Question

In a car pressure wash the average arrival rate is 12 cars per hour and are serviced at an average rate of 15 cars per hour, with service times exponential.

It is requested:
a) Probability that the system is empty.
b) Average number of clients in the washing system.
c) Average number of clients in the row.
d) Average time a customer waits in line.
e) Probability of having a row of more than 2 clients.
f) Probability of waiting more than 25 minutes in line and in the washing system

Answer 1

(a) 0.2

(b) 4

(c) 3.2

(d) 0.27

(e) 0.512

(f) 0.234

Arrival rate (l)	12		Average server utilization(r)	0.8
Service rate (m)	15		Average number of customers in the queue(Lq)	3.2
Number of servers	1		Average number of customers in the system(L)	4
			Average waiting time in the queue(Wq)	0.266667
			Average time in the system(W)	0.333333
			Probability (% of time) system is empty (P0)	0.2
Probabilities
Number	Probability	Cumulative Probability
0	0.200000	0.200000
1	0.160000	0.360000
2	0.128000	0.488000