Polling places¶

Due: Friday, November 9, 4pm

You may work alone or in a pair on this assignment.

Every two years, many people around the country wait in long lines to vote due, in part, to inadequate provisioning of voting booths. In this assignment you will write code to simulate the flow of voters through precincts. The information generated by your simulator could be used by an election official as a crude lower bound to help determine the number of voting booths needed at a precinct.

We will view this problem as an instance of the more general problem of simulating an $M$/$M$/$N$ queue, where:

the first $M$ indicates that arrivals (voters arriving at the polls) obey a Markov process;
the second $M$ indicates that the service times obey a Markov process (the amount of time a voter takes to complete a ballot); and finally
the $N$ indicates that there are $N$ servers (the number of voting booths).

We will tell you how to structure your implementation at a high level, but you will be responsible for the design details.

Getting started¶

See these start-up instructions if you intend to work alone.

See these start-up instructions if you intend to work with the same partner as in a previous assignment.

See these start-up instructions if you intend to work in a NEW pair.

The pa4 directory includes a file named simulate.py, which you will modify, a file named util.py that contains a few useful functions, a directory named data, which contains precint configuration files (described below), and a series of tests contained in files test_avg_wait_time.py, test_simulate_election_day.py and test_find_number_of_booths.py.

Please put all of your code for this assignment in simulate.py. Do not add extra files for the required classes.

Precinct Configuration¶

The configuration for a precinct is specified using a dictionary containing this information:

The name of the precinct (name)
number of voters assigned to the precinct (num_voters),
number of hours the polls are open (hours_open),
The number of voting booths (num_booths)
The voter distribution (voter_distribution).

For example:

{'name': 'Downtown',
 'num_voters': 5,
 'hours_open': 1,
 'num_booths': 1,
 'voter_distribution': {'type': 'poisson',
                        'arrival_rate': 0.11,
                        'voting_duration_rate': 0.1}

Notice how the voter_distribution field contains another dictionary containing these fields:

The type of distribution (type). In this assignment, we will only deal with one type of distribution: poisson
The rate at which voters arrive (arrival_rate) and the rate at which voters complete their voting (voting_duration_rate). The significance of these rates is explained later.

Information about precincts is stored in a JSON file that contains a dictionary with two keys: precincts, containing a list of precinct configurations as specified above, and seed, containing a random seed. Similar to PA1, the random seed will be used to ensure that a simulation involving randomness produces the same result (which will allow us to test whether your code produces the expected results). We recommend reviewing PA1 (and how it used random seeds) if you’re unsure of how random seeds are used in the context of running a simulation.

We have provided a function, load_precincts in util.py that takes the name of a JSON precincts file and returns two values: a list of precinct configurations (as specified above) and the random seed.

This function is already called from the code we provide for you, so you should not make any calls to load_precincts in the code you’ll add to simulate.py. However, it can be a useful function when testing your code. In particular, you should take a moment to familiarize yourself with the data stored in these JSON files, and how to access each value once you’ve loaded the file with load_precincts. We suggest you start by looking at data/config-single-precinct-0.json, and loading that file from IPython:

In [1]: import util

In [2]: precincts, seed = util.load_precincts("data/config-single-precinct-0.json")

In [3]: precincts
Out[3]:
[{'hours_open': 1,
  'name': 'Downtown',
  'num_booths': 1,
  'num_voters': 5,
  'voter_distribution': {'arrival_rate': 0.11,
   'type': 'poisson',
   'voting_duration_rate': 0.1}}]

In [4]: seed
Out[4]: 1468604453

In [5]: len(precincts)
Out[5]: 1

In [6]: p = precincts[0]

In [7]: p["num_voters"]
Out[7]: 5

In [8]: p["voter_distribution"]["arrival_rate"]
Out[8]: 0.11

Representing Voters¶

In this assignment you will need to model voters using a Voter class. This class must include the time the voter arrives at the polls, voting duration, that is, the amount of time the voter takes to vote, and the time the voter is assigned to a voting booth (aka, the start time). For simplicity, we will model time as a floating point number, representing the number of minutes since the polls opened. So, if we say a voter arrived at the polls at time 60.5, that means they arrived an hour and thirty seconds after the polls opened.

