This paper presents a mean-value analysis for closed multichain queuing networks with product-form solutions. The authors propose recursive computational procedures to compute mean queue sizes, mean waiting times, and throughputs without explicitly computing normalization constants. These procedures are shown to have improved properties, such as avoiding numerical issues and requiring fewer operations compared to previous algorithms. The algorithms are based on a mean-value equation that relates the mean waiting time and mean queue size of a system with one fewer customer. The paper also introduces a heuristic extension that allows for the approximate solution of networks with a large number of closed chains, which is asymptotically valid for large chain populations. The heuristic is particularly useful for modeling communication networks with many closed chains, which are otherwise intractable using exact methods. The main principles governing the mean-value behavior of these networks are an arriving customer "sees" the system with himself removed in equilibrium, Little's equation applied to chains, and Little's equation applied to service centers. The paper concludes with a discussion of the insights gained from the analysis and the potential for further generalizations.This paper presents a mean-value analysis for closed multichain queuing networks with product-form solutions. The authors propose recursive computational procedures to compute mean queue sizes, mean waiting times, and throughputs without explicitly computing normalization constants. These procedures are shown to have improved properties, such as avoiding numerical issues and requiring fewer operations compared to previous algorithms. The algorithms are based on a mean-value equation that relates the mean waiting time and mean queue size of a system with one fewer customer. The paper also introduces a heuristic extension that allows for the approximate solution of networks with a large number of closed chains, which is asymptotically valid for large chain populations. The heuristic is particularly useful for modeling communication networks with many closed chains, which are otherwise intractable using exact methods. The main principles governing the mean-value behavior of these networks are an arriving customer "sees" the system with himself removed in equilibrium, Little's equation applied to chains, and Little's equation applied to service centers. The paper concludes with a discussion of the insights gained from the analysis and the potential for further generalizations.