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In this paper we consider a single server queue with two phase arrival and two phase services. Arrival are Poison variables with different rates. For each input, the server provides private service with exponential distribution. The rates of services are different. The policy of service is FCFS, where the server changes the king of service according to the customer in the front of queue. After the completion of each service, the server either goes for a vacation with probability (1-theta), or may continue to server the next customer with probability theta, if any. Otherwise, it remains in the system until a customer arrives. Vacation times are assumed to have exponential distribution. We obtain steady-state probability generating function for queue size distribution for each input and expected busy period.

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In this paper, first spatial point processes and their characteristics are briefly introduced. Then after defining the spatial Cox processes in general terms, a special subclass that is shot noise Cox processes, are investigated. Finally a Thomas process is fitted to the locations of Zagros earthquakes.

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Recurrent events are one type of multivariate survival data. Correlation between observations on each subject is the most important feature of this type of data. This feature does not allow using the ordinary survival models. Frailty models are one of the main approaches to the analysis of recurrent events. Ordinary Frailty models assumed the frailty is constant over time, that is not realistic in many applications. In this paper we introduce a time-dependent frailty model. The introduced model is based on piecewise semiparametric proportional hazard and frailty variable followed a Gamma distribution. The frailty variable in the model has a gamma process that is constant during each interval and has independent increments in the beginning of each interval. We found a close form function for integrated likelihood function and estimated parameters of model. The efficiency of introduced model was compared with an ordinary constant gamma model by a simulation study

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Given the widespread usage of software systems in all aspects of modern life, the need to produce almost error free and high quality software has become more and more important. Software reliability is considered as an important approach to software quality assessment. Software reliability modeling based on non- homogeneous Poisson process is a quite successful method in software reliability engineering. In this paper, we first study the general growth model of software reliability, and then we extend the general model by considering two types of simple and complex errors, dependency between complex errors and time delay between detecting and removing complex errors. Estimating the model parameters has been done by using two failure data sets of real software projects through MATLAB software. We compare the proposed model with two existing models using various criteria. The results show that the proposed model better fits the data, providing more accurate information about the software quality.

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The non-homogeneous bivariate compound Poisson process with short term periodic intensity function is used for modeling the events with seasonal patterns or periodic trends. In this paper, this process is carefully introduced. In order to characterize the dependence structure between jumps, the Levy copula function is provided. For estimating the parameters of the model, the inference for margins method is used. As an application, this model is fitted to an automobile insurance dataset with inference for margins method and its accuracy is compared with the full maximum likelihood method. By using the goodness of fit test, it is confirmed that this model is appropriate for describing the data.