Stochastic Processes · 免费预览
马尔可夫队列
M/M/1 队列是一个生灭链，其平稳分布为移位几何分布，其平均量可由几何级数立即求得；有限等候室会使该分布被截断；而处于平衡状态的 M/M/s 队列的输出过程恰好是泊松过程，这一性质使排队网络得以分析。
1. The M slash M slash 1 chain
The M slash M slash 1 chain
2. Averages for free from the geometric
Averages for free from the geometric
3. A finite waiting room
A finite waiting room
4. More servers and a surprising output
More servers and a surprising output
5. The geometric queue
What is the stationary distribution of the M/M/1 queue when lambda is below mu?
6. Averages from the geometric series
For the M/M/1 queue, why do all the standard averages follow from power series?
7. The price of high utilization
What happens to the average wait in an M/M/1 queue as the arrival rate approaches the service rate?
8. Walls protect the queue
What does a finite waiting room change about the stationary distribution?
9. One barber, two chairs
A barber serves at rate 3, arrivals at rate 2, and only two customers can wait. What fraction of time is the system empty?
10. Departures that look Poisson
Why is the output process of an equilibrium M/M/s queue a Poisson process of rate lambda?
11. Empty at the haircutter's
An M/M/1 queue has arrival rate 2 per hour and service rate 3 per hour. Compute the stationary probability that the system is empty, and write the answer as a fraction or decimal.
12. Two deep on average
For the same M/M/1 queue with lambda 2 and mu 3, compute the average number in the system L, using rho over one minus rho, and write the number.
13. An hour of your life
Using Little's formula W equals L over lambda for the same queue, compute the average time in system W and write the number of hours.