Analysis of Collision Probability in a Parallel Machines Model When the Number of Jobs Is Constrained

抄録

This paper analyses collision probability in a production line. Collision probability is the probability of a collision occurring between jobs in a production line. One element that determines collision probability is the time interval between materials which are being fed into a production line. When the time interval is shortened, the probability of a collision occurring increases. However, in order to reduce production completion time, this time interval should be as short as possible. When determining the appropriate time interval, evaluating collision probability for a given time interval is important. Methods to compute collision probability in an in-line and a parallel machines model already exist. Moreover, in an in-line machines model, an approximate formula of collision probability has also been presented. In a parallel machines model, there are no results on analysis of collision probability. This paper shows a theoretical formula of collision probability in a parallel machines model when the number of jobs is constrained. Further, when the processing time follows an Erlang distribution, we show that this theoretical formula of collision probability can be described as a closed form. In addition, when the processing time follows an exponential distribution,we show a concrete closed form of collision probability. Finally, from computational experimentation, we compare the results obtained from the closed form presented with a known simulation method.