565 research outputs found
Determining The Optimal Order Picking Batch Size In Single Aisle Warehouses
This work aims at investigating the influence of picking batch size to average time in
system of orders in a one-aisle warehouse under the assumption that order arrivals follow a
Poisson process and items are uniformly distributed over the aisle's length. We model this
problem as an M/G[k]/1 queue in which orders are served in batches of exactly orders. The
average time in system of the M/G[k]/1 queue is difficult to obtain for general service
times. To circumvent this obstacle, we perform an extensive numerical experiment on the
average time in system of the model when the service time is deterministic (M/D[k]/1) or
exponentially distributed (M/M[k]/1). These results are then compared with the corresponding
times in system of the actual model taken from simulation runs. A variance analysis is
carried out and its result elicits that the M/D/[k]/1 queue is a very good approximation for
the average time in system of orders. Correspondingly, the optimal picking batch size of the
real system ca
Adversarial blockchain queues and trading on a CFMM
We describe a plausible probabilistic model for a blockchain queueing
environment in which rational, profit-maximising schedulers impose adversarial
disciplines on incoming messages containing a payload that encodes a state
transition in a machine. The model can be specialised to apply to chains with
fixed or variable block times, traditional priority queue disciplines with
`honest' schedulers, or adversarial public mempools. We find conditions under
which the model behaves as a bulk-service queue with priority discipline and
derive practical expressions for the relative block and message number of a
transaction.
We study this setup in the context of orders to a CFMM DEX where the
execution price a user receives may be quite sensitive to its positioning in
the chain -- in particular, to a string of transactions scheduled for prior
execution which is not knowable at the time of order creation. We derive
statistical models for the price impact of this order flow both in the presence
and absence of MEV extraction activity.Comment: 20 pages. Keywords: queue, blockchain, mempool, cfmm, mev, dex,
priority discipline, model, sandwich, slippag
Distributionally robust views on queues and related stochastic models
This dissertation explores distribution-free methods for stochastic models. Traditional approaches operate on the premise of complete knowledge about the probability distributions of the underlying random variables that govern these models. In contrast, this work adopts a distribution-free perspective, assuming only partial knowledge of these distributions, often limited to generalized moment information. Distributionally robust analysis seeks to determine the worst-case model performance. It involves optimization over a set of probability distributions that comply with this partial information, a task tantamount to solving a semiinfinite linear program. To address such an optimization problem, a solution approach based on the concept of weak duality is used. Through the proposed weak-duality argument, distribution-free bounds are derived for a wide range of stochastic models. Further, these bounds are applied to various distributionally robust stochastic programs and used to analyze extremal queueing models—central themes in applied probability and mathematical optimization
Distributionally robust views on queues and related stochastic models
This dissertation explores distribution-free methods for stochastic models. Traditional approaches operate on the premise of complete knowledge about the probability distributions of the underlying random variables that govern these models. In contrast, this work adopts a distribution-free perspective, assuming only partial knowledge of these distributions, often limited to generalized moment information. Distributionally robust analysis seeks to determine the worst-case model performance. It involves optimization over a set of probability distributions that comply with this partial information, a task tantamount to solving a semiinfinite linear program. To address such an optimization problem, a solution approach based on the concept of weak duality is used. Through the proposed weak-duality argument, distribution-free bounds are derived for a wide range of stochastic models. Further, these bounds are applied to various distributionally robust stochastic programs and used to analyze extremal queueing models—central themes in applied probability and mathematical optimization
Multi-agent pathfinding for unmanned aerial vehicles
Unmanned aerial vehicles (UAVs), commonly known as drones, have become more and
more prevalent in recent years. In particular, governmental organizations and companies
around the world are starting to research how UAVs can be used to perform tasks such
as package deliver, disaster investigation and surveillance of key assets such as pipelines,
railroads and bridges. NASA is currently in the early stages of developing an air traffic
control system specifically designed to manage UAV operations in low-altitude airspace.
Companies such as Amazon and Rakuten are testing large-scale drone deliver services in
the USA and Japan.
