Queueing network has widely applied to signify and investigate the resource sharing the system such as computer system, communication network. In many applications servers, like Web servers file servers, database servers, a huge amount of transaction has to be handled properly in a specified time limit. Each transaction typically consists of several sub-transactions that have to be processed in a fixed sequential order. One of the most important quality of service parameters for these applications is expected response time, which is the total time it takes a users request to be processed. In  multi class queueing network, where a job moves from a queue to another queue with some probability  after getting  a service . The portrayal of the queue stability is obtained based on the following parameters: general arrival, service time distributions, multiple classes with specific arrival rate. A multiple class of customer could be open or closed where each class has its own set of queueing  parameters. In distributed multi-server network in which the customer transitions have exemplified by more than one closed Markov chain. The main objective is to maximize the total source utility by posing the optimization network control  which  shown that the rate control problem has been solved  completely . Graphical representation shows that the new method improves the performance measure in terms of reduction computational effort.