This paper presents a general model for networks of queues with different classes of customers and various types of service centers. The equilibrium state probabilities for such networks are derived and expressed in the form $ P(S) = Cd(S)f_{1}(x_{1})f_{2}(x_{2}) \cdot f_{N}(x_{N}) $, where $ S $ is the system state, $ x_{i} $ represents the configuration of customers at service center $ i $, $ d(S) $ is a function of the system state, and $ f_{i} $ depends on the type of service center. The model considers four types of service centers: first-come-first-served (FCFS), processor sharing, no queueing, and last-come-first-served (LCFS). Each customer belongs to a class and may change classes when leaving a service center. The model accounts for both open and closed networks, where open networks have state-dependent arrival processes and closed networks have no external arrivals. The equilibrium probabilities are derived using Whittle's concept of independent balance, leading to a product form solution. The model allows for different service time distributions and routing probabilities for different customer classes. Examples demonstrate how different customer classes affect system performance. The paper also discusses marginal distributions and state-dependent service rates, showing how they can be incorporated into the model. The results unify and extend previous findings on queueing networks, providing a general framework for analyzing complex computer systems. The model is applicable to various types of service centers and can handle different service time distributions and customer classes. The paper concludes that the model offers a significant advancement in the analysis of complex computer systems.This paper presents a general model for networks of queues with different classes of customers and various types of service centers. The equilibrium state probabilities for such networks are derived and expressed in the form $ P(S) = Cd(S)f_{1}(x_{1})f_{2}(x_{2}) \cdot f_{N}(x_{N}) $, where $ S $ is the system state, $ x_{i} $ represents the configuration of customers at service center $ i $, $ d(S) $ is a function of the system state, and $ f_{i} $ depends on the type of service center. The model considers four types of service centers: first-come-first-served (FCFS), processor sharing, no queueing, and last-come-first-served (LCFS). Each customer belongs to a class and may change classes when leaving a service center. The model accounts for both open and closed networks, where open networks have state-dependent arrival processes and closed networks have no external arrivals. The equilibrium probabilities are derived using Whittle's concept of independent balance, leading to a product form solution. The model allows for different service time distributions and routing probabilities for different customer classes. Examples demonstrate how different customer classes affect system performance. The paper also discusses marginal distributions and state-dependent service rates, showing how they can be incorporated into the model. The results unify and extend previous findings on queueing networks, providing a general framework for analyzing complex computer systems. The model is applicable to various types of service centers and can handle different service time distributions and customer classes. The paper concludes that the model offers a significant advancement in the analysis of complex computer systems.