On departure process in the batch arrival queue with single vacation and setup time

A single-server queueing system of MX/G/1 type with unlimited buffer size is considered. Whenever the system becomes empty, the server takes a single compulsory vacation that is independent of the arrival process. The service of the first customer after the vacation is preceded by a random setup time. We distinguish two cases of the evolution of the system: when the setup time begins after the vacation only, or if it begins at once when the first group of customers enters. In the paper we investigate the departure process h(t) that at any fixed moment t takes on a random value equal to the number of customers completely served before t. An explicit representation for Laplace Transform of probability generating function of departure process is derived and written down by means of transforms of four crucial input distributions of the system and factors of a certain factorization identity connected with them. The results are obtained using the method consisting of two main stages: first we study departure process on a single vacation cycle for an auxiliary system and direct the analysis to the case of the system without vacations, applying the formula of total probability; next we use the renewal-theory approach to obtain a general formula

On transient queue-size distribution in the batch arrival system with the N-policy and setup times

In the paper the $M^{X}/G/1$ queueing system with the $N$-policy and setup times is considered. An explicit formula for the Laplace transform of the transient queue-size distribution is derived using the approach consisting of few steps. Firstly, a "special\u27\u27 modification of the original system is investigated and, using the formula of total probability, the analysis is reduced to the case of the corresponding system without limitation in the service. Next, a renewal process generated by successive busy cycles is used to obtain the general result. Sample numerical computations illustrating theoretical results are attached as well

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

summary:Non-stationary behavior of departure process in a finite-buffer $M^{X}/G/1/K$-type queueing model with batch arrivals, in which a threshold-type waking up $N$-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the $N$th message occurrence, where the threshold value $N$ is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time $t$ is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached

On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well

Słowo Redakcji

Niniejszy zeszyt „Śląskich Studiów Historyczno-Teologicznych” gromadzi artykuły zogniskowane przede wszystkim wokół dwóch chrześcijańskich myślicieli: Anzelma z Canterbury i Johna Henry’ego Newmana. Takie zestawienie może wydać się nietypowe dla naszego śląskiego periodyku, nawet jeśli pojedyncze prace związane z tymi osobami były tu już nieraz publikowane. Naszym zdaniem wrażenie to nie powinno sugerować odejścia od lokalnego charakteru naszego pisma (Fragment tekstu)

Reduction of defibrillation threshold and safety of usage of a new model of subcutaneous defibrillation lead

This study was designed to evaluate the performance of a new single coil model of a subcutaneous defibrillation lead (Medtronic, 6996S) by assessing its capability to lower the defibrillation threshold. The 6996S lead is a permanent unipolar subcutaneous lead with a short (15 cm) defibrillation coil. Additionally, the safety of the lead and its chronic stability were evaluated. The investigation was performed in patients who underwent implantation of an ICD system consisting of a single coil RV lead with a left sub-clavicular Active Can ICD. In these patients, the DFT was determined twice during the implantation procedure with a binary search protocol, once with an ICD system which included the 6996S lead (RV → Can + SQ), and once without the 6996S lead (RV → Can). The order in which the implanted system configurations were tested was randomised. Between June 2004 and February 2006, 32 patients were enrolled into the study. Post-implantation follow-up was of at least three-month duration. The DFT test results of 31 patients have been analysed. The average DFT of (Can → RV) and (Can + 6996S → RV) were respectively 14.3 ± 9.9 J and 10.5 ± 6.2 J (p = 0.007). The addition of the 6996S lead with 15 cm coil reduced the average DFT by 27%, which is about 80% of the DFT reduction obtained with the 6996 lead with 25 cm coil. Adverse events, predominantly related to progression of heart failure, were observed in eight (26%) patients during the study and were related neither to the particular 6996S lead model, nor to the implant procedure. The short-coil (6996S) SQ lead significantly reduced mean DFT. The implant procedure is safe, but the 6996S lead requires / warrants long-term surveillance / observation due to retraction of the tip of the lead, ranging from 1 to 4 cm, found in eight of 14 patients (57%) implanted with this lead model

The perception of lip aesthetics in the context of facial proportions—An eye-tracking-based analysis

Background: Minimally invasive lip volumizing and contouring soft tissue filler procedures are frequently requested by both female and male aesthetic patients. Guidance on how to achieve the most beautiful outcome is inconsistent. Objective: To investigate what the most beautiful proportions are in relation to vermillion thickness, the distance of the upper and lower lip in relation to nose and chin, and relation to the bigonial distance. Methods: This study included a total of n = 101 volunteers (52 females, 49 males, 100% Caucasian) who inspected frontal images of modified facial proportions and answered a related questionnaire showcasing the same images. Image presentation followed a randomized sequence both for the eye tracking and for the survey component of this study but was equal for all observers. Results: The most attractive vertical position of lips was the 1:2 ratio in which the distance between lips and chin is double the length as the distance between lips and nose. For the ratio between the width of the lips and the bigonial distance, it was the 1:2.5 ratio, whereas for the thickness of the upper lip vermilion in relation to the upper lip ergotrid it was the 1:3/1:2 (male/female) ratio and for the lower lip vermilion and lower lip ergotrid it was the 1:4 ratio for both genders. Conclusion: The results of this eye tracking and survey-based investigation revealed that instead of one single universal ratio, multiple facial proportions exist that are perceived as most attractive/masculine/feminine. Regarding the perception of facial aesthetics, it appears there is a distinction between attractiveness and masculinity/femininity: the most attractive male/female face is not necessarily the most masculine or feminine.</p

The perception of lip aesthetics in the context of facial proportions—An eye-tracking-based analysis

Background: Minimally invasive lip volumizing and contouring soft tissue filler procedures are frequently requested by both female and male aesthetic patients. Guidance on how to achieve the most beautiful outcome is inconsistent. Objective: To investigate what the most beautiful proportions are in relation to vermillion thickness, the distance of the upper and lower lip in relation to nose and chin, and relation to the bigonial distance. Methods: This study included a total of n = 101 volunteers (52 females, 49 males, 100% Caucasian) who inspected frontal images of modified facial proportions and answered a related questionnaire showcasing the same images. Image presentation followed a randomized sequence both for the eye tracking and for the survey component of this study but was equal for all observers. Results: The most attractive vertical position of lips was the 1:2 ratio in which the distance between lips and chin is double the length as the distance between lips and nose. For the ratio between the width of the lips and the bigonial distance, it was the 1:2.5 ratio, whereas for the thickness of the upper lip vermilion in relation to the upper lip ergotrid it was the 1:3/1:2 (male/female) ratio and for the lower lip vermilion and lower lip ergotrid it was the 1:4 ratio for both genders. Conclusion: The results of this eye tracking and survey-based investigation revealed that instead of one single universal ratio, multiple facial proportions exist that are perceived as most attractive/masculine/feminine. Regarding the perception of facial aesthetics, it appears there is a distinction between attractiveness and masculinity/femininity: the most attractive male/female face is not necessarily the most masculine or feminine.</p