While not strictly necessary, we found it convenient for debugging purposes to store the time the voter leaves the voting booth (i.e., the departure time) as well.

The start time for a voter, which is not available at construction time, should be initialized to None when the voter object is constructed. This value should be reset to the correct value when the voter is assigned to a voting booth. Similarly, voters’ departure times cannot be determined until we know their start times.

Your implementation must include at a minimum: a constructor and public attributes named arrival_time, voting_duration, and start_time. Our utility function for printing voters, described below, relies on the existence of these attributes. Please note that you are welcome to use properties instead of attributes for some or all of these required attributes, but are not required to do so.

This class is straightforward. It merely serves as a way to encapsulate information about a voter. Our implementation is roughly 30 lines, although it is possible to come up with implementations that are much shorter than that.

Please note, the voter generator class, described next, is the only class that is allowed to call the voter constructor.

Generating voters¶

Your implementation must include a VoterGenerator class for generating voters. You may ask yourself why this merits its own class, instead of simply constructing the voter objects in the precinct class we describe below. One reason for this is that it allows us to define a class for generating voters according to some random distribution, and then create multiple instances with different parameters to that random distribution. For example, if the time it takes a voter to vote followed a normal distribution, we could create a voter generator with mean = 5 minutes, stdev = 2 minutes, and another voter generator with mean = 15 minutes, stdev = 5 minutes. We could then use those two instances to explore the behaviour of voters according to those two distributions (both normal, but each with different parameters).

We will revisit the usefulness of having a voter generator class once we’ve discussed how to represent precincts and their booths; if this section feels too abstract or unclear, you may want to re-read it once we’ve discussed precincts and voting booths.

For now, let’s focus on discussing how the voters are generated. Both the arrival time and the voting duration will follow a Poisson process. From Wikipedia: a Poisson process, named after the French mathematician Simeon-Denis Poisson (1781-1840), is a stochastic process in which the time to the next event is independent of past events. We can use the following fact to generate a voter sample: if the number of arrivals in a given time interval [0,t] follows the Poisson distribution, with mean $t*\lambda$, then the gap between arrivals times follows the exponential distribution with rate parameter $\lambda$.

So, our voter generator must keep track of time. We will assume that we keep track of time in minutes starting at time zero. To generate a voter, you will need to generate an arrival time and a voting duration. To generate the arrival time of the next voter, you will draw an inter-arrival time ($gap$) from the exponential distribution using the specified arrival rate as $\lambda$ and add it to the current time ($t$). You’ll then move time forward by updating the time from $t$ to $t+gap$.

For example, let’s say we create a voter generator (the exact parameters of the exponential distribution are not relevant to this simple example). We generate a voter, and the random number generator returns 5.7 for that voter’s gap. Since this is the first voter we generate, their arrival time will be 5.7, and we advance the voter generator’s current time from 0 to 5.7. We then generate another voter, and the random number generator returns 2.4 for the voter’s gap. This means that this second voter arrives 2.4 minutes after the previous voter, so the second voter’s arrival time will be 8.1 (5.7 + 2.4) and we advance the voter generator’s current time to 8.1.

When we generate a voter, we also need to assign a voting duration to that voter. You will draw the voter’s voting duration from the exponential distribution using the specified voting duration rate as $\lambda$.

For testing purposes, it is important that you draw the gap and the voting duration in the same order as our code. To reduce the likelihood that the testing process fails simply because the values were drawn in the wrong order, we have provided a function, gen_poisson_voter_parameters, in util.py that takes the arrival rate and the voting duration rate as arguments and returns a pair of floats to use for the gap and voting duration (in that order).

Your implementation should, at the very least, have a constructor and a next method that returns the next voter.

