Effects of resource utilization on Response time
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A naive cost-performance design assumes 100% utilization of I/O resources. This assumption leads to a servere increase in response time as we approach 100% utilization. This can be illustrated by a simple calculation for one disk, and we will also ignore SCSI strings and controller.

Assumptions:

  • average disk service time=7.8ms
  • poisson arrivals with an exponential service time
  • use M/M/1 queuing model
    •

    Characteristics of M/M/1 queue:

  • The system is equilibrium.
  • The times between two successive requests arriving, are exponentially distributed.
  • The number of sources of requests is unlimited (infinite population model).
  • The server can start on the next job immediately after finishing with the prior one.
  • The queue is a FIFO and there is no limit to the length of the queue.
  • There is a single server.
    •

    Equations used to evaluate response time:

    Server utilization

    = Arrival rate * TimeServer

    Time queue

    = Timeserver * Server utilization/(1 - Server utilization)

    Time system(Response time)

    = Timeserver + Timequeue

    Example: For 64 I/O requests per second

    Server utilization = 64 * 0.0078 = 0.50 ie 50%

    Time queue = 7.8ms * 0.50/(1-0.50) = 7.8ms

    Time system(response time) = 7.8ms + 7.8ms = 15.6ms  
     

    The table below shows the server utilization and response time for differnet request rates.

    The Graph below plots the response time versus request rate

    From the graph, we see that 100% utilization of disks is quite unrealistic. The response time tremendously increases as we try to use 100% of the server.

    The organization of a realistic cost-performance design should be performance-tuned. It should be aimed at limiting the utilization of I/O resources in order to keep reponse time and contention low. Below is an example of rules of thumb that could guide I/O designers to meet the above goals:-