You can use equivalence testing here. Since you are testing to see if the two population distributions are similar I think it is a mistake to base conclusions off of a two sample t-test.
Here is the approach. Take the ratio of the two service times and construct the CI for a given significance level.
Now, the hard part, you need to scientifically determine what cutoffs indicate they are the same (the cutoffs do not come from the data). For example the FDA might specify the 90% CI of the ratio must be in the range of .80 to 1.25 to consider two drugs equivalent.
If your entire CI is within the cutoffs then you can conclude the two distributions are similar. If part of the CI is in the cutoff and part outside the results are inconclusive. If the entire CI is outside the cutoffs then you can conclude they are different.