# A small town with one hospital has 2 ambulances to supply ambulance service. Requests for...

## Question:

A small town with one hospital has 2 ambulances to supply ambulance service. Requests for ambulances during non holiday weekends average 50 per hour and tend to be Poisson-distributed. Travel and assistance time averages 2 hours per call and follows and exponential distribution.

A. Find system utilization.

B. Find the average number of customers waiting.

C. Find the average time customers wait for an ambulance.

D. If there are 2 ambulances, find the probability that all ambulances will be busy when a call comes in.

## Poisson Distribution

The Poisson distribution is a distribution which helps us estimate the probability of an event occurring when the average values associated with that event are given. The probability of independent events is calculated in this distribution. Poisson distributions are usually used when the number of observations is nearly 50.

A. Utilization is calculated as request arrival rate divided by the number of servers tie the service rate. We calculate the service rate as one divided by the service time. So, the utilization time is 0.5 or 50 %.

B. Average number of customers waiting for the ambulance is 0.333. It is calculated by locating the request arrival rate divided by the service rate and service time in the Poisson distribution table.

C. The average time customers wait for an ambulance is number of customers waiting for an ambulance divided by the request arrival rate. So, it is 0.666 hours.

D. The probability that both the ambulances will be busy when a call comes in is 0.333.