To perform these tasks, safe and conflict-free routes for concurrently operating UAVs must
be found. This can be done using multi-agent pathfinding (mapf) algorithms, although
the correct choice of algorithms is not clear. This is because many state of the art mapf
algorithms have only been tested in 2D space in maps with many obstacles, while UAVs
operate in 3D space in open maps with few obstacles. In addition, when an unexpected
event occurs in the airspace and UAVs are forced to deviate from their original routes
while inflight, new conflict-free routes must be found. Planning for these unexpected
events is commonly known as contingency planning. With manned aircraft, contingency
plans can be created in advance or on a case-by-case basis while inflight. The scale at
which UAVs operate, combined with the fact that unexpected events may occur anywhere
at any time make both advanced planning and planning on a case-by-case basis impossible.
Thus, a new approach is needed. Online multi-agent pathfinding (online mapf) looks to
be a promising solution. Online mapf utilizes traditional mapf algorithms to perform path
planning in real-time. That is, new routes for UAVs are found while inflight.
The primary contribution of this thesis is to present one possible approach to UAV
contingency planning using online multi-agent pathfinding algorithms, which can be used
as a baseline for future research and development. It also provides an in-depth overview
and analysis of offline mapf algorithms with the goal of determining which ones are likely
to perform best when applied to UAVs. Finally, to further this same goal, a few different
mapf algorithms are experimentally tested and analyzed
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"
Throughput and Yield Improvement for a Continuous Discrete-Product Manufacturing System
A seam-welded steel pipe manufacturing process has mainly four distinct major design and/or operational problems dealing with buffer inventory, cutting tools, pipe sizing and inspection-rework facility. The general objective of this research is to optimally solve these four important problems to improve the throughput and yield of the system at a minimum cost.
The first problem of this research finds the optimal buffer capacity of steel strip coils to minimize the maintenance and downtime related costs. The total cost function for this coil feeding system is formulated as a constrained non-linear programming (NLP) problem which is solved with a search algorithm. The second problem aims at finding the optimal tool magazine reload timing, magazine size and the order quantity for the cutting tools. This tool magazine system is formulated as a mixed-integer NLP problem which is solved for minimizing the total cost. The third problem deals with different type of manufacturing defects. The profit function of this problem forms a binary integer NLP problem which involves multiple integrals with several exponential and discrete functions. An exhaustive search method is employed to find the optimum strategy for dealing with the defects and pipe sizing. The fourth problem pertains to the number of servers and floor space allocations for the off-line inspection-rework facility. The total cost function forms an integer NLP structure, which is minimized with a customized search algorithm.
In order to judge the impact of the above-mentioned problems, an overall equipment effectiveness (OEE) measure, coined as monetary loss based regression (MLBR) method, is also developed as the fifth problem to assess the performance of the entire manufacturing system. Finally, a numerical simulation of the entire process is conducted to illustrate the applications of the optimum parameters setting and to evaluate the overall effectiveness of the simulated system. The successful improvement of the simulated system supports this research to be implemented in a real manufacturing setup. Different pathways shown here for improving the throughput and yield of industrial systems reflect not only to the improvement of methodologies and techniques but also to the advancement of new technology and national economy
Redundancy Scheduling with Locally Stable Compatibility Graphs
Redundancy scheduling is a popular concept to improve performance in
parallel-server systems. In the baseline scenario any job can be handled
equally well by any server, and is replicated to a fixed number of servers
selected uniformly at random. Quite often however, there may be heterogeneity
in job characteristics or server capabilities, and jobs can only be replicated
to specific servers because of affinity relations or compatibility constraints.
In order to capture such situations, we consider a scenario where jobs of
various types are replicated to different subsets of servers as prescribed by a
general compatibility graph. We exploit a product-form stationary distribution
and weak local stability conditions to establish a state space collapse in
heavy traffic. In this limiting regime, the parallel-server system with
graph-based redundancy scheduling operates as a multi-class single-server
system, achieving full resource pooling and exhibiting strong insensitivity to
the underlying compatibility constraints.Comment: 28 pages, 4 figure
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