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Question: The Reem Clinic is also responsible for general emergency cases around the country. They have eme...
The Reem Clinic is also responsible for general emergency cases around the country. They have emergency service and currently have 8 ambulances. On average,emergencies are reported to the Reem Clinic every 15 minutes (with coefficent variation of 1,no seasonality exists). If the Reem Clinic has available ambulances, it immediately dispatchesone. If there are no ambulances available, the incident is served by the emergency services at a neighboring community,
The data collected by the Mc ISYE consulting firm reveal that :
There is always an ambulance available at a neighbour community.
On average, an ambulance and its crew are engaged for 1.5 hours(with coeffecient of variation of 1 ) on every call.
The Reem Clinic operaates 24 hours a day.
a)
New regulations require that every emergency service respond to at least 95% of all incidents reported in its area of service. Does the Reem clinic need to buy more ambulances to meet this requiremrnt? if yes, how many ambulances will be requied? (Assume that the meaan time spend on each trip cannot be changed)
show the steps please
Explanation / Answer
This is a G/G/s
Where s = 8 here.
Mean Arrival rate: 15 mins = 4 in an hour
Std Dev = 1
Mean Service rate = 1.5 hours = 0.6667 in an hour
Std dev = 1
As the num of servers = s= 8
The queueing formla for G/G/s
we get Utilization is at 75%.
And the Po = Probability of server is idle = 0.214%
Hence the service level is 99.786 %.(Or busy for)
Hence the level of 95% is satisfied and they do not need to get more ambulances.
(The formulae used:
r = l/m
Pn = rn/n! P0, " 0 < n £ C
Pourcentage of lost customers = PC
Server utilization ratio = (1 – PC) l/Cm
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