A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of $RG$-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method

General solution of the Poisson equation for Quasi-Birth-and-Death processes

We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm u$ is the unknown. Our main result is to provide the general solution of this equation. To this purpose we use the block tridiagonal and block Toeplitz structure of the matrix $P$ to obtain a set of matrix difference equations, which are solved by constructing suitable resolvent triples

Modeling, optimization, and sensitivity analysis of a continuous multi-segment crystallizer for production of active pharmaceutical ingredients

We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the mean crystal size, minimizing the coefficient of variation, or minimizing the sum of the squared errors when attempting to hit a target distribution. Such optimizations are all highly nonconvex, necessitating the use of the genetic algorithm. Our results for the optimization of a process for crystallizing flufenamic acid showed improvement in crystal size over prior literature results. Through the use of a novel simultaneous design and control (SDC) methodology, we have further optimized the flowrates and crystallizer geometry in tandem.^ We have further investigated the robustness of this process and observe significant sensitivity to error in antisolvent flowrate, as well as the kinetic parameters of crystallization. We have lastly performed a parametric study on the use of the MSMA-PFC for in-situ dissolution of fine crystals back into solution. Fine crystals are a known processing difficulty in drug manufacture, thus motivating the development of a process that can eliminate them efficiently. Prior results for cooling crystallization indicated this to be possible. However, our results show little to no dissolution is used after optimizing the crystallizer, indicating the negative impact of adding pure solvent to the process (reduced concentration via dilution, and decreased residence time) outweighs the positive benefits of dissolving fines. The prior results for cooling crystallization did not possess this coupling between flowrate, residence time, and concentration, thus making fines dissolution significantly more beneficial for that process. We conclude that the success observed in hitting the target distribution has more to do with using multiple segments and having finer control over supersaturation than with the ability to go below solubility. Our results showed that excessive nucleation still overwhelms the MSMA-PFC for in-situ fines dissolution when nucleation is too high

Expanding the Horizons of Manufacturing: Towards Wide Integration, Smart Systems and Tools

This research topic aims at enterprise-wide modeling and optimization (EWMO) through the development and application of integrated modeling, simulation and optimization methodologies, and computer-aided tools for reliable and sustainable improvement opportunities within the entire manufacturing network (raw materials, production plants, distribution, retailers, and customers) and its components. This integrated approach incorporates information from the local primary control and supervisory modules into the scheduling/planning formulation. That makes it possible to dynamically react to incidents that occur in the network components at the appropriate decision-making level, requiring fewer resources, emitting less waste, and allowing for better responsiveness in changing market requirements and operational variations, reducing cost, waste, energy consumption and environmental impact, and increasing the benefits. More recently, the exploitation of new technology integration, such as through semantic models in formal knowledge models, allows for the capture and utilization of domain knowledge, human knowledge, and expert knowledge toward comprehensive intelligent management. Otherwise, the development of advanced technologies and tools, such as cyber-physical systems, the Internet of Things, the Industrial Internet of Things, Artificial Intelligence, Big Data, Cloud Computing, Blockchain, etc., have captured the attention of manufacturing enterprises toward intelligent manufacturing systems

A Fluid Limit for an Overloaded X Model Via a Stochastic Averaging Principle

We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed in a recent paper as a way for one service system to help another in face of an unexpected overload. Under FQR-T, customers are served by their own service pool until a threshold is exceeded. Then, one-way sharing is activated with customers from one class allowed to be served in both pools. After the control is activated, it aims to keep the two queues at a pre-specified fixed ratio. For large systems that fixed ratio is achieved approximately. For the fluid limit, or FWLLN, we consider a sequence of properly scaled X models in overload operating under FQR-T. Our proof of the FWLLN follows the compactness approach, i.e., we show that the sequence of scaled processes is tight, and then show that all converging subsequences have the specified limit. The characterization step is complicated because the queue-difference processes, which determine the customer-server assignments, remain stochastically bounded, and need to be considered without spatial scaling. Asymptotically, these queue-difference processes operate in a faster time scale than the fluid-scaled processes. In the limit, due to a separation of time scales, the driving processes converge to a time-dependent steady state (or local average) of a time-varying fast-time-scale process (FTSP). This averaging principle (AP) allows us to replace the driving processes with the long-run average behavior of the FTSP.Comment: There are 55 pages, 46 references and 0 figure

Formulation Design and Evaluation of Amorphous and Crystalline Nanoparticles of BCS Class II and II/IV Drugs

