This paper presents a comprehensive analysis of queueing networks with different classes of customers and four types of service centers: first-come-first-served (FCFS), processor sharing, no queueing, and last-come-first-served (LCFS). The authors derive the equilibrium distribution of queue sizes in such networks, which is expressed as a product of functions depending on the system state, customer configuration, and service center type. The model allows for state-dependent arrival processes and different service time distributions for different customer classes. Key contributions include the derivation of equilibrium state probabilities, the development of marginal distributions for open networks, and the consideration of state-dependent service rates. The paper also provides examples to illustrate the impact of different customer classes on system performance, such as utilization levels and response times. The analysis is motivated by the need to model complex computer systems, particularly multiprogrammed and time-shared systems, and the results unify and extend previous work in queueing theory.This paper presents a comprehensive analysis of queueing networks with different classes of customers and four types of service centers: first-come-first-served (FCFS), processor sharing, no queueing, and last-come-first-served (LCFS). The authors derive the equilibrium distribution of queue sizes in such networks, which is expressed as a product of functions depending on the system state, customer configuration, and service center type. The model allows for state-dependent arrival processes and different service time distributions for different customer classes. Key contributions include the derivation of equilibrium state probabilities, the development of marginal distributions for open networks, and the consideration of state-dependent service rates. The paper also provides examples to illustrate the impact of different customer classes on system performance, such as utilization levels and response times. The analysis is motivated by the need to model complex computer systems, particularly multiprogrammed and time-shared systems, and the results unify and extend previous work in queueing theory.