A local coffee shop in its busy period gets about 10 customers per minute. A typical serverworking at the counter can help customers at a rate of 2 per minute.4(a). [2pts] What is the minimum number of servers the shop needs to have to make this astable system, i.e. rho < 1?4(b). [10pts] We will assume that the server’s rate of service stays constant. However, therate at which customers come in might fluctuate. Consider customer arrival rates rangingfrom 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number ofservers the shop should have during its busy period. Range the number of servers fromyour 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 thevalues of R0. Plot the c values on the x-axis and create a separate line plot for each value oflambda(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). [5pts] Comment on the behavior in the graph and the change in R0 vs the number ofservers.
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). [2pts] What is the minimum number of servers the shop needs to have to make this a
stable system, i.e. rho < 1?
4(b). [10pts] 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.
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). [5pts] Comment on the behavior in the graph and the change in R0 vs the number of
servers.
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