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46 Part 1 ½ Fundamentals Section 2 ½ The Computer Space

performance attributes. Each channel (e.g., a typewriter) has a certain data rate and direction (half-duplex for two-way communication but in only one direction at a time, full-duplex for simultaneous two-way communication). Collectively, the data rates and the number of channels connected to each of the three different environments (people, computers, other electronically encoded processes) signify quite different styles of computing capability, structure, and function. For example, the absence of any communications connection to other computers implies a stand-alone system. Interconnection only to mechanical processes via electronically encoded links implies a real time structure. Similarly, only human intercommunication with multiple terminals denotes a timesharing or transaction-processing orientation.

Kiviat Graphs

Figure 2 uses a Kiviat graph1 to display the six main dimensions-processing, primary and secondary memory capacity, and the three communication channels-in a single six- dimensional graph, with three secondary dimensions. Each dimension is shown on a logarithmic scale up to a factor of 1 million, with the value 1 denoting the absence of an attribute (e.g., where there is no communication with external systems beyond human interaction). Various secondary measures are also represented. In the case that a dimension takes on values greater than 1 million, all axes are multipled by a scale factor such that the largest value will fit. The scale factor, if other than 1, is noted at the top of each Kiviat graph. When a scale factor is used, the value for some dimensions (e.g., communications with humans) may not be large enough to plot. Rather than erroneously indicate the absence of a dimension, the global scale factor is negated by dividing by a local scale factor denoted by the divide sign (I). All values are for the aggregated system. For example, the Ms dimension represents the total number of bytes on secondary storage (usually assumed to be disk unless otherwise noted). Parameters of individual components can be plotted with a multiplication factor (denoted by x) indicating the number of identical components in the system. Multiplication factors, usually found on the Ms and T.human dimensions, are applied when there is one dominant component type dictating the value of a dimension. Occasionally dimensions are further specified (e.g., audio, video). The graph conventions include subtleties of showing fixed points (i.e., ROM, or hardwired), averages, and range. The arrangement of the six dimensions allows easy recognition of a structure in terms of the relative mix of the resource and performance attributes. Figure 3 gives a diagram of a computer system in the same order as the graph's dimensions.

While designing the IBM System/360, Gene Amdahl postulated two rules of thumb for a balanced system. The first rule related Pc speed with Mp size, stating that 1 byte of Mp was required to support each instruction per second. The second rule related Pc speed with I/O bandwidth, stating that one bit of I/O was required to support each instruction per second. Note that if the Pc speed is "balanced" with Mp size according to Amdahl's constant (1 byte of Mp per ips), then the value of the two dimensions should be about the same. (In Fig. 2 Pc is accessing 2 million byte/s, corresponding to, say, 600,000 i/s, with Mp of 8 million bytes.)

Thus the Kiviat graph not only summarizes major performance parameters but also graphically depicts the balance of a system. The relative capacity of processor, memory, and I/O is immediately discernible from the Kiviat graphs.

Figure 4 shows how the six-dimensional plot can be used to represent and differentiate various computing structures in which we are interested. The first two structures are keyboard I/O; i.e., they use a single information transducer we know as the typewriter that has half-duplex I/O at 10 characters (or bytes) per second. A 10-char/s teletypewriter is formed by adding a line interface.

The simple, early, fixed-function hand-held calculator, e.g., the HP 35, had a fixed processing/memory structure with about 4 X

1Kiviat graphs were first used to summarize work load-specific performance with dimensions such as Pc, Ms, P~0 busy, and relative amount of time the Pc or Ms or Pio is the only active subsystem [Ferrari, 1978]. The Kiviat graph concept has been adopted and modified in this text as a means for summarizing hardware performance.
 
 

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