Matched Queues with Flexible Customers and Impatient Customers

This paper studies a double-ended queue with four Poisson inputs and flexible customers, and its stability is guaranteed by customers’ impatient behavior. We show that such a queue can be expressed as a quasi birth-and-death (QBD) process with infinitely many phases. For this purpose, we provide a detailed analysis for the QBD process, including the system stability, the stationary probability vector, the sojourn time, and so forth. Finally, numerical examples are employed to verify the correctness of our theoretical results, and demonstrate how the performance measures of this queue are influenced by key system parameters. We believe that the methodology and results described in this paper can be applied to analyze many practical issues, such as those encountered in sharing economy, organ transplantation, employee recruitment, onlinedating, and so on.

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

Human-Mimetic Estimation of Food Volume from a Single-View RGB Image Using an AI System

It is well known that many chronic diseases are associated with unhealthy diet. Although improving diet is critical, adopting a healthy diet is difficult despite its benefits being well understood. Technology is needed to allow an assessment of dietary intake accurately and easily in real-world settings so that effective intervention to manage being overweight, obesity, and related chronic diseases can be developed. In recent years, new wearable imaging and computational technologies have emerged. These technologies are capable of performing objective and passive dietary assessments with a much simplified procedure than traditional questionnaires. However, a critical task is required to estimate the portion size (in this case, the food volume) from a digital image. Currently, this task is very challenging because the volumetric information in the two-dimensional images is incomplete, and the estimation involves a great deal of imagination, beyond the capacity of the traditional image processing algorithms. In this work, we present a novel Artificial Intelligent (AI) system to mimic the thinking of dietitians who use a set of common objects as gauges (e.g., a teaspoon, a golf ball, a cup, and so on) to estimate the portion size. Specifically, our human-mimetic system “mentally” gauges the volume of food using a set of internal reference volumes that have been learned previously. At the output, our system produces a vector of probabilities of the food with respect to the internal reference volumes. The estimation is then completed by an “intelligent guess”, implemented by an inner product between the probability vector and the reference volume vector. Our experiments using both virtual and real food datasets have shown accurate volume estimation results.

A new proof of the dimension gap for the Gauss map

In [4], Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map T(x)=1/x mod 1 satisfy a ‘dimension gap’ meaning that for some c > 0, sup p dim μ p < 1– c, where μp denotes the (pushforward) Bernoulli measure for the countable probability vector p. In this paper we propose a new proof of the dimension gap. By using tools from thermodynamic formalism we show that the problem reduces to obtaining uniform lower bounds on the asymptotic variance of a class of potentials.

Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models

In this paper, an ordinal multilevel latent Markov model based on separate random effects is proposed. In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.

Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns

In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or equal to c. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach.

Novel Protein Sequence Comparison Method Based on Transition Probability Graph and Information Entropy

Aim and Objective: Sequence analysis is one of the foundations in bioinformatics. It is widely used to find out the feature metric hidden in the sequence. Otherwise, the graphical representation of biologic sequence is an important tool for sequencing analysis. This study is undertaken to find out a new graphical representation of biosequences. Materials and Methods: The transition probability is used to describe amino acid combinations of protein sequences. The combinations are composed of amino acids directly adjacent to each other or separated by multiple amino acids. The transition probability graph is built up by the transition probabilities of amino acid combinations. Next, a map is defined as a representation from transition probability graph to transition probability vector by k-order transition probability graph. Transition entropy vectors are developed by the transition probability vector and information entropy. Finally, the proposed method is applied to two separate applications, 499 HA genes of H1N1, and 95 coronaviruses. Results: By constructing a phylogenetic tree, we find that the results of each application are consistent with other studies. Conclusion: The graphical representation proposed in this article is a practical and correct method.

Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors

In this paper, we investigate stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. We show that there are two special symmetric transition probability tensors of order [Formula: see text] dimension 2, which have and only have two stationary probability vectors; and any other symmetric transition probability tensor of order [Formula: see text] dimension 2 has a unique stationary probability vector. As a byproduct, we obtain that any symmetric transition probability tensor of order [Formula: see text] dimension 2 has a unique positive stationary probability vector, and that any symmetric irreducible transition probability tensor of order [Formula: see text] dimension 2 has a unique stationary probability vector.

ASYMPTOTIC ORDER OF THE GEOMETRIC MEAN ERROR FOR SELF-AFFINE MEASURES ON BEDFORD–MCMULLEN CARPETS

Let [Formula: see text] be a Bedford–McMullen carpet associated with a set of affine mappings [Formula: see text] and let [Formula: see text] be the self-affine measure associated with [Formula: see text] and a probability vector [Formula: see text]. We study the asymptotics of the geometric mean error in the quantization for [Formula: see text]. Let [Formula: see text] be the Hausdorff dimension for [Formula: see text]. Assuming a separation condition for [Formula: see text], we prove that the [Formula: see text]th geometric error for [Formula: see text] is of the same order as [Formula: see text].