The Reem Clinic is also responsible for general emergency cases around the count

Question

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) what fraaction of the emergencies reported to the reem clinic are handled by the emergency services at the neighboring community? (use erlang loss table if required)

b) how many emergenices are served by the Reem Clinic during an average 24-hour day?

c) 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)

Explanation / Answer

Frequency of emergency reporting at Reem= 15 minutes

Number of emergencies reported at Reem in 1 hour= 60/15=4 emergencies

An ambulance and its crew are engaged for 1.5 hours on every call.

Number of cases 1 ambulance and crew can handle in 24 hours=24/1.5=16

Number of emergencies happening in 24 hours= 24 x 4=96

4 Reem ambulances are engaged every hour.

Number of cases the 8 ambulances can handle in 24 hours=16 x 4=64

a) The fraction of the emergencies reported to the reem clinic handled by the emergency services at the neighboring community:

Referred to the neighboring community=96-64=32

Fraction=32/64=0.5

b) Emergencies served by Reem Clinic on an average in 24 hours=32

c) For 95 %, the number of emergencies to be attended to=0.95 x 96 = 91

They need 2 more ambulances, 16 x 6=96

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