In the last few decades, the pharmaceutical industry has employed a quality by design (QbD) approach for conventional drug product development to minimize errors in product optimization and validation. Lately, this has been extended to novel pharmaceutical drug products (such as nanocrystalline and nanoamorphous drug products). The present research emphasizes the design and development of stable nanocrystalline and nanoamorphous formulations of BCS class II and II/IV drugs via a comprehensive QbD approach. This approach was used to identify, optimize, validate and control different critical process parameters and critical formulation parameters of solid nano-formulations. The objectives of this research were to: (1) investigate any correlation between critical process parameters and critical formulation parameters as well as critical quality attributes using a comprehensive QbD approach; (2) investigate the effect of temperature and relative humidity during accelerated and/or long term stability studies; and (3) investigate drug-stabilizer interaction mechanisms. Based on proof-of-concept studies, BCS class II and II/IV drugs with different physicochemical properties were utilized for the successful development of stable and robust nanocrystalline and nanoamorphous formulations. Different top-down and bottom-up manufacturing techniques: wet media milling (nanocrystalline formulations); and sonoprecipitation (nanoamorphous formulations) followed by spray drying were used to prepare the solid nanoformulations. Based on the pre-formulation studies, drug-stabilizer interaction mechanisms were investigated via different solid-state tools (DSC, FTIR and PXRD). The DSC data was used to determine whether drug-stabilizer interactions occurred and the type of interaction was investigated using FTIR. PXRD was used to detect the solid-state form and any polymorphic transition in the drug-stabilizer complexes. Low and intermediate molecular weight polymers, high glass transition (Tg) sugars and anionic surfactants were determined to be the strong stabilizers during processing and storage stability of the solid nanoformulations. A quality by design approach was used to establish a correlation between critical process parameters, critical formulation parameters and critical quality attributes for the development of the robust solid nanoformulations. Critical process parameters related to manufacturing techniques: wet media milling (milling speed, milling time, pump speed); sonoprecipitation (ultra-sonication speed, time); and spray drying (inlet temperature, aspirator rate, feed flow rate) were investigated. Critical formulation parameters: drug and stabilizer concentrations were investigated. The process speed, time, inlet temperature, flow rates, drug concentrations and stabilizer concentration significantly affected the particle size and total product yield of the solid nanoformulations. Following the DoE studies, validation was performed to ensure reproducibility and robustness of different CQAs (particle size, total product yield, drug loading, moisture content and zeta potential) of solid nanoformulations prepared using the optimized and predicted process and formulation parameters. Stability studies were performed at three different conditions: 4°C, 25°C/60% RH and 40°C/75% RH for different time-points (1, 3, 6 and 12 month/s) to investigate the effect of temperature and relative humidity on the nanoamorphous and nanocrystalline formulations. Stability studies revealed the following trend: 4°C (most stable) \u3e 25°C/60% RH \u3e 40°C/75% RH (least stable) for the optimized spray-dried nanocrystalline and nanoamorphous formulations in terms of physicochemical attributes, crystallinity and in vitro dissolution testing. An array of orthogonal solid-state tools (DSC, ATR-FTIR, PLM, PXRD and AFM) were utilized to characterize the solid-state form (crystalline, amorphous, semi-crystalline and semi-amorphous) and polymorphic transitions in the freshly prepared solid nanoformulations and those stored at different stability conditions. Particle size distribution and moisture content analysis were performed via Zetasizer (ZS90) and Karl fisher titration, respectively. RP-HPLC was used to detect drug loading in the solid nanoformulations. The solid nano-formulations prepared via the comprehensive QbD approach resulted in a remarkably high total product yield (~70-80% w/w) with small, uniform and homogenous particle size (200-300 nm, 0.05-0.2 PDI). In vitro dissolution testing were performed to investigate the effect of pH, solid-state form, particle size, temperature and relative humidity on drug release from the solid nano-formulations. USP apparatus I and II were utilized to study and differentiate the drug release from the nanoamorphous and nanocrystalline formulations based on their solid-state form and particle size. Drug release from the solid nanoformulations followed a particle size dependent dissolution trend. Nanoamorphous and nanocrystalline formulations showed a high dissolution rate/kinetic solubility compared to the macro-sized formulations. To sum up, the comprehensive QbD approach performed in the present research delineates an important and time-saving strategy to develop successful, robust and stable solid nanoamorphous and nanocrystalline formulations with the desired physicochemical attributes/CQAs, solid-state form and in vitro and/or in vivo performance

The derivation of bioprocess understanding from mechanistic models of chromatography

