Analysis of Production Line with Finite Buffers and a General Service Term

A method that uses an open-end diagram of queueing system functioning and relative probabilities is applied to study the queueing system with two heterogeneous servers, which is functioning within a given time period. According to the method a service process diagram is drawn. A feature of the method is the calculation of durations of the processes residual from the previous state. It allows describing in detail the functioning process of the queueing system for both infinite and finite time periods. The difference of the method from other approaches is the application of relations for computation of states without formulation and solution of any equations, absence of constraints on distribution of service time and inter-arrival time. The authors analysed the queueing system with arbitrary distributed service time and inter-arrival time, which is functioning within a random time period. Each state is characterized by idle time of devices or availability of the queue that allows, as a result, computing probabilities and average durations of idle time of servers, distribution of queue length, average time of stay in queue.

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Model of unreliable devices system

Korolkova

Mashrabov

Panfilov

et al. 2019

J. Phys.: Conf. Ser.

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The purpose of the research is to develop a model of a production system consisting of n parallel devices and having a standby device of lower reliability. Under complex failure conditions, a spare device in a cold standby allows quickly replacing the failed primary unit. The system operation is investigated from the beginning of work up to a certain point in time tW. A good approximation to reality is the acceptance that failure time follows general time distribution. The authored approach consists in drawing up an open scheme for the functioning system. Due to the complex failure of one of the devices, the process passes to the next state, which is characterized by residual failure time or residual time of the process. The calculation of residual durations is a feature of the investigated model, which, along with detailed schematization, makes it possible to calculate the set of state indicators and, on their basis, obtain the more general indicators of the functioning of investigated system. A numerical example is given for a system consisting of five devices.

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Analysis of Production Line with Finite Buffers and a General Service Term

Cited by 5 publications

References 9 publications

Non-stationary Characteristics of a Two-Phase Queueing System

Non-stationary Characteristics of a Two-Phase Queueing System

Transient analysis of queueing system with two heterogeneous servers

Model of unreliable devices system

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