Printing a voter sample

We have provided a function named print_voters in util.py that takes a list of Voter instances and an optional file name. This function will either print a representation of the voters to screen or to a file, depending on whether a filename is specified.

Testing

The code for generating the voter sample should be fairly simple (our implementation is only 15 lines long, not including comments). That said, it is important that you generate the voters correctly for the rest of your code to work. We strongly urge you to test your voter generator class carefully before you move on to the next step.

When we were working on our code, we wrote a short function (8 lines) called generate_and_print to test whether we were generating voters correctly. This is a standalone function that is not part of any of the classes you are designing.

The function takes the name of a precincts configuration file and then:

Loads the configuration using util.load_precincts
Creates a VoterGenerator object with the arrival rate and voting duration rate specified for the first precinct in the file
Generates voters one by one, placing them in a list.
Calls util.print_voters with the list.

While writing this function is not required (and will not be graded), you may want to consider writing it to aid in your testing.

To help with testing your voter generator class, we have provided two sets of sample parameters. The first set, (see data/config-single-precinct-0.json), includes the following:

number of voters in the sample: 5
hours open: 1
arrival rate: 0.11 (corresponds to mean time between voters of approximately 9 minutes)
voting duration rate: 0.1 (corresponds to a mean voting duration of 10 minutes)
seed for random number generator: 1468604453

and corresponds to a sample in which all the voters arrive before the polls close.

Here is the result of calling our sample testing function with data/config-single-precinct-0.json:

In [4]: generate_and_print("data/config-single-precinct-0.json")
Arrival Time   Voting Duration   Start Time    Departure Time
78         2.11             None              None

01         5.13             None              None

27         2.68             None              None

89         1.10             None              None

48        10.08             None              None

The second set, data/config-single-precinct-1.json, is the same except the arrival rate is set to 0.04, which corresponds to a mean gap of 25 minutes:

In [5]: generate_and_print("data/config-single-precinct-1.json")
Arrival Time   Voting Duration   Start Time    Departure Time
64         2.11             None              None

28         5.13             None              None

49         2.68             None              None

94         1.10             None              None

08        10.08             None              None

Notice how, in the above set, only the first two voters would arrive before the polls close. However, the voter generator is unconcerned with this. This leads to a nice separation of concerns, where we can test the generation of voters separate from the more complex logic of determining if and when a voter can start voting, which will reside in a separate precinct class that will use the voter generator class. Your results may be different from the results above if you do not set the random seed before you start generating voters.

Task 0: Implement the Voter and VoterGenerator classes¶

Before moving on to the rest of the assignment, you should implement a Voter class and a VoterGenerator class as described above. We do not provide tests for either, so it is up to you to ensure that these classes are correctly implemented before moving on to the rest of the assignment. We strongly encourage you to test your VoterGenerator class in the manner described above, even if you only do so informally by writing a small testing function like the one we used.

Task 1: Simulate election day for one precinct¶

In this task, you will be simulating an election for a single precinct. You will do this by implementing a Precinct class that stores information about a precinct, and which can simulate an election day on that precinct.

Modeling Precincts¶

Cities are broken up into voting precincts, each of which has a number of voting booths. Your Precinct class will model a precinct with a specified number of voting booths and must include, at least, one public simulate method that runs a simulation of an election day on that precinct. The exact parameters and return value(s) of this method are up to you; later on, we describe how we will be testing your implementation, and that may provide some hints on what parameters and return value(s) to use in your simulation method.

The simulation itself will be similar to the M/D/1 queue example from class. In the M/D/1 example, we have a single server, such as a toll booth, that serves a queue of clients, such as cars, that arrive with a specified distribution and have a fixed service time. In this assignment, your simulation will need to simulate multiple servers (voting booths) and variable service times (voting durations), but the structure of your simulation will be similar.

