Consider a computer system to which two types of computer jobs are submitted. Th
ID: 384978 • Letter: C
Question
Consider a computer system to which two types of computer jobs are submitted. The mean time to run each type of job is 1/µ. The interarrival times for each type of job are exponential, with an average of i type i jobs arriving each hour. Consider the following three situations.
(i) Type 1 jobs have priority over type 2 jobs, and preemption is allowed.
(ii) Type 1 jobs have priority over type 2 jobs, and no preemption is allowed.
(iii) All jobs are serviced on a FCFS basis.
(a) Compute Wq for each system.
(b) Determine the best and worst systems for type 1 jobs, and type 2 jobs.
Explanation / Answer
Chebyshev's inequality (also known as Tchebysheff's inequality) is a measure of the distance from the mean of a random data point in a set, expressed as a probability. It states that for a data set with a finite variance, the probability of a data point lying within k standard deviations of the mean is 1/k2. Alternately stated, no more than 1/k2 data points can be greater than k standard deviations away from the mean. Chebyshev's inequality is useful for making inferences about data sets that do not follow a normal distribution (in a normal distribution the standard deviation intervals are known precisely).
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