近年来，北京大学图书馆的存包柜被长期占用的情况十分严重。尽管图书馆在《北京大学图书馆存包柜使用须知》中明确规定了闭馆前不带走物品和挂锁的行为为占柜，并应该被清理，而因为种种原因这一规定并没有得到彻底的执行。
近来，随着图书馆方面加强了对存包柜的清理，一些利益相关者在北大未名BBS的PKULibrary版面上产生了很多的争执。有一些网友认为，清理存书柜的行为不具有正当性，而违规占柜是正当的。他们的理由包括清理存包柜会导致实际的利用效率下降。
针对这些争论，我对北京大学图书馆的存包过程进行了简化假设，并构建了模拟模型，利用python语言对其进行了实现和求解，并研究了不同参数下的模型结果。
该模型的假设简要概括如下：
- 北京大学图书馆（PKULib）每天开放10小时。
- PKULib有1000位读者，其中100位为不遵守规定的读者（badreader），900位为遵守规定的读者（goodreader）。
- 北京大学图书馆提供150个存包柜（locker）供读者使用。
- 每天，所有读者都会一个个的进馆，并都会使用存包柜。其进入图书馆的时间基本满足均匀分布，即每小时进入的人数相差不大。每人进馆后都会寻找空的储物柜，如果找到，该读者会感到开心（happiness）；如果存包柜都被沾满，该读者会感到郁闷（madness）。
- goodreader每天会在图书馆呆到下一个整点，且这一天就不再来图书馆。他们走的时候会带走存包柜里自己的东西。
- badreader走的时间谁也不知道，而且他们不会带走自己在存包柜里的东西。
- 每隔一段时间（emptyperiod），图书馆会在闭馆后清理存包柜，此时badreader占用的存包柜会被清空。直到下一次badreader来到图书馆，他们才会重新占据一个存包柜。
我编写并求解了这一模型。在参数emptyperiod不同的情况下，获得了不同的结果。经过多次尝试，发现参数不变的情况下结果的差异不大（可以算方差表征）。典型的值如下：
当每天清一次柜时，happiness为90209，madness为9791；
当每30天清一次柜时，happiness为1314，madness为98686。
这样的模拟结果说明，在模型假设条件下，每天清柜相比每30天清柜，会显著的增加happiness，降低madness。
附：代码LibSim_1_0_0.py
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# FileName: LibSim.py
'''Libsim 1.0.0
LibSim program is an agent-based simulation program to study
the occupation of lockers in Peking University library. It is
a python 3 styled code written in object-oriented fashion.
Programmer:
Meng Xiangxi
PhD student, Peking University
mengxiangxibme(>_<)gmail.com
History:
1.0.0 Released 20141213
'''
import random
# Model specifications, constants
hours = 10 # Total openning hours of PKULib
emptyperiod = 30 # Period of evacuation
simdays = 100 # Days to simulate
numlocker = 150 # Set number of lockers
numgoodreader = 900 # Set number of good readers
numbadreader = 100 # Set number of bad readers
#=====================Classes====================#
class Locker:
'''The locker in PKULib'''
empty = True # If the locker is empty
readerID = 'null' # The reader occupying the locker
def chkempty(self): # Check if the locker is empty
return self.empty
def setempty(self, value): # Change the empty status
self.empty = value # value is Boolean
def getreaderID(self): # Return the occupyer
return self.readerID
def setreaderID(self, ID): # Change the occupyer
self.readerID = ID
def emptygoodreader(self): # Only good readers leave
if self.readerID[0] == 'G':
self.empty = True
self.readerID = 'null'
class Reader:
'''Parent class for the readers'''
numlocker = -1 # The last used locker number
def chklocker(self, locker): # When entering PKULib, reader look for locker
for lockernum in range(0,numlocker): # Traverse the lockers
if locker[lockernum].chkempty(): # If locker is empty
inchappy() # Feel happy
locker[lockernum].setempty(False) # Occupy it
self.numlocker = lockernum # Record the locker number
return 0 # Stop looking for lockers
self.numlocker = -1 # Cannot find locker
def getlockernum(self): # Return the number of locker last used
return self.numlocker
def leave(self,locker): # Leaving PKULib, release the locker
if self.numlocker > 0:
locker[self.numlocker].setreaderID('Null')
locker[self.numlocker].setempty(True)
self.numlocker = -1
class GoodReader(Reader):
'''Readers taking their own belongings'''
def __init__(self): # Inherit the __init__() and parameter of Reader
Reader.__init__(self)
numlocker = -1
self.numlocker = numlocker
def chklocker(self,locker,ID): # The chklocker() function of child class
