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Analysis of an N-policy GI/M/1 queue in a multi-phase service environment with disasters

Jiang T., Ammar S. I., Chang B., Liu L.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 2

375--386

This paper investigates an N-policy GI/M/1 queue in a multi-phase service environment with disasters, where the system tends to suffer from disastrous failures while it is in operative service environments, making all present customers leave the system simultaneously and the server stop working completely. As soon as the number of customers in the queue reaches a threshold value, the server resumes its service and moves to the appropriate operative service environment immediately with some probability. We derive the stationary queue length distribution, which is then used for the computation of the Laplace– Stieltjes transform of the sojourn time of an arbitrary customer and the server’s working time in a cycle. In addition, some numerical examples are provided to illustrate the impact of several model parameters on the performance measures.

Preliminary statistical identification and prediction of the container gantry crane operation process

Kołowrocki K., Soszyńska J.

Journal of Polish Safety and Reliability Association

2010

Vol. 1, No. 1

173--180

In the paper a Semi-markov process is used to construct a general model of complex industrial systems’ operation processes. Main parameters of this model are defined and its main characteristics are determined as well. In particular case, for a gantry crane, the operation states are defined, the relationships between them are fixed and particular model of its operation process is constructed and finally its main characteristics are determined.

Methods and algorithms for evaluating unknown parameters of operation processes of complex technical systems

Kołowrocki K., Soszyńska J.

Journal of Polish Safety and Reliability Association

2009

Vol. 2

211--222

The paper objectives are to present the methods and tools useful in the statistical identifying unknown parameters of the operation models of complex technical systems and to apply them in the maritime industry. There are presented statistical methods of determining unknown parameters of the semi-markov model of the complex technical system operation processes. There is also presented the chi-square goodness-of-fit test applied to verifying the distributions of the system operation process conditional sojourn times in the particular operation states. Applications of these tools to identifying and predicting the operation characteristics of a ferry operating at the Baltic Sea waters are presented as well.