There are three main differences, though. First, instead of generating arrival times for the clients directly in the simulation code, you will be using a VoterGenerator object, and get voters from the generator as needed. Second, you should implement private methods in the Precinct class to determine whether a voting booth is available and, if not, when a booth will become available. This will be necessary to determine when a given voter will finish voting (since it depends on when they can access a booth). Third, you will need to limit the number of booths in use to be no more than the number of booths assigned to the precinct.

Don’t queue voters!

You may be tempted to create a queue of Voter objects. Don’t! This is a common pitfall when designing this type of simulation. When you generate a Voter using the VoterGenerator, it could be the case that all the voting booths are occupied at the time the voter arrives. Instead of placing the voter in a queue, we will instead use a priority queue (described below) to model the voting booths. This will allow us to efficiently answer the question “When will a voting booth become available in this precinct?”. If we can easily answer that question, then we will know the voting start time of any new Voter.

In this simulation, you will generate voters until you reach one of the simulation’s stopping conditions. In this case, we need to stop the simulation once there are no more voters who can vote. This can happen in two situations: (1) you have generated the maximum number of the voters specified for the precinct, or (2) you generate a voter who arrives after closing time. In the second case, the late voter should be discarded and no further voters should be drawn from the sample. We will refer to voters who arrive before the polls close as valid.

The Precinct and the VoterGenerator

Notice how the stopping condition depends on information that is “owned” by different classes: the Precinct is where we should store the number of hours that the precinct is open, but the VoterGenerator is where we should store the maximum number of voters to generate (otherwise, a VoterGenerator object would not know when to stop generating voters). So, it may be convenient for one object to have the other as an attribute, so we can access all the necessary information during the simulation. Recalling the “A good rule of thumb” section of the lab, which of these phrases makes more sense?

A Precinct has a VoterGenerator
A VoterGenerator has a Precinct

Alternatively, let’s use “precinct simulator” and “voter generator” in the above phrases:

A precinct simulator has a voter generator
A voter generator has a precinct simulator

Alternatively, if we want to simulate a precinct with different VoterGenerator objects, we could think about simply passing a VoterGenerator object as a parameter to our simulation method.

Example¶

Let’s walk through an example. The file data/config-single-precinct-2.json contains the following precinct:

{
 "name": "Little Rodentia",
 "hours_open": 1,
 "num_voters": 10,
 "num_booths": 2,
 "voter_distribution": {
                         "type": "poisson",
                         "voting_duration_rate": 0.1,
                         "arrival_rate": 0.16666666666666666
                       }
}

And the seed 1438018944.

The precinct has 10 voters who arrive at the precinct once every 6 minutes on average and take 10 minutes on average to vote.

When working through an example, it can be useful to call the generate_and_print function we suggested above, so we can see what voters would be generated in this simulation:

In [6]: generate_and_print("data/config-single-precinct-2.json")
Arrival Time   Voting Duration   Start Time    Departure Time
29         5.39             None              None

39         5.74             None              None

68        24.45             None              None

78         6.08             None              None

76        39.64             None              None

52         5.79             None              None

33        16.65             None              None

23         3.07             None              None

75         5.24             None              None

04        15.43             None              None

Let’s consider what happens when we simulate this precinct using two voting booths. The first call to util.gen_poisson_voter_parameters generates (3.29, 5.39) as the gap and voting duration, which means that our first voter arrives at 3.29, enters a voting booth immediately at time 3.29, and finishes voting at 8.69 (3.29 + 5.39). (All times have been rounded to two digits for clarity.)

The second call to util.gen_poisson_voter_parameters yields (9.10, 5.74), which means that the second voter arrives at time 12.39 (3.29 + 9.10). This second voter starts voting immediately, because a booth is open, and finishes voting at time 18.13 (12.39 + 5.74).

The third voter arrives at time 12.68 (gap: 0.29) and has a voting duration of 24.45 minutes. Since the first voter departed at 8.69, this voter can start voting immediately, and finishes voting at 37.13.

The fourth voter arrives at 15.78 (gap: 3.10) and has a voting duration of 6.08 minutes. Both booths are occupied when the fourth voter arrives, so this voter must wait until a booth becomes free, which happens when the second voter finishes at time 18.13. Thus, the fourth voter’s start time will be 18.13 and their finish time will be 24.21. Notice that this voter finishes before the third voter.

