Nogan Airport has three runways. The airport uses one runway to serve landing fl

Question

Nogan Airport has three runways. The airport uses one runway to serve landing flights and two runways to serve departing flights. If used for departure, a runway can serve 10 flights per hour; if used for landing, a runway can serve 15 flights per hour. The time it takes a plane either to depart or to land is exponentially distributed.

The schedule of the flights in the morning is described as follows. The time between two successive departing requests is always 5 minutes. The time between two successive landing requests is exponentially distributed, with an average of 10 minutes. When a landing flight approaches the airport, it radios the control tower and requests permission to land. The air traffic controller responds instantly by assigning the plane a position in queue on a first-come-first-serve basis.

Fill the following table for the departing requests in the morning. Fill integer numbers. For the utilization, fill an integer number without the “%” symbol.

a (avg. inter-arrival time, in minutes)

p (avg. service time, in minutes)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

On average, how long (in minutes) is the average delay for departing requests in the morning?

Fill the following table for the landing requests in the morning. Fill integer numbers. For the utilization, fill an integer number without the “%” symbol.

a (avg. inter-arrival time)

p (avg. service time)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

On average, how much timeelapses (in minutes) between a plane’s radioing of the control tower and its eventual completion of the entire landing process in the morning?

The schedule of the flights in the afternoon is different. In the afternoon, the time between two successive departing requests is always 10 minutes. The time between two successive landing requests is exponentially distributed, with an average of 5 minutes. Assume that (i) the airport still uses one runway to serve landing flights and two runways to serve departing flights in the afternoon, and (ii) all flights (either departing or landing) have a delay cost of $300 per flight per hour.

In the afternoon, how much is the average delay cost (in $/flight) per landing flight?

a (avg. inter-arrival time, in minutes)

p (avg. service time, in minutes)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

Explanation / Answer

We are given some point .

1) there is 1 runway used for landing and in one hour 15 flight is landing .

so it means 60/15 = 4 min per flight landing time .

but actually for next flight there is gap of 10 minute .

so after 10 min next flight land .

so we take one example .

at 10:00 AM one landing flight send singnal and 10:04 flight land .    so total time =4 min

then from 10:04 to 10:14 its waiting time for next landing .          so waiting time = 10 min

at 10:14 AM2nd flight send singnal forlanding and 10:18 flight land .    so total time =4+4=8 min

then from 10:18 to 10:28 its waiting time for next landing .          so waiting time = 10+10=20 min

and so on

till 10:56 .. 4flight land and in next 4 min next flight land .

so for 1st hour 5 is land and 40 min is waiting time .

so it means in 14 min one flight land and in which 10 min is waiting time .

so avg utilization is =4*100/14 = 28% .... (4 min utization in 14 minute )

so our 2nd table :

Fill the following table for the landing requests in the morning.

p (avg. service time, in minutes)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

5

28

72

28

2) similarly for dept flight .

it can dept 10 flight in 60 minute so that it will take

60/10 =6 minute per flight for departure .

and then it take 5 minute break .

so total 6+5 =11 minute for completing one cycle .

utilization in one cycle is 6 min

waiting =5 min

so utilization % = 6/11 = 55%

departure : (in 1 hour )

p (avg. service time)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

35

6

55

45

55

if we use both the platform of departure .

then there is no waiting time .

platform 1 : 10:00 - 10:06 first flight dept .. then 10:06 to 10:11 waiting time .

but at that time 10:06 to 10:12 .. 2nd platform is avalible for flight

and we check after that platform one is availble for flight .

so there is no waste of time if we compine both the condtion .

ques 2: if we change conditon . like gap between flight .

then using above style we will get the answer .

for any issue please write comment .

a (avg. inter-arrival time, in minutes) in hour

p (avg. service time, in minutes)

m (number of servers)

u (avg. utilization)

CVa (coef. of var.- arrival)

CVp (coef. of var.- service)

40 20

5

28

72

28

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