Question

The sandwich maker of the EE-Cole-Eye Sandwich Truck was just fired (for a reason described below) and EE-Cole-Eye needs to find a replacement. They want to make sure that the replacement is fast enough so that customers don't have to wait too long on line. Customers arrive according to a Poisson process with arrival rate 2 customers/min and sandwich makers take an exponentially distributed length of time to make a sandwich, with mean time service time of 29 seconds. There are no limits to the number of customers that wait for sandwiches. Consider the queue of customers and analyze it assuming it is in steady state.

What is the probability there are 20 customers or fewer in the system?

What is the average wait time in the in the system in minutes?

Answer 1

The arrival rate is

Service rate is

Hence, the utilization factor is

Hence, the probability there are 20 customers or fewer in the system is

Average time a customer spends in the system is given by