• Journal of the Korean Statistical Society
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• 제31권4호
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1155-1171
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• 2023

This paper investigates a non Markovian M/G/1 queue with retrial policy, different kind of service rates as well as unsatisfied clients which is inspired by an example of a transmission medium access control in wireless communications. The server tends to work continuously until it finds at least one client in the system. The server will begin its maintenance tasks after serving all of the clients and if the system becomes empty. Provisioning periods in regular working periods and maintenance service periods should be evenly divided. Using supplementary variable technique, the amount of clients in the system as well as in the orbit were found. Further few performance measures of the system were demonstrated numerically.

• Asian-Australasian Journal of Animal Sciences
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• 제8권5호
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• pp.505-513
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• 1995

The major factors affecting productivity on daily farms in Queensland, Australia, were determined using the stepwise linear regression approach. The data were obtained from a survey conducted on the total population of daily farms in Queensland in 1987. These data were divided into six major dailying regions. The technique was applied using 12 independent variables believed by a panel of experienced research and extension personnel to exert the most influence on milk production. The regression equations were all significant (p < 0.001) with the percentage coefficients of determination ranging from 62 to 76% for equations developed using' total farm milk: production as the dependent variable. Three of the variables affecting total farm milk: production were found to be common to all six regions. These were; the amount of supplementary energy fed, the area set aside to irrigate winter feed and the size of the area used for dailying. Higher production farms appeared to be more efficient in that they consistently produced milk production levels higher than those estimated from the regression equation for their region. Other methods of analysis including robust regression and non linear regression techniques were unsuccessful in overcoming this problem and allowing development of a model appropriate for farms at all levels of production.

• International Journal of Reliability and Applications
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• 제11권2호
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• pp.107-122
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• 2010

This paper deals with the reliability analysis of a complex system, which consists of two subsystems A and B connected in series. Subsystem A has only one unit and B has two units $B_1$ and $B_2$. Marked process has been applied to model the complex system. Present reliability model incorporated two repairmen: supervisor and novice to repair the failed units. Supervisor is always there and the novice remains in vacation and is called for repair as per demand. The repair rates for supervisor and novice follow general and exponential distributions respectively and the failure time for both the subsystems follows exponential distribution. The model is analyzed under "Head of line repair discipline". By employing supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula various transition state probabilities, reliability, availability and cost analysis have been obtained along with the steady state behaviour of the system. At the end some special cases of the system have been taken.