Question

TOTAL POINTS: 5 points Problem 1. True or False Question (1 point, 0.25 points for each sub-question) (a) In a single-server queue system, utilization affects the average waiting time ina proportionally. For example, if utilization increases by 10%, the average waiting time will also increase by 10%. True False If you choose False, please indicate which part of the statement is wrong and how to correct the statement: (b) The off-peak pricing approach, like happy hour, is an approach to reduce waiting time by reducing customer arrival rate during the peak hours by charging a lower price over off peak hours. True False If you choose False, please indicate which part of the statement is wrong and how to correct the statement: (c) Comparing to a multiple-server system with multiple lines, a pooled (single-line) system reduces the average waiting time by improving the average service rate. True False If you choose False, please indicate which part of the statement is wrong and how to correct the statement: Question 1 (d) is related to Lecture 16 (d) WSPT assigns the highest priority to job(s) with the highest weight. True False If you choose False, please indicate which part of the statement is wrong and how to correct the statement:

Answer 1

(a) Average waiting time in queue = lambda / mu ( mu-lambda)

If utilisation is increased by 10%, either lambda increases by 10% or mu decreases be corresponding degree. In any case, the effect will be more than 10% as the denominator would decrease.

Thus the statement is false.

(b) true

(c) True, because performance of a line is affected by variations and result in delay for all people waiting in that line. resulting in higher avg waiting time as compared to a pooled line where the variations are evened out, and the resultant effect on waiting time is low.

(d)False. The priority is assigned to the tasks which have least value of (time/weight). It is not only sufficient for the weight to be more, but also the time to be less, so that the time/weight ratio is smallest.