紀錄一下，走出家裡第一天，來到圖書館A199，其實我只是想要做下面finds的備份
這部分可以當作queue的介紹
再延伸到不同的service rate distribution 這部分
我的東西好淺白
We could start from a simple M/M/1 queue. The
two Ms refer to the assumption that
both the interarrival and the service distributions are exponential, and the 1 to that there is a single server. Suppose
the sediment particles arrive control volume in accordance with a Poisson
process having rate λ. That means the time between successive arrivals are independent
exponential ransom variables having means 1/λ. And in this special case,
sediment transport capacity in the control volume is exactly one sediment
particle. The sediment transport capacity corresponds to M/M/1 queue is the
number of server, which is one in this case. Each sediment particles, upon
arrival, would either keep transporting or deposit immediately. The transport
from the beginning to the end of the control volume is defined as a ‘service’
in M/M/1 queue. In order to tally with M/M/1 queue, the successive service
times, the transport time, are assumed to be independent exponential random
variables having mean 1/μ.
所以我們要知道什麼?
幹我好想睡覺~!= =
If the
system is in steady state, we could find
1.
The limiting probability
2.
The probability that next arrival finds n in the system
3.
The average number of customers in the system
4.
The average number of customers waiting in the queue
5.
The average amount of time a customer spends in the system
6.
The average amount of time a customer spends in queue
~
上面的例子service time 是exponential distribution
但是seiment transport 不會真的依照exponential distribution 進行事吧!
因此，我們用幾個方是常是解決這個問題
第一個當然是選擇合適的sediment transport formula，這樣我們不僅僅是可以有(sediment transport distribution)(←看有沒有要換，怕大家認為是極配QAQ)
我們還可以描述出粒子的隨機路徑，像是caseAs，我們使用(解釋caseAs….)
如果像是bed load transport 可能沒有適合的描述只有bedloadparticle軌跡的’formula，當然如果我們找到合適的transport distribution 也是個好方法(check愛因斯坦的distribution)
當時機成熟，我們可以合適的把不同的sediment particles當成在同一家商店需要不同服務的不同種客人，我們就可以同時模擬suspended bed load particles in the same control volume
一些其他的應用
我們也許可以用一些常識?(顯而易見清松可以直接聯想的方式逕行假設，然後從琳瑯滿目的定律是終結合我們stochastic framework ，將觀察的對象改成deposit
particles ，我們就可以得到觀察區域中粒子沉澱的情況!像是caseCb
Further application