This thesis, completed in collaboration with Purification Process Development of Pfizer Biotherapeutics, is concerned with how mechanistic models of chromatographic bioseparations can be applied in industry to accelerate development and increase robustness of industrial protein purification processes, whilst also realising the benefits of a systematic development approach based on fundamental process and product understanding. The first results chapter considers the application of mechanistic models to provide a link between high throughput screening (HTS) and scouting runs conducted during early process development. The chapter focuses on an anion exchange (AEX) weak partitioning chromatography (WPC) polishing step in a platform monoclonal antibody purification process. Adsorption isotherms are formulated from experimental multicomponent batch adsorption studies of monomer – aggregate. A new approach is taken where the adsorption equilibria is characterised as a function of the product partition coefficient, enabling the model to be applied to new candidate monoclonal antibodies without additional experimental effort. Stochastic simulations conducted at an early stage of process development identify promising operating parameter ranges for challenging separations, directs optimal performance, and reduces development times. A detailed analysis of model predictions increases fundamental knowledge and understanding of the complex WPC multidimensional design space, which enables better informed process development at Pfizer. Resin fouling over a chromatography columns lifetime can cause significant (undesired) changes in process performance. A lack of fundamental knowledge and mechanistic understanding of fouling in industrial bioseparations limits the application of mechanistic models in industry. An experimental investigation was conducted into fouling of the AEX WPC considered in the first results chapter. Analysis of fouled resin samples by batch uptake experiments, scanning electron microscopy, confocal laser scanning microscopy and scale down column studies, indicated significant blockage of the pores at the resin surface occurred that after successive batch cycles. Mass transport into resin particles was severely hindered, but saturation capacity was not affected. The increased understanding of resin fouling can direct future efforts to mitigate this detrimental phenomenon and maintain process performance, whilst providing a basis for the development of new fouling models. The third results chapter considers an industrial hydrophobic interaction chromatography (HIC) separation at a late stage of process development. Resin lot variability, combined with a variable feed stream, had resulted in serious performance issues during the purification of a therapeutic protein from crude feed material. The traditional approach to tackling this type of problem involves defining a design space based on an extensive experimental effort directed by factorial design of experiments conducted at great cost. The result is a fixed, inflexible manufacturing process, with a control strategy based on reproducibility rather than robustness, and little fundamental understanding of the source of the issue. In the third results chapter, the application of mechanistic models to identify robust operating conditions for the HIC is considered. A model is developed, validated experimentally, and used to generate probabilistic design spaces accounting the historical variability in the resin lots and load material. The stochastic simulation approach is extended to explore the impact of reducing variability in the load material on the design space. With historical process variability, no operating condition was found where the probability of meeting product quality specifications remained > 0.95 for all resin lots. Model simulations indicated that adopting an adaptive design space, where operating conditions are changed according to which resin lot is in use, is favorable for ensuring process robustness, which is a step change concept for bioprocessing. The conclusions and outcomes resulting from the application of mechanistic models to the two industrial systems in this thesis, provides a basis for the next generation purification process development platform

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Effect of curing conditions and harvesting stage of maturity on Ethiopian onion bulb drying properties

The study was conducted to investigate the impact of curing conditions and harvesting stageson the drying quality of onion bulbs. The onion bulbs (Bombay Red cultivar) were harvested at three harvesting stages (early, optimum, and late maturity) and cured at three different temperatures (30, 40 and 50 oC) and relative humidity (30, 50 and 70%). The results revealed that curing temperature, RH, and maturity stage had significant effects on all measuredattributesexcept total soluble solids

Mechanistic modelling of microscale chromatography

Ph. D. Thesis.Microscale chromatography as an experimental tool has shown much utility in process development due to reduced material consumption and ease of parallelisation which are of major benefit when compared to conventional lab-scale studies. Microscale columns are commonly used in early process development where the most impactful decisions, such as choice of unit operation, purification strategy, resin, and the choice of candidate are made with limited resources and knowledge. Understanding the behaviour of microscale chromatography and better applying the knowledge gained from microscale studies to large scale chromatography may allow faster, more efficient and more robust early process development, and therefore more effective processes once a bioprocess is fully developed and products commercialised. It is the overall aim of the project to develop a model to determine large scale mass transfer parameters describing a lab-scale chromatographic process from microscale data, and allow one to simulate and optimise large scale separations whilst enjoying the benefits of reduced resource consumption of the microscale domain. From the outset, characterisation ofthe differences between lab-scale columns operated on a conventional Fast Protein Liquid Chromatography (FPLC) system and microscale columns on a robotic Liquid Handling System (LHS) was performed. Determining the common metrics of column performance, HETP, asymmetry and experimentto-experiment or column-to-column variation between columns and experiments provides an understanding of some of the key differences between lab-scale and microscale column formats with regards to system, scale and data quality, as well as providing an opportunity to optimise the experimental design of microscale experiments. This was performed through evaluating methods of improving resolution, including fashioning rigs to use microscale columns on a conventional system, evaluating various tracer substances and evaluating a novel strategy of pre-filling collection plates. Investigations into ascertaining the dynamic binding capacity (DBC) of IgG to Protein A resin using microscale data has been performed with 3 microscale column volumes at several residence times using the high throughput system, and repeated at lab scale, with further work into understanding the effect of intermittent flow on resin: target interaction by mimicking the microscale operation on a larger system. This effort has led towards data used to calibrate a mechanistic model of chromatography at both lab scale and microscale with the intention of predicting lab scale behaviour. By correcting for scale, operational and flow effects, one may predict large scale performance through calibrating a model with microscale data, enabling better process understanding with reduced material consumption.EPSR