Marginal Productivity Indices and Linear Programming Relaxations for Dynamic Resource Allocation in Queueing Systems

Many problems concerning resource management in modern communication systems can be simplified to queueing models under Markovian assumptions. The computation of the optimal policy is however often hindered by the curse of dimensionality especially for models that support multiple traffic or job classes. The research focus naturally turns to computationally efficient bounds and high performance heuristics. In this thesis, we apply the indexability theory to the study of admission control of a single server queue and to the buffer sharing problem for a multi-class queueing system. Our main contributions are the following: we derive the Marginal Productivity Index (MPI) and give a sufficient indexability condition for the admission control model by viewing the buffer as the resource; we construct hierarchical Linear Programming (LP) relaxations for the buffer sharing problem and propose an MPI based heuristic with its performance evaluated by discrete event simulation. In our study, the admission control model is used as the building block for the MPI heuristic deployed for the buffer sharing problem. Our condition for indexability only requires that the reward function is concavelike. We also give the explicit non-recursive expression for the MPI calculation. We compare with the previous result of the indexability condition and the MPI for the admission control model that penalizes the rejection action. The study of hierarchical LP relaxations for the buffer sharing problem is based on the exact but intractable LP formulation of the continuous-time Markov Decision Process (MDP). The number of hierarchy levels is equal to the number of job classes. The last one in the hierarchy is exact and corresponds to the exponentially sized LP formulation of the MDP. The first order relaxation is obtained by relaxing the constraint that no buffer overflow may occur in any sample path to the constraint that the average buffer utilization does not exceed the available capacity. Based on the Lagrangian decomposition of the first order relaxation, we propose a heuristic policy based on the concept of MPI. Each one of the decomposed subproblems corresponds to the admission control model we described above. The link to the decomposed sub-problems is the Lagrangian multiplier for the relaxed buffer size constraint in the first order relaxation. Our simulation study indicates the near optimal performance of the heuristic in the (randomly generated) instances investigated

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Incorporating declared capacity uncertainty in optimizing airport slot allocation

Slot allocation is the mechanism used to allocate capacity at congested airports. A number of models have been introduced in the literature aiming to produce airport schedules that optimize the allocation of slot requests to the available airport capacity. A critical parameter affecting the outcome of the slot allocation process is the airport’s declared capacity. Existing airport slot allocation models treat declared capacity as an exogenously defined deterministic parameter. In this presentation we propose a new robust optimization formulation based on the concept of stability radius. The proposed formulation considers endogenously the airport’s declared capacity and expresses it as a function of its throughput. We present results from the application of the proposed approach to a congested airport and we discuss the trade-off between the declared capacity of the airport and the efficiency of the slot allocation process

Clustering surgical procedures for master surgical scheduling

The sound management of operating rooms is a very important task in each hospital. To use this crucial resource efficiently, cyclic master surgery schedules are often developed. To derive sensible schedules, high-quality input data are necessary. In this paper, we focus on the (elective) surgical procedures stochastic durations to determine reasonable, cyclically scheduled surgical clusters. Therefore, we adapt the approach of van Oostrum et al (2008), which was specifically designed for clustering surgical procedures for master surgical scheduling, and present a two-stage solution approach that consists of a new construction heuristic and an improvement heuristic. We conducted a numerical study based on real-world data from a German hospital. The results reveal clusters with considerably reduced variability compared to those of van Oostrum et al(2008)

Efficient scheduling of batch processes in continuous processing lines

This thesis focuses mainly on the development of efficient formulations for scheduling in industrial environments. Likewise, decisions over the processes more related to advanced process control or production planning are included in the scheduling; in this way, the schedule obtained will be more efficient than it would be if the additional restrictions were not considered. The formulations have to emphasize obtaining online implementations, as they are planned to be used in real plants. The most common scheduling problems handled in the industrial environments are: the assignment of tasks to units, the distribution of production among parallel units and the distribution of shared resources among concurrent processes. Most advances in this work are the result of a collaborative work.Departamento de Ingeniería de Sistemas y AutomáticaDoctorado en Ingeniería Industria

Distributed Coordination and Optimisation of Network-Aware Electricity Prosumers

Electricity networks are undergoing a transformation brought on by new technologies, market pressures and environmental concerns. This includes a shift from large centralised generators to small-scale distributed generators. The dramatic cost reductions in rooftop solar PV and battery storage means that prosumers (houses and other entities that can both produce and consume electricity) will have a large role to play in future networks. How can networks be managed going forward so that they run as efficiently as possible in this new prosumer paradigm? Our vision is to treat prosumers as active participants by developing a mechanism that incentivises them to help balance power and support the network. The whole process is automated to produce a near-optimal outcome and to reduce the need for human involvement. The first step is to design an autonomous energy management system (EMS) that can optimise the local costs of each prosumer in response to network electricity prices. In particular, we investigate different optimisation strategies for an EMS in an uncertain household environment. We find that the uncertainty associated with weather, network pricing and occupant behaviour can be effectively handled using online optimisation techniques using a forward receding horizon. The next step is to coordinate the actions of many EMSs spread out across the network, in order to minimise the overall cost of supplying electricity. We propose a distributed algorithm that can efficiently coordinate a network with thousands of prosumers without violating their privacy. We experiment with a range of power flow models of varying degrees of accuracy in order to test their convergence rate, computational burden and solution quality on a suburb-sized microgrid. We find that the higher accuracy model, although non-convex, converges in a timely manner and produces near-optimal solutions. We also develop simple but effective techniques for dealing with residential shiftable loads which require discrete decisions. The final part of the problem we explore is prosumer manipulation of the coordination mechanism. The receding horizon nature of our algorithm is great for managing uncertainty, but it opens up unique opportunities for prosumers to manipulate the actions of others. We formalise this form of receding horizon manipulation and investigate the benefits manipulative agents can obtain. We find that indeed strategic agents can harm the system, but only if they are large enough and have information about the behaviour of other agents. For the rare cases where this is possible, we develop simple privacy-preserving identifiers that monitor agents and distinguish manipulation from uncertainty. Together, these components create a complete solution for the distributed coordination and optimisation of network-aware electricity prosumers