An extensive Monte Carlo study is performed to analyze a multi-server, bulk arrival (M [x] /M/C; C-1/FCFS) queuing system. The system breakdown limits the system to serve with either C or (C-1) servers. The server breakdown has equal chance over all servers in the system while the arrival process is a Poisson process and the distribution of the bulk size X is a positive Poisson bulk size. Measures of system efficiency including mean queue length, mean waiting time, and blocking probability are introduced. Numerical results are obtained by simulation of the entire system.

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Background and study aim: Bleeding esophageal varices is a life threatening complication in cirrhotic patients. So, studying risk factors for bleeding esophageal varices is a must. Because of complexity and dynamic nature of coagulation process in cirrhotic patients, INR is considered a false method to measure bleeding risk in such patients. This study aims at evaluating INR elevation in cirrhotic patients as a risk factor for esophageal variceal bleeding. Patients and Methods: This case control study was conducted at the Intensive Care Unit and inpatient wards of Tropical Medicine Department affiliated to Zagazig University Hospitals in the period from April 2016 to January 2017. According to inclusion and exclusion criteria, 202 patients with liver cirrhosis and esophageal varices were included in this study. Cases were cirrhotic patients admitted to the hospital due to first attack of actively bleeding esophageal varices. Controls were cirrhotic patients without bleeding esophageal varices admitted with ascites, SBP or hepatic encephalopathy. Results: Median admission INR was 1.3 in bleeders compared to 1.9 in non-bleeders with a highly significant statistical difference between both groups. Conclusion: Study concluded that INR elevation reflects the degree of liver dysfunction not the risk of bleeding from esophageal varices.

We present in this paper a discrete analogue of the continuous generalized inverted exponential distribution denoted by discrete generalized inverted exponential (DGIE) distribution. Since, it is cumbersome or difficult to measure a large number of observations in reality on a continuous scale in the area of reliability analysis. Yet, there are a number of discrete distributions in the literature; however, these distributions have certain difficulties in properly fitting a large amount of data in a variety of fields. The presented DGIE β , θ has shown the efficiency in fitting data better than some existing distribution. In this study, some basic distributional properties, moments, probability function, reliability indices, characteristic function, and the order statistics of the new DGIE are discussed. Estimation of the parameters is illustrated using the moment's method as well as the maximum likelihood method. Simulations are used to show the performance of the estimated parameters. The model with two real data sets is also examined. In addition, the developed DGIE is applied as color image segmentation which aims to cluster the pixels into their groups. To evaluate the performance of DGIE, a set of six color images is used, as well as it is compared with other image segmentation methods including Gaussian mixture model, K-means, and Fuzzy subspace clustering. The DGIE provides higher performance than other competitive methods.

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