Dynamic Allocation of Mobile Servers in a Network

Tian, Dongnuan and Shone, Robert and Glazebrook, Kevin (2026) Dynamic Allocation of Mobile Servers in a Network. PhD thesis, Lancaster University.

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Abstract

Many operations research problems focus on optimizing network flows and routing in deterministic settings, yet real-world systems are inherently stochastic and dynamic. Allocating resources efficiently in such environments requires decision-making that responds to both spatial and temporal variations in demand. This thesis studies such problems in stochastic networks, where customer demand arrives randomly over time. Demand points generate jobs according to independent Poisson processes, and homogeneous servers travel across the network to provide service, with exponentially distributed service and switching times. Service and switching times are interruptible, allowing servers to adjust tasks in response to new changes. The objective is to minimize long-run average holding costs by balancing immediate responsiveness with long-term efficiency. The system is modeled as a Markov Decision Process, but the large state space renders exact optimization infeasible. To address this, the thesis develops scalable approximation methods that combine structural insights from index heuristics with computational approaches from approximate dynamic programming and reinforcement learning. The first part of the thesis focuses on single-server systems. Chapter 2 analyzes an infinite-state model and develops index-based policies with desirable structural properties. Chapter 3 considers a finite-state model and introduces reinforcement learning techniques to refine index heuristics through approximate policy improvement. The second part, introduced in Chapter 4, extends the analysis to multi-server systems, where additional challenges of coordination and workload balancing arise. In this setting, multiple servers may occupy the same node and provide service simultaneously. To address these, new heuristics are proposed, involving proportional assignment of demand points to servers to form server-specific local regions, allowing a modified version of the index-based heuristic from Chapter 2 to be applied. Numerical experiments across a variety of network configurations demonstrate that the proposed policies deliver strong performance while remaining computationally tractable.