The DMV employs 3 servers that serve cust omets in one line. Customers amve following a Poisson process with rate 10 per minute, Service times are distributed exponentially with rate S per minute.
management
Description
(20 pts) The DMV employs 3 servers that serve cust omets in one line. Customers amve following a Poisson process with rate 10 per minute, Service times are distributed exponentially with rate S per minute.
a. (10 pts) Calculate W. Wq. L. Lq.
b. (10 pts) The DMV decides to replace its 3 servers with one automated server, and the manager must decide what service rate the machine should have. The serer cost is S3 per unit rate per minute. and the waiting cost of the customers is S0.8 per minute per customer. ‘Vhat is the optimal service rate?
2. (15 pts) Qualitatively compare the following two queuing systems. in terms of utilization. average waiting times, and the average number of people in the systems. Also, give a brief description of the practical differences between the two systems (i.e.. if you’re a business deciding on which system to use. vhat might be some additional considerations?).
Both systems are MM’2 (two servers) queuing systems with mean customer arrival rate of 2)... and mean service rate of each server is i The first system has customers lining up in a single queue: the person at the front of the line gets served by the next available server. The second system has two separate queues. with each queue going to one of the servers: where customers atuve at rate 2)., and when a customer arrives they join the shorter of the two lines.
(Consider two different cases for this system where switching between queues is allowed and
not allowed.)
