During the evening busy period, passengers of Tom Jackson's airline at the Flagstaff the Airport arrive at a rate of 71 per hour and an agent can serve 26 passengers per hour. The check-in queue system the airline follows is illustrated below:

(1) Using the appropriate queuing model template, generate the performance measures of the queue. Attach (cut and paste special > picture) the appropriate queuing template with the correct information below.

(2) What is the average length of the line when there are three agents on duty?

8.4719

(3) What is the average waiting time (in minutes) for passengers at this check-in counter?

Avg. waiting time

minutes in hour

Total in minutes

0.1429

60

8.6

(4) Airline management would like to reduce the average waiting time for check in to no more than 5 minutes. How many agents would have to be on duty to meet this service standard?

Minutes

Minutes in hr.

Agent

5

60

0.083333333

4

Copy and paste onto this worksheet the output used in anwering the questions above.

When copying and pasting, use Copy > Paste Special > Picture

Multiple Channel Waiting Line Model

Arrival rate l =

71

Service rate m =

26

Increment Dl =

0.1

Increment Dm =

0.1

Interarrival Time 1/l =

0.0141

Service time 1/m =

0.0385

Number of servers (max 12)

M =

3

4

5

6

7

8

System Utilization

r =

0.9103

0.6827

0.5462

0.4551

0.3901

0.3413

Probability system is empty

P₀ =

0.0221

0.0551

0.0627

0.0645

0.0650

0.0651

Probability arrival must wait

P_w =

0.8353

0.4022

0.1747

0.0682

0.0240

0.0076

Average number in line

L_q =

8.4719

0.8653

0.2103

0.0570

0.0153

0.0039

Average number in system

L_s =

11.2026

3.5961

2.9410

2.7878

2.7461

2.7347

Average time in line

W_q =

0.1193

0.0122

0.0030

0.0008

0.0002

0.0001

Average time in system

W_s =

0.1578

0.0506

0.0414

0.0393

0.0387

0.0385

Average waiting time

W_a =

0.1429

0.0303

0.0169

0.0118

0.0090

0.0073

for #4 the answer should be 4 servers. Can you explain how to get that answer?