Comparative Throughput Analysis of Queueing Networks with Exponential and Deterministic Service Time in the Nodes

We consider a queueing network consisting of $\cdot|M|m$- and $\cdot|GI|\infty$ systems. Poisson arrivals are assumed (if the network is open). We show that the throughput characteristics are not degraded when the exponential service time in one or several $\cdot|M|1$ systems is replaced with a deterministic service time with the same mean: if the network is open, the total number of customers in the modified network is stochastically less that in the original network; if the network is closed, the average load coefficients of the systems in the modified network are not less than in the original network.