l*********o
发帖数: 88 | 1 1. There are two types of arrangement of a waiting queue for N ticket window
. The queue could be a single line, the people as the first in the queue go
to the window is available, The queue could also be divided into N sub-queue
in front of each window, the people can't switch queue and has go to
corresponding window.
Assume each person is reasonable and arrive randomly and will pick up the
shortest queue. Which way is better?
2. In an election, candidate A receives n votes, B receives m votes.
Assuming all ordering equally likely. What is the probability that A is
always ahead of B in the count of votes? | y****e
发帖数: 28 | 2 1. One queue is better
2. reflection principle
The answer for the prob of ahead (including equal votes) is
n>=m
1-C_{n+m}^{m-1}/C_{n+m}^m = (n+1-m)/(n+1)
If excluding the equal votes since the first vote counting started,
The prob is
n/(n+m) * (n-m)/n =(n-m)/(n+m) | e*****u
发帖数: 337 | 3 can anyone explain the first question, thx | z****g
发帖数: 1978 | | y****e
发帖数: 28 | 5 The expectation of the waiting time in one queue strategy is no greater than
that in N queue strategy.
however, the variation of the waiting time in one queue strategy is
definitely less than that in N queue strategy.
You guys can think hard why the two above statements are true.
【在 e*****u 的大作中提到】
: can anyone explain the first question, thx
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