Study of Average Losses Caused by Ill-Processing in a Production Line with Immediate Feedback and Multi Server Facility at Each of the Processing Units

Abstract

In this paper, we have modeled a production line consisting of an arbitrary number of processing units arranged in a series. Each of the processing units has multi-server facility. Arrivals at the first processing unit are according to Poisson distribution and service times at each of the processing units are exponentially distributed. At each of the processing units, the authors have taken into account immediate feedback and the rejection possibility. Taking into account the stationary behavior of queues in series, the solution for infinite queuing space have been found in the product form. Considering the processing cost at each of the processing units, the average loss to the system due to rejection, caused by ill processing at various processing units, is obtained.

Keywords: Queuing Network, Processing Units, Production Line, Multi-Server, Immediate Feedback,      Stationary behavior.