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Table 9.5 Some seek parameters for arm motors (seek time in ms = a + b  ). |
| | | | | Hitachi DK516 | 3.0 | 0.45 | | IBM 3380D | 2.34 | 0.81 | | IBM 3380J | 3.23 | 0.57 |
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Open-queue models are frequently used to describe disk behavior. Such models simply assume a fixed user demand on the system and then are used to predict such parameters as total response time. These models are obviously attractive because they do not require extensive knowledge of the user or processor behavior model. Their attractiveness is, of course, also their weakness. Systems simply do not continue to manufacture requests in the absence of a reply. |
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The primary danger in using the open-queue model is that the designer may fail to completely understand its limitations. |
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The same processor then manages the I/O request with system utility program(s) and resource management support programs. It finally issues the read or write command to the disk controller and then either (1) resumes user state processing (executing an alternate task) or (2) goes idle (awaiting the I/O response). |
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Very simple processor-I/0 systems such as programmed I/O are systems at capacity: the processor effectively must wait for the I/O response before proceeding with other useful work. These systems can be adequately modeled by closed-queue models; either M/G/1 or, for a first estimate, the closed-queue M/M/1 (c2 = 1). More complex systems that are not limited by I/O can often be approximated by using the open-queue model. Suppose there are multiple alternative tasks and the I/O system is responsive enough to access the required data before control is returned to the original requesting task. The overall system is unaffected by the I/O because the I/O requests are sufficiently buffered. While there is a waiting time (Tw) that a request spends in the buffer (queue), the offered request rate l is the same as the achieved rate la. In this case, we can determine the waiting time by using the open-queue model. This waiting time can be used to estimate the number of alternative tasks that must be available before the system slows down due to I/O capacity limitations (and l > la). |
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Since the system does not reach a capacity limit, an open-queue model is appropriate. Also, as there is a long time between requests, we use the Poisson arrival distribution to model the request distribution. The service distribution is not constant, so the M/G/1 open queue model provides the most accurate results. |
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In order to use the M/G/1 open queue, we need to know the coefficient of variance (c2) associated with the service distribution. This, in turn, de- |
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