Question

1) A queuing model that follows the M/M/1 (single channel) assumptions has λ = 10 per hour and μ = 2.5 minutes. What is the average time in the system (in minutes)? Group of answer choices: .41 minutes .5 minutes 25 minutes 1.78 minutes 4.29 minutes

2)

A waiting-line system that meets the assumptions of M/M/S (multi-channel) has λ = 4 every 12 minutes, μ = 4 minutes, and M = 2. For these values, Po is approximately 0.2, and Ls is approximately 2.4.

What is the average time a unit spends in the queue (in minutes)?

Group of answer choices

.053 minutes

3.2 minutes

2.4 minutes

.12 minutes

7.2 minutes

please show all your work, thanks!

Answer 1

1)

M/M/1 system

λ = 10 per hour = 10/60 = 0.1667 per minute

μ = 1/2.5 minutes = 0.4 per minute

What is the average time in the system (in minutes), W = 1/(μ-λ)

= 1/(0.4-0.1667)

= 4.29 minutes

.

ANSWER: 4.29 minutes

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2)

M/M/S system

λ = 4 every 12 minutes = 4/12 = 0.33 per minute

μ = 1/4 minutes = 0.25 per minute

M = 2

For these values,

P0 = 0.2

Ls = 2.4

Lq = Ls-λ/μ = 2.4-0.33/0.25 = 1.0667

Average time a unit spends in the queue (minutes), Wq = Lq/λ

= 1.0667/0.33

= 3.2 minutes

.

ANSWER: 3.2 minutes