Question: Need help understanding these Operations problem, can someone explain it to me. Irvine Regional Hospital (IRH) has 8 beds in its Intensive Care Unit (ICU).

Need help understanding these Operations problem, can someone explain it to me.

Irvine Regional Hospital (IRH) has 8 beds in its Intensive Care Unit (ICU). Whenever all beds are full, the hospital goes on "diversion status", which means any ambulances picking up new patients will instead take their patients to another nearby hospital.

Average demand for the ICU is 2.5 patients/day (coming from 9-1-1 calls), while the ICU serves patients at a rate of 3.333/day. All patients in ICU beds are served in parallel (i.e., there are enough doctors and nurses that beds are the limiting resource). For modeling purposes, we assume that arrivals are Poisson and service times are exponentially distributed.

Question 1.a:

How many servers are there in this queueing system?

Question 1.b:

What is the expected amount of time between successive ambulance arrivals bringing patients to the ICU (also known as the inter-arrival time)?

Question 1.c:

What is the expected amount of time between a patient's admission to the ICU and his/her discharge?

Question 1.d:

Assuming all beds are used equally often, then what is the probability that any given bed has a patient in it? Hint: This is the same as computing the utilization of the beds.

Question 1.e:

What is the probability that all beds in the ICU are full (this is when IRH goes on diversion status)?

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