On influence of model parameters on time-dependent queue-size distribution in a production model with failures and batched arrivals

Sensitivity of the fleeting behaviour of the distribution of number of jobs waiting in the line in a single-machine manufacturing line with machine damages, on changing of the “input” system parameters is investigated numerically. As a mathematical model of the production system a finite-buffer queueing system with batched Poisson arrivals, exponential processing times, and with cyclic succession of failure-free and repair periods is assumed. We study the influence of such parameters as the intensity of job arrivals, sizes of the arriving batches of jobs, processing time and failure- free and repair period durations. In particular, we estimate the relaxation time of the fleeting distribution of the number of jobs waiting in the line in dependence on the initial buffer state for the system with double arrivals (the arriving batches consist of two jobs) and being critically loaded. Next, we investigate the transitory progress of this characteristic in a function of intensity of job arrivals, the processing (service) speed and different values of mean failure-free and repair times. Finally, we investigate dependence of the stationary distribution of the number of jobs on the function describing the size of the arriving portion of jobs. Numerical analysis of different scenarios of the system behaviour is performed by using the Mathematica 9.0 environment.