A DIFFUSION APPROXIMATION FOR THE G/G/r MACHINE INTERFERENCE PROBLEM WITH SPARE MACHINES AND WITH RENEGING Dr. Hukam Singh Exact solution to queueing problems with machines interfailure time and repair time drawn from generalized distributions have not

Abstract

                 Exact solution to queueing problems with machines interfailure time and repair time drawn from generalized distributions have not been found. We are therefore much interested in good quality approximate solutions to such problems. This paper presents a methodology for obtaining the approximation for the G/G/r machine interference problem with reneging, while spare machines have also been provided. The approximation is termed as the diffusion approximation. In this system the discrete flow of failed machines is approximated by continuous one and the diffusion equation has been constructed for the mean number of failed machines in the system by using the means and variances of inter failure time and repair time distribution. We have also modified the boundary conditions to improve the approximation.