The fifth voter arrives at time 19.76 (gap: 3.99) and will not start voting until the fourth voter finishes at time 24.21. Notice that the third voter is still voting when the fifth voter starts!

And so on.

All ten voters arrive before the polls close and so all ten get to vote even though the last two will not start voting until after the polls have closed at time 60 (remember that we specify time in minutes, but the precinct dictionary specified the number of hours)

Here’s the output of our simulation:

Arrival Time   Voting Duration   Start Time    Departure Time
29         5.39             3.29              8.69

39         5.74            12.39             18.13

68        24.45            12.68             37.13

78         6.08            18.13             24.21

76        39.64            24.21             63.85

52         5.79            37.13             42.92

33        16.65            42.92             59.57

23         3.07            59.57             62.64

75         5.24            62.64             67.88

04        15.43            63.85             79.28

Modelling voting booths within a precinct¶

You will need a data structure to keep track of the voters who are currently occupying voting booths and to determine which voter will depart next. Your implementation should use the PriorityQueue class the from the python queue library for this purpose. A minimum priority queue is a data structure that includes operations for (1) adding items along with their priorities to the queue, (2) removing the item with the lowest priority from the queue, and (3) determining whether the queue is empty. The PriorityQueue library also allows you to specify an upper bound on the number of items allowed to be in the queue at the same time and provides a method for determining whether the queue is full. Please look through the queue library for details on how to use the this class.

For this assignment, the priorities will be the voters’ departure times.

Take into account that your implementation should not need a voting booth class. There could certainly be models that require modelling the voting booth as its own class but, in the model we are assuming, it is enough to have a precinct class that uses a priority queue to model the state of the voting booths.

Furthermore, your simulation method should not need to access the priority queue directly. Instead, you should implement private methods that encapsulate operations like adding a voter to a booth, or removing the next voter who will finish voting.

Blocking on get and put

You should be careful with one specific aspect of priority queues: the get method is a blocking method, meaning that if you call get (to extract a value from the priority queue) and the queue has no values, the operation will block (or hang) until a value is available.

In this assignment, you should never call get on an empty queue so, if your code seems to mysteriously hang, the first thing you should check is whether you’re calling get on an empty queue somewhere in your code. Alternatively, you can call get like this:

my_queue.get(block=False)

This way, get will raise an Empty exception if you try to extract a value from an empty queue (immediately alerting you to the fact that there may be an error somewhere in your code, since you should never be calling get on an empty queue in this assignment)

Similarly, if you call put on a queue that is full, your code will also block. However, if you call put like this:

my_queue.put(value, block=False)

Then putting a value into a full queue will raise a Full exception.

The `simulate_election_day` function¶

Since we don’t know the exact design you will choose (and since each student can come up with equally valid designs), you must also complete the function simulate_election_day in simulate.py so it will invoke the simulation method in your Precinct implementation. This is the function that our tests will be calling so, in a sense, it acts as an intermediary between the tests and your Precinct class (this is what is often referred to as glue code).

This function takes a list of precinct dictionaries and a random seed, and returns a dictionary that maps precinct names to a list of the voters who voted in that precinct. For now, you can assume the list of precincts will contain a single precinct (we will add support for multiple precints in the next task)

The Voter objects returned by this function should have their start_time attribute filled in. Furthermore, for a given precinct, our tests expects the list of voters to be sorted by the voters’ arrival time; since your VoterGenerator should generate voters in the order in which they arrive, producing a list of voters sorted by arrival time should not require any additional steps to sort the list. If you do find that you need to sort the list explicitly, it is likely that your solution is headed in the wrong direction; ask on Piazza if that is the case.

