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15 customers arrive every hour​ at Andy​ Johnson's food truck when it parks outside the Orlando Courthouse from...

Fifteen customers arrive every hour (Poisson distributed) at Andy Johnsons food truck when it parks outside the Orlando Cour

Table: Average Number of Customer in Waiting Line

Poisson​ Arrivals, Exponential Service Times

Number of Service​ Channels, M

rhoρ

1

2

3

4

5

0.1

0.0111

0.15

0.0264

0.0008

0.2

0.05

0.002

0.25

0.0833

0.0039

0.3

0.1285

0.0069

0.35

0.1884

0.011

0.4

0.2666

0.0166

0.45

0.3681

0.0239

0.0019

0.5

0.5

0.0333

0.003

0.55

0.6722

0.0449

0.0043

0.6

0.9

0.0593

0.0061

0.65

1.2071

0.0767

0.0084

0.7

1.6333

0.0976

0.0112

0.75

2.25

0.1227

0.0147

0.8

3.2

0.1523

0.0189

0.85

4.8166

0.1873

0.0239

0.0031

0.9

8.1

0.2285

0.03

0.0041

0.95

18.05

0.2767

0.0371

0.0053

1

0.3333

0.0454

0.0067

1.2

0.6748

0.0904

0.0158

1.4

1.3449

0.1778

0.0324

0.0059

1.6

2.8444

0.3128

0.0604

0.0121

1.8

7.6734

0.532

0.1051

0.0227

2

0.8888

0.1739

0.0398
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Homework Answers

Answer #1

ANSWER :

The Given information is

Arrival rate lambda =15 per hour

service rate mu =60/3

=30 per hour

rho =lambda /mu

=15/30

=0.5

(a)

Avg number in queue Lq= (lambda)^2 / mu*(mu-lambda)

Lq =225 / 30*(30-15)

= 225 /450

=0.5

(b)

Waiting time Wq =Lq /lambda

= 0.5/15

=0.0333 hour

=2 min.

(c)

If Andy's wife joins him, the new Lq with rho =0.5 and

2 channels is 0.0333

Wq = Lq /lambda

= 0.0333 /15

=0.00222 hour

=0.1332 minutes

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