In this study, we consider a queuing model extension for a production system composed of several parallel machines and the same number of transporters. To obtain the minimum waiting time of the jobs in the queue, we present an exact solution for the proposed queuing model. The solution integrates M/M/C system with M/M/1 system. We obtain explicit expressions for its steady-state behavior under M/M/C and M/M/1 assumptions. Further, in order to illustrate the usefulness of the proposed methods, numerical examples are solved. On the basis of the results of these examples, some important conclusions are drawn.