A local coffee shop in its busy period gets about 10 customers per minute. A typical server working at the counter can help customers at a rate of 2 per minute. 4(a). What is the minimum number of servers the shop needs to have to make this a stable system, i.e. rho < 1? 4(b). We will assume that the server’s rate of service stays constant. However, the rate at which customers come in might fluctuate. Consider customer arrival rates ranging from 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number of servers the shop should have during its busy period. Range the number of servers from your answer in 4(a) up to 5 more (that is, if you said x in (a), let c = x, x+1,…,x+5) Create simultaneous line plots similar to what was done in the M/M/c practice for the values of R0. Plot the c values on the x-axis and create a separate line plot for each value of lambda(customer arrival rate). Give the appropriate titles and labels and include a legend. Make sure each graph is clear and easy to read. 4(c). Comment on the behavior in the graph and the change in R0 vs the number of servers.

Question

A local coffee shop in its busy period gets about 10 customers per minute. A typical server
working at the counter can help customers at a rate of 2 per minute.

4(a). What is the minimum number of servers the shop needs to have to make this a
stable system, i.e. rho < 1?

4(b). We will assume that the server’s rate of service stays constant. However, the
rate at which customers come in might fluctuate. Consider customer arrival rates ranging
from 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number of
servers the shop should have during its busy period. Range the number of servers from
your answer in 4(a) up to 5 more (that is, if you said x in (a), let c = x, x+1,…,x+5)

Create simultaneous line plots similar to what was done in the M/M/c practice for the
values of R0. Plot the c values on the x-axis and create a separate line plot for each value of
lambda(customer arrival rate). Give the appropriate titles and labels and include a legend.

Make sure each graph is clear and easy to read.

4(c). Comment on the behavior in the graph and the change in R0 vs the number of
servers.