Question

Problem 11-19 (Algorithmic)

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 3 passengers per minute. On Monday morning the arrival rate is 5.6 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning.

Note: Use P₀ values from Table 11.4 to answer the questions below.

1. The facility manager's goal is to limit the average number of passengers waiting in line to 9 or fewer. How many screening stations must be open in order to satisfy the manager's goal?
   
   Having 3  station(s) open satisfies the manager's goal to limit the average number of passengers in the waiting line to at most 9.
   
2. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.
   
   W =  minutes

Answer 1

Solution:-

Given that

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area.

The airport has three screening stations available, and the facitlity manager must decide how many have to open at any particular time.

The service rate for processing passengers at each screening station is 3 passengers per minute. On Monday morning the arrival rate is 5.6 passengers per minute.

When the security level is raised to high, the service rate for processing is reduced to 2 passengers per minute at each station.

a) The facility manager's goal is to limit the average number of passengers waiting in line to 9 or fewer. How many screening stations must be open in order to satisfy the manager's goal?

Having 3  station(s) open satisfies the manager's goal to limit the average number of passengers in the waiting line to at most 9.

The exponential distribution can be parametrised in terms of parameter

the cdf of distribution can be given by

In the poisson distribution

Discrete random variable x has poisson distribution with if k = 0, 1, 2, ...

The probability mass function of x is given by

is given by the rate of the event.

b) What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.

W =  minutes

Average value of time required per passenger =

According to exponential distribution

The standard mean of the distribution is given by inverse

Since the three screening stations with rate 2 each can be considered as one station with rate 6.

minutes

After rounding off the answer = 0.11 minutes

= 0.1666 x 60

= 10.02 seconds

Thanks for supporting...

Please give positive rating...

Feel to comment if you have any doubts...