This paper presents a new method to get approximate solutions to queueing networks with multiple servers and a certain type of blocking. The basic structure of the queueing network model consists of one class of jobs, exponential service times, and multiple-server service stations. The nontrivial feature is the possibility of blocking. In this paper, the term blocking means that if the next destination station is full at the completion time of a job’s service, the job continues to reserve its current server until a server in the destination station becomes free. This type of blocking is needed in communication models and in IO-models.

The solution is quite interesting; it involves first creating the state space of the original queueing network without any blocking and then normalizing the infeasible states that violate the station capacities. The idea behind the normalization is to remove the jobs that exceed the capacity limitations and redistribute them to the preceding stations. The equilibrium state probabilities allow the computation of the mean number of jobs. The throughput values are obtained using a state space transformation. Here the idea is to find a nonblocking network with an appropriate number of jobs and a state space size equal to the number of feasible states of the original blocking network. The solution of the transformed network produces approximately right throughput values for the original blocking network.

The approximations are validated using 200 simulation experiments. All these simulations give excellent results: the deviations in throughputs are usually less than two percent. However, the extent to which the experiments reflect different behavioral types of queueing networks has not been reported. The reader might wonder, for example, how the distribution of the service demands over the stations (and especially the bottleneck) affects the accuracy of the method. Some discussions about the limits of the validity are always desirable, even if they must be based on heuristic reasoning. In this case, heuristic reasoning based on the dynamic behavior of the queueing network could have been useful, especially because the derivation of the method is based on heuristic reasoning at the state space level. The performance aspects of the method also deserve further treatment. It is a rather meager statement that the method requires less computer time than does the solving of the global balance equation or extensive simulation experimentation.

The paper is easy to read. Some minor editorial notes could be mentioned. For example, all figures should have informative captions (not “Histogram 1”). Also, if a formula needs a reference, the name of a book does not help the reader too much.

The ideas behind this work are interesting and probably worthy of further research.