A solution to bank simulation exercise.
The solution is a haskell stack project. Assuming