Consider the following scenario. You know from your running apps that you can run 1 mile pretty reliably, meaning 99 percent of the time, you can run a mile between 9 and 10 minutes. A (5)/(5.1)/1 queue is 1 mile away–here it is a rate of 5 customers per minutes. Estimate the probability that you will make to through the queue within 20 minutes. Make clear any assumptions you are using for your calculations/simulations. Part of this exercise is to come up with reasonable modelling assumptions. Give one answer than you can do without any complicated calculations–like one that you can perform while you are running and deciding if you will make it or now, and give another answer that you think is more accurate and makes better use of the available information. Discuss the differences in your numerical answers. I did the simple one just by calculating but not coding. For =5 and =5.1: =1/0.1=10 minutes. Total Time: Running + Queue Time = 9.5+10=19.5 minutes. This assumes nobody is in the queue. For the accurate one, I think simulation should be used, but have no idea of how to code it. Continue reading...
