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

This paper studies transient behavior of a series configuration queueing system of two servers. All durations, such as inter-arrival and service times and the given time period, are taken randomly distributed. For characterization of the queueing system, a method is used which is based on constructing an open-loop scheme of system operation and calculation of residual durations from previous states that make up the process. The scheme is a branching sequence of states and transitions between them. Each state is characterized by conditional durations, which take into account the process, on the completion of which the onset of a new state depends. To calculate the distribution functions of the residual durations and conditional durations of states, the method uses apparatus for calculating the difference of functions, the calculation of the duration distribution function and provided that it is less than or more than one or a group of functions. Constructing the scheme and calculation of state characteristics on it allows analysis of the system operation indicators. In particular, the numerical example shows the influence of equipment utilization and the coefficient of variation for service time on the probability and duration of operation and downtime of servers.

Ronggui Luo

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