Computing probabilities for the buffer level in a two-machines production line with geometric inputs to and outputs from the buffer. (1986f).

M. A. Javaid; Christ K. Wright

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Computing probabilities for the buffer level in a two-machines production line with geometric inputs to and outputs from the buffer. (1986f).

Author(s)

M. A. Javaid Mathematics Department, University of Peshawar, Peshawar, Pakistan

Christ K. Wright Mathematics Department, University of Bermingham, Bermingham, England, UK

Abstract

A production line is studied in which there are two machines and a single finite buffer. The model arises partly because the movement of work-pieces and passage of time can both independently be regarded as discrete. Random Geometric inputs to and outputs from the buffer in a. cycle time are discussed. The principal assumption of the model is that: at the beginning of a cycle there is a possible geometric input which is considered lost if the buffer is at its maximum level and at the end of a cycle there is a probable geometric output/demand which is supplied from the buffer if possible. A set of homogeneous probability equations for the model is obtained which have some special characteristics. An analysis of this set leads to an analytic solution in closed form (in terms of the probabilities of inputs and output of the buffer) for the steady state of the size of inter-machine buffer, which is a singly truncated geometric distribution.

Publication Details

Page(s) 31-54

DOI DOI not available

Published Journal: Research journal, Volume: 2, Issue: 1, Year: 1988

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