Stochastic Processes · 免费预览
退出分布与时间
连续时间链的退出问题可归结为使用受限速率矩阵的线性代数问题，其负逆矩阵给出在每个瞬态状态中所花费的期望时间，求解该问题既可得到命中概率，也可得到期望退出时间，这些内容以办公时间和理发店为例加以说明。
1. Two doors out of a waiting room
Two doors out of a waiting room
2. The inverse is a time ledger
The inverse is a time ledger
3. Office hours, who leaves last
Office hours, who leaves last
4. Expected exits and the stationary cross-check
Expected exits and the stationary cross-check
5. The embedded chain route
Why can discrete-time exit machinery be used for a continuous-time chain?
6. Reading the ledger
What does the i comma j entry of the negated inverse of R represent?
7. The exit probability formula
In the formula h equals the negated inverse of R times v, what is the column v?
8. Who overstays their welcome
Ron, Sue, and Ted stay for exponential times with means 1, one half, and one third hour. Who is most likely to be the last one in the office?
9. A cross-check worth doing
How does the stationary distribution of the two-barber shop help verify the computed value of E sub 1 T sub 0?
10. One door only
When the region has a single exit door, what does the expected exit time formula become?
11. The exit rate of the full office
Ron, Sue, and Ted remain in the office with exponential sojourn rates 1, 2, and 3 per hour. Compute the rate at which the first departure occurs when all three are present, and write the number.
12. The professor's countdown
Continuing the office hours story, the expected time until the office empties is 73 over 60 hours. Compute this in hours as a decimal, rounding to three places.
13. Three customers against the capacity door
In the two-barber shop with capacity 4, the probability of reaching empty before the shop fills, starting from two customers, is 36 over 41. Write this probability as a decimal.