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.