Question9 What is the transition rate from state (0, 2, 3, 4) to state (0, 1, 3, 4)? (Four (4) marks for the correct answer. Zero (0) marks for a wrong answer or if unanswered. )Select only one of the following options: [math: 2λL] [math: 3λH] [math: λL] [math: μ] The end state of the given transition is invalid. 0 [math: 4λH] [math: 3λL] [math: 2μ] [math: 4μ] [math: 4λL] The starting state of the given transition is invalid. [math: 2λH] [math: 3μ] [math: λH] ResetMaximum marks: 4 Flag question undefinedSingle choice
A
2 𝜆 𝐿
B
3 𝜆 𝐻
C
𝜆 𝐿
D
𝜇
E
The end state of the given transition is invalid.
F
0
G
4 𝜆 𝐻
H
3 𝜆 𝐿
I
2 𝜇
J
4 𝜇
K
4 𝜆 𝐿
L
The starting state of the given transition is invalid.
M
2 𝜆 𝐻
N
3 𝜇
O
𝜆 𝐻

Question

Question9 What is the transition rate from state (0, 2, 3, 4) to state (0, 1, 3, 4)? (Four (4) marks for the correct answer. Zero (0) marks for a wrong answer or if unanswered. )Select only one of the following options: [math: 2λL] [math: 3λH] [math: λL] [math: μ] The end state of the given transition is invalid. 0 [math: 4λH] [math: 3λL] [math: 2μ] [math: 4μ] [math: 4λL] The starting state of the given transition is invalid. [math: 2λH] [math: 3μ] [math: λH] ResetMaximum marks: 4 Flag question undefinedSingle choice

A

2 𝜆 𝐿

B

3 𝜆 𝐻

C

𝜆 𝐿

D

𝜇

E

The end state of the given transition is invalid.

F

0

G

4 𝜆 𝐻

H

3 𝜆 𝐿

I

2 𝜇

J

4 𝜇

K

4 𝜆 𝐿

L

The starting state of the given transition is invalid.

M

2 𝜆 𝐻

N

3 𝜇

O

𝜆 𝐻

BlackTom AI · Accepted Answer

There are 4 busy servers, so the total rate of service completions in the system is 4·μ. This is the key to the transition.

1) Relevant concepts
- In continuous-time Markov models of queues, a decrease in a queue-component by one (with no change in the number of busy servers) typically results from a service completion that immediately starts serving a waiting customer. 
- Each busy server completes service independently at rate μ, so the total service-completion rate when s servers are busy is s·μ.
- Arrival rates (λ_H, λ_L) cause increases in counts, not decreases; they are not responsible for this transition.

2) Step-by-step reasoning
- Starting state is (0, 2, 3, 4). The fourth entry = 4 indicates there are 4 busy servers.
- The target state is (0, 1, 3, 4): the second component decreased by 1 (2 → 1) while the fourth component remained 4.
- Because the number of busy servers does not change, the only way the queue-length of the second component can drop is that a busy server completed service and immediately began serving one of the waiting low-priority customers, moving that customer from queue into service. That operation reduces the waiting count by one but keeps the server count the same.
- Any of the 4 busy servers could complete service to cause this; each completes at rate μ, so the total rate for such completions is 4·μ.

3) Intermediate calculation
- s = number of busy servers = 4
- total completion rate = s · μ = 4 · μ

4) Why the correct answer is correct
- The transition is driven by a service completion among the 4 busy servers. Summing independent exponential completions gives total rate 4μ, so the transition rate to (0,1,3,4) is 4μ.

5) Why other options are incorrect
- Any option involving λ (λ_L or λ_H) corresponds to arrivals (increases), not the observed decrease in the second component.
- μ, 2μ, 3μ are too small because there are 4 busy servers (s·μ must use s=4).
- Options stating the start/end state is invalid or 0 are incorrect because the move is valid and has a nonzero service-completion rate.