Take into account that the bulk of your implementation must be in your Precinct class (alongside your Voter and VoterGenerator classes). The simulate_election_day function itself should only be about 10 lines long, and all of the actual simulation code should reside inside your Precinct class. If you find yourself writing substantially more than 10 lines in the simulate_election_day function, it is likely that the design of your class needs some improvement. Please come to office hours or ask on Piazza so we can provide some preliminary feedback on your class design.

The random seed

Remember that the precincts file includes a seed value (returned by load_precincts). This seed must be passed to simulate_election_day (using the seed paramter) and you must use the random.seed(seed) function to set the seed inside simulate_election_day. The seed only needs to be set once per each precinct you simulate (since we’re only simulating one precints, that means the seed only gets set once; this will change in Task 2).

Remember that PA1 includes a longer discussion of random seeds, and their significance in testing simulations.

Testing¶

We have provided several automated tests that will test your implementation of the simulate_election_day function. To run only the tests that assume a single precinct, run the following from the Linux command-line:

$ py.test -xv -k single test_simulate_election_day.py

(Recall that we use $ to indicate the Linux command-line prompt. You should not include it when you run this command.)

However, remember that the first approach to testing and debugging your code should not rely exclusively on the tests. If you run the tests, and it is not immediately clear what the issue is, you should manually run your simulation code either from IPython or by using a command we describe below. These two approaches will generally produce error messages that may be easier to interpret and debug.

From IPython, first load the simulate.py and util.py modules as follows:

In [1]: %load_ext autoreload

In [2]: %autoreload 2

In [3]: import util

In [4]: import simulate

Next, you will need to use load_precincts to load a configuration file. We have provided six configuration files (named config-single-precinct-N.json, where N is a number) that you can use to test your implementation. For example, you can load config-single-precinct-0.json like this:

In [5]: precincts, seed = util.load_precincts("data/config-single-precinct-0.json")

And now you are ready to call simulate_election_day:

In [6]: voters = simulate.simulate_election_day(precincts, seed)

To easily inspect the values of the voters, you can use the print_voters function provided in the util module:

In [7]: util.print_voters(voters["Downtown"])
Arrival Time   Voting Duration   Start Time    Departure Time
78         2.11             6.78              8.89

01         5.13             8.89             14.02

27         2.68            25.27             27.94

89         1.10            27.94             29.04

48        10.08            33.48             43.56

If you’d like to manually verify whether the values are correct, each configuration file has a corresponding CSV file with the expected values (take into account that these are the files the automated tests use; if you find that your implementation seems to produce correct values, you may want to switch to running the automated tests).

We also provide a main function in simulate.py that allows you to run simulate.py from the command-line. If you run simulate.py with just the name of a configuration file, it will print a summary of the simulation results. For example:

$ python3 simulate.py data/config-single-precinct-0.json

PRECINCT 'Downtown'
- 5 voters voted.
- Polls closed at 60.0 and last voter departed at 43.56.
- Avg wait time: 0.59

You can use the --print-voters options to, instead, print all the voters:

$ python3 simulate.py data/config-single-precinct-0.json --print-voters

PRECINCT 'Downtown'
Arrival Time   Voting Duration   Start Time    Departure Time
      6.78         2.11             6.78              8.89

      7.01         5.13             8.89             14.02

     25.27         2.68            25.27             27.94

     26.89         1.10            27.94             29.04

     33.48        10.08            33.48             43.56

Task 2: Simulating multiple precincts¶

The precinct configuration files we have used up to this point contain only a single precinct. However, the file format allows for multiple precincts to be specified in the same file. For example, the config-multiple-precincts-1.json file specifies two identical precincts, except for the number of booths:

{
 "name": "Little Rodentia (1 booth)",
 "hours_open": 1,
 "num_voters": 10,
 "num_booths": 1,
 "voter_distribution": {
                         "type": "poisson",
                         "voting_duration_rate": 0.1,
                         "arrival_rate": 0.16666666666666666
                       }
}

{
 "name": "Little Rodentia (2 booths)",
 "hours_open": 1,
 "num_voters": 10,
 "num_booths": 2,
 "voter_distribution": {
                         "type": "poisson",
                         "voting_duration_rate": 0.1,
                         "arrival_rate": 0.16666666666666666
                       }
}

You must modify simulate_election_day so that it will simulate all the precincts specified in the file, in the same order in which they are listed. The return value of the function will be the same as before: a dictionary mapping precinct names to lists of voters. However, your dictionary will now have more than one key in it.

