This paper considers the selection of capacities, in two classes of open queueing network models of computer communication systems: 1) local-balanced queueing networks with multiple classes of customers and 2) the Reiser-Kobayashi diffusion approximation model. The problem of selecting optimal bandwidths for communication lines and switches and computing machinery is difficult due to 1) the economy of scale exhibited by components (i.e., the bandwidth per dollar increases with the total cost of the component) and 2) the discrete nature of computer/communication components (for instance it is possible to lease communication lines with 2400-Bd or 4800-Bd band-widths but not one with a 2401.3-Bd bandwidth). This paper develops aun algorithm to select servers taking both of these characteristics of server costs into account. The contribution of this paper is to discuss 1) the optimization of more general network models with 2) the consideration of more realistic tariffs and 3) more constraints on network behavior than were previously analyzed.

This paper investigates some of the effects of varying the number of central processing units (CPU's) available to a multiprogramming system both when parallel processing of a single task (multitasking) is allowed and is not allowed. The variables investigated are those that would be expected to control the CPU queue length distribution and include the degree of multiprogramming, CPU service discipline, CPU service distribution, the degree of cooperation between processors engaged in multitasking, and the ratio of CPU to I/O service capacity. The computer systems are modeled by queueing networks. Analytic results are displayed in many cases with supplementation by numeric and simulation solutions when convenient or necessary. It is demonstrated that under properly defined conditions doubling the number of CPU's in a system can more than double throughput. The effectiveness of multitasking in improving throughput is found to be fairly small if the degree of multiprogramming ranges from modest to high.