scarce observations can be directed toward the most informative parts of a dynamically evolving system. More broadly, the results illustrate how uncovering and exploiting stochastic structure can turn uncertainty into a source of actionable information, enabling more efficient and informed decisions even when resources are fundamentally limited.

Link to DiVA