If you designed your classes properly, this will require adding 3-4 lines of code to simulate_election_day (in our own implementation, adding support for multiple precincts required adding just a single line of code to simulate_election_day). The main thing you need to watch out for is that you must make sure to create a new voter generator object for each precinct. You must also make sure to reset the random seed to the given value before simulating each precinct.

If you find that adding support for multiple precincts requires substantially more than 3-4 lines of code, it is likely that your class design needs improvement. Please go to office hours or ask on Piazza so you can get some feedback on your class design.

If you make the modifications correctly, you can test this functionality from IPython or from the command-line simply by using one of the configuration files with multiple precincts. For example, for the configuration file shown above:

$ python3 simulate.py data/config-multiple-precincts-1.json

PRECINCT 'Little Rodentia (1 booth)'
- 10 voters voted.
- Polls closed at 60.0 and last voter departed at 134.48.
- Avg wait time: 46.43

PRECINCT 'Little Rodentia (2 booths)'
- 10 voters voted.
- Polls closed at 60.0 and last voter departed at 79.28.
- Avg wait time: 15.00

Notice how the results make sense intuitively: with more booths, it is possible to accommodate new voters sooner, which means waiting times will go down.

You can also run the automated tests that use multiple precincts like this:

$ py.test -xv -k multiple test_simulate_election_day.py

Task 3: Finding the average waiting time of a precinct¶

At this point, we have the ability to simulate precincts under a variety of parameters. As we saw above, an interesting parameter to tweak is the number of booths, since it has a direct effect on the average waiting time of the voters.

In this task, you will implement a function that, given a single precinct and a number of booths, computes the average waiting time when simulating that precinct with that number of booths:

def find_avg_wait_time(precinct, num_booths, ntrials, initial_seed=0):

Where:

precinct is a precinct dictionary
num_booths is the number of booths to use in the simulation. Notice that this will override whatever value is specified in the precinct dictionary. However do not modify the num_booths field of the precinct dictionary.
ntrials is a number of trials (this is explained below)
initial_seed is an initial seed (also explained below)

Given a single simulation of a precinct, computing the average waiting time of the voters is not difficult. In fact, if you look at the code we provide(see the cmd function in simulate.py), you’ll find some code to do just that! However, as with any simulation, it is unreasonable to accept the result of a single simulation (or “trial”). So, instead you will simulate the precinct ntrials times, compute the average wait time for each trial, sort the resulting average wait times, and return the median value (which, for simplicity, we will define simply as element ntrials//2 in the sorted list of average wait times).

In this task, you will set the random seed to initial_seed before you run the first trial. Then, before any subsequent trial, you will increment the seed by one and set the random seed to be that value.

To test your implementation of the function, you can call the function from IPython. For example:

In [1]: %load_ext autoreload

In [2]: %autoreload 2

In [3]: import util

In [4]: import simulate

In [5]: precincts, seed = util.load_precincts("data/config-single-precinct-3.json")

In [6]: p = precincts[0]

In [7]: simulate.find_avg_wait_time(p, num_booths=1, ntrials=20, initial_seed=seed)
Out[7]: 2203.0502079782727

In [8]: simulate.find_avg_wait_time(p, num_booths=8, ntrials=20, initial_seed=seed)
Out[8]: 4.630351652014112

You can also run the automated tests for this function like this:

$ py.test -xv -k avg

Task 4: Finding the optimal number of booths¶

At this point, we have all the necessary pieces to answer the following question: “Given a target waiting time $W$, how many booths does the precinct need to ensure that the average waiting time is less that $W$?”.

