Explanation:
Given: -
The number of ambulances is(m) = 2.
Arrival rate = 0.45 per hour
Service time = 2 per hour
Service rate =?
service time = 2 (Travel and assistance time averages two hours per call)
Therefore, Service rate will be 1/2 = 0.5 per hour.
a). System utilization(p) = arrival rate/mean of ambulances*service time
p = 0.45/2×0.5 = 0.45.
(b) :- The average number of customer waiting or waiting time for an ambulance is equal to:-
Arrival rate divided by the service rate ( on its corresponding service time as per table value)
I.e. Arrival time = 0.45 ÷ service rate =0.5
= 0.9 ( see table value for 0.9 with service rate as 2)
It comes to 0.229.
Therefore, the average number of customers waiting. 0.229.
(c) :- The average time customers wait for an ambulance is equal to :
No. of customers waiting for ÷ arrival rate
0.229 ÷ 0.45 = 0.508
Or 0.509 (approx. )
D) probability of Both ambulances is idle is Po = 0.378 (from the table for the value of and M=2)
So Probability of both ambulance is busy = 1-Po
= 1 - 0.378
= 0.622