for lockernum in range(0,numlocker):
if locker[lockernum].chkempty():
inchappy()
locker[lockernum].setempty(False)
self.numlocker = lockernum
locker[lockernum].setreaderID('G'+str(ID)) # G for 'GoodReader'
return 0
self.numlocker = -1
incmad()
class BadReader(Reader):
'''Readers leaving their own belongings'''
def __init__(self): # Inherit the __init__() and parameter of Reader
Reader.__init__(self)
numlocker = -1 # Don't know why have to write this... But bugs if not
self.numlocker = numlocker
def chklocker(self,locker,ID): # The chklocker() function of child class
for lockernum in range(0,numlocker):
if locker[lockernum].chkempty():
inchappy()
locker[lockernum].setempty(False)
self.numlocker = lockernum
locker[lockernum].setreaderID('B'+str(ID)) # B for 'BadReader'
return 0
self.numlocker = -1
incmad()
#====================Paramters===================#
# Total number of readers
numtotreader = numgoodreader + numbadreader
# Hourly entrance number
hrnumreader = (numgoodreader+numbadreader)//hours
hrnumreaderres = (numgoodreader+numbadreader)%hours
# Initialize the parameters
locker = [Locker() for _ in range(numlocker)]
goodreader = [GoodReader() for _ in range(numgoodreader)]
badreader = [BadReader() for _ in range(numbadreader)]
# Target variable
happiness = 0
madness = 0
def inchappy():
'''Access and alter the variable 'happiness'.'''
global happiness
happiness += 1
def incmad():
'''Access and alter the variable 'madness'.'''
global madness
madness += 1
#=====================Function===================#
def readerenter(namelistpara, numreaderenterpara):
'''A certain reader enters.'''
numreaderenter = namelistpara[numreaderenterpara]
# Convert to the subscript of the reader
if numreaderenter < 0:
goodreader[-numreaderenter-1].chklocker(locker,-numreaderenter-1)
# Convert the negative values to the subscript of goodreader
else:
badreader[numreaderenter].chklocker(locker, numreaderenter)
#=======================Main=====================#
for day in range(0,simdays): # Simulate for each day
if day%emptyperiod == 0: # Empty the lockers periodically
for i in badreader: # Propell badreaders
i.leave(locker)
namelist = [] # Initialze namelist container
### Here, namelist combines goodreader and badreader. Negative values are
### for goodreader and vice versa. The subscript of goodreader is obtained by
### convertion: -numnamelist - 1.
for numnamelist in range(-numgoodreader, numbadreader):
# Construct original namelist
namelist.append(numnamelist)
random.shuffle(namelist) # Shuffle(): change the order of element randomly
for varhour in range(0, hours-1): # Simulate hour by hour
for numreaderenterori in range(varhour*hrnumreader, (varhour+1)*hrnumreader):
# Every hour except the last, an equal number of readers enter
readerenter(namelist, numreaderenterori)
for goodreaderleave in goodreader: # goodreader leave after one hour
goodreaderleave.leave(locker)
varhour = hours - 1 # The last opening hour
for numreaderenterori in range(varhour*hrnumreader, numtotreader):
# In the last hour, all unentered readers enters
readerenter(namelist, numreaderenterori)
for goodreaderleave in goodreader: # All goodreader leave
goodreaderleave.leave(locker)
#======================Output====================#
print('happiness:', happiness)
print('madness:', madness)
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