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Queuing theory and its application in mines
Published in Amit Kumar Gorai, Snehamoy Chatterjee, Optimization Techniques and their Applications to Mine Systems, 2023
Amit Kumar Gorai, Snehamoy Chatterjee
The queuing parameters mentioned in the left side of the colon (:) are always defined to indicate the characteristics of the queuing model, but the parameters mentioned after the colon are not mandatory to define for default characteristics. The codes used to describe the different queuing characteristics are as follows: Arrival patterns (a)Markovian or memoryless (M) – Poisson arrival process, which has exponential inter-arrival times.Degenerate distribution (D) – A deterministic or fixed inter-arrival time.Erlang distribution (Ek) – An Erlang distribution with k as the shape parameter.General distribution (G) – It usually refers to independent arrivals.Service patterns (b)The codes used for representing the distribution of the service times are similar to that of arrival patterns like M, D, Ek, or G. But, in a typical queuing model, the distribution of arrival pattern and service pattern may be different.Number of the server (c)The number of servers in a queuing system is represented by a natural number, n. (n = 1, 2, …, n).Capacity of the queue (d)The maximum number of customers or dump trucks allowed in a queue may be finite or infinite. The finite capacity is represented by a finite number N, and the infinite capacity is represented by ∞.Size of the calling population (e)The finite calling population of customers (dump trucks) is by a finite number N, and the infinite capacity is represented by ∞.Queue or service discipline (f)The service discipline is denoted by FIFO, LIFO, SIRO, and PQ.
Multi-Output Gaussian Processes for Inverse Uncertainty Quantification in Neutron Noise Analysis
Published in Nuclear Science and Engineering, 2023
Paul Lartaud, Philippe Humbert, and Josselin Garnier
The Metropolis-Hastings algorithm is robust, but has some limitations in the case of very degenerate target distributions as is the case in this work. A degenerate distribution is a distribution whose support lies mainly on a subspace (or a manifold) of the parameter space, whose dimension is strictly lower. It can be, for example, a curve or a plane in the 7-D parameter space. This definition of degeneracy is not rigorous. More precisely, a degenerate distribution is rigorously defined as a distribution whose support has a Lebesgue measure equal to zero. However, the notion of degeneracy is considered in this work as a practical limitation to MCMC methods and not as a formal mathematical definition.