American University of Beirut

DCSN 310

Please answer the following questions. Question 1 (10 points) Say whether the following statements are true or false. Briefly explain why. (2 points for true or false – additional 3 points per explanation). 1. Suppose the profit per customer served in an M/M/2 system is $10 and that Ra< Rs = 2/Ts. The rate at which the system is making profit is $10 x 2 x 1/Ts. 2. The utilization of the servers (u) in a system where each server has its own queue (S x M/M/1) is lower than in an M/M/S system for the same arrival, service rate and number of servers (Assume that customers are assigned randomly to a queue in the case of separate queues and they are not allowed to switch queues). Question 2 (10 points) Answer the following questions briefly 1. (5 points) Holding other quantities a constant, which of the following increases the average waiting time in a queue? a. Increasing the service rate b. Decreasing the average inter-arrival time of customers c. Increasing the number of servers d. Risk pooling e. None of the above