The current checkout format is individual lines. For example, on Monday afternoons, there is one line and one cashier. On average, a customer arrives to the checkout line every 90 seconds, exponentially distributed. The cashier is fast, and can on average checkout one customer in 65 seconds, also exponentially distributed.

Fill in the next table. (Don't forget the units.) Show your work in the table or below.

Question: I need help understanding what the Ca, Cs, & the probability that the system is empty. I'm not sure how to calculate that with the provided information.

What type of queuing system is this?	This is a M|M|1 queuing system
Arrival rate	Arrival rate () = 1 customer every 90 secs = 40 customers/ hour
Average inter-arrival time	Interarrival time = 1/l = 1/40 = 1.5 mins = 90 secs
Service rate	Service rate ()= 1 customer every 65 secs = 55.38 customers / hour
Average service time	Average service time = 65 seconds
# of servers	# of servers (s) = 1
Utilization	Utilization = / = 40/55.38 = 0.7222 = 72.22 %
CA
CS
Avg. # of customers in the line (Lq)	Average Number of Customers in the System = ^2 / () = p^2 / (1 - p) Average Number of Customers in the System = .7222^2 / (1 - .7222) Average Number of Customers in the System = 1.88 Customers
Avg. # of customers in the system (Ls)	Average Number of Customers in the System = / () = p / (1-p) Average Number of Customers in the System = .7222 / (1 - .7222) Average Number of Customers in the System = 2.6 Customers
Avg. time a customer waits in the line (Wq)	Average Time Customer Spends in the System = Lq / Average Time Customer Spends in the System = 1.88 / 40 Average Time Customer Spends in the System = 0.047 hours
Avg. time a customer waits in the system (Ws)	Average Time Customer Spends in the System = Ls / Average Time Customer Spends in the System = 2.6 / 40 Average Time Customer Spends in the System = 0.065 hours
Probability the system is empty