performanceuniform-distributionexponential-distribution

Exponential vs Uniform vs Exact Mean Response Times

so I have a hard time with this question. It is asking what I should choose that will give me the fastest mean response time.

So option 1 I have exponential distribution with service rate of 2 per minute. Which gives me service time of 0.5m = 30s.

Option 2, I have uniform distribution between 10s and 50s so this gives me uniform time between 10s and 50s so the average of that is the median which is 30s.

Option 3, I have 50% probability of getting 10s exactly response time or 50% probability that I'm getting 50s exact response time. So I if I do this calculation: (0.5)(10/60) + (0.5)(50/60) I get 0.5m or 30s.

All these options give me the same mean response time so I'm not sure what to choose here.

Solution

  • You want to know the expected value a RV in each of these cases.

    For an exponential RV:

    E[X] = 1/lambda (lambda = rate) 
E[X] = 1/2

    For a uniform distribution, the expected value will just be the mean.

    For option 3, use the definition of expected value:

    E[X] = sum(E[x_i]P(x_i)) over all i

    Then your best option is the one with the lowest expected value. If they are all the same, and that is your only selection criteria, then it doesn't matter which option you pick.