You will write the following function to answer this question:

def find_number_of_booths(precinct, target_wait_time, max_num_booths, ntrials, seed=0):

Where:

precinct is a precinct dictionary
target_wait_time is $W$ as defined above.
max_num_booths is the maximum number of booths the precinct is willing to have.
ntrials is the number of trials to run when finding the average waiting time of a precinct.
seed is a random seed.

Your function will do a simple linear search: you will first simulate the precinct with one booth, and check whether the average waiting time of the voters (as produced by find_avg_wait_time from Task 3) is strictly below target_wait_time. If it isn’t, you will simulate the precinct with two booths, and check the average waiting time, and so on up to max_num_booths or until you find a number of booths that achieves an average waiting time less than target_wait_time. Take into account that it could also be the case that the provided target_wait_time is infeasible with a number of booths less than or equal to max_num_booths.

So, the result of this search with be a tuple with two values: the optimal number of booths, and the average waiting time with that number of booths. If the provided target waiting time is infeasible, return (0,None).

To test your implementation of the function, you can call the function from IPython. For example:

In [1]: %load_ext autoreload

In [2]: %autoreload 2

In [3]: import util

In [4]: import simulate

In [5]: precincts, seed = util.load_precincts("data/config-single-precinct-3.json")

In [6]: p = precincts[0]

In [7]: simulate.find_number_of_booths(p, ntrials=20, target_wait_time=10, max_num_booths=10, seed=seed)
Out[7]: (8, 4.630351652014112)

In [8]: simulate.find_number_of_booths(p, ntrials=20, target_wait_time=10, max_num_booths=5, seed=seed)
Out[8]: (0, None)

You can also run the function from the command-line by using the --target-wait-time and --max-num-booths options:

$ python3 simulate.py data/config-single-precinct-3.json --max-num-booths 10 --target-wait-time 10
Precinct 'Sahara Square' can achieve average waiting time of 4.63 with 8 booths

$ python3 simulate.py data/config-single-precinct-3.json --max-num-booths 5 --target-wait-time 10
The target wait time (10.00) is infeasible in precinct 'Sahara Square' with 5 or less booths

Note: The command-line tool sets the value of ntrials to 20.

And, finally, you can run the automated tests for this function like this:

$ py.test -xv -k find

Grading¶

Programming assignments will be graded according to a general rubric. Specifically, we will assign points for completeness, correctness, design, and style. (For more details on the categories, see our PA Rubric page.)

The exact weights for each category will vary from one assignment to another. For this assignment, the weights will be:

Completeness: 50%
Correctness: 10%
Design: 30%
Style: 10%

Design is an important part of this assignment, because you have to design the voter generator class, the voter class, and the precinct class. There are a few things we will be looking out for in your design:

The only purpose of the voter generator class is to generate voters. If any simulation code is included inside the voter generator, that is a sign of a bad design.
Similarly, the voter generator is the only class that is allowed to construct voter objects. Creating voter objects anywhere else typically denotes a bad design.
This assignment does not require implementing a voting booth class. If you do, you are likely overthinking how to implement a precinct.
Your simulate_election_day function (Tasks 1+2), find_avg_wait_time function (Task 3), and find_number_of_booths function (Task 4) should be fairly short and straightforward, with absolutely no simulation logic in them (which should, instead, be in your precinct class). If your classes are poorly designed, then these functions will tend to be long and convoluted.

You must include header comments in all the methods you implement except getters/setters and properties. You do not need to include a docstring for a class (but it certainly doesn’t hurt to do so).

Obtaining your test score¶

Like previous assignments, you can obtain your test score by running py.test followed by ../common/grader.py.

Continuous Integration¶

Continuous Integration (CI) is available for this assignment. For more details, please see our Continuous Integration page. We strongly encourage you to use CI in this and subsequent assignments.

Submission¶

See these submission instructions if you are working alone.

See these submission instructions if you are working in the same pair as for PA #2 or PA #3.

See these submission instructions if you are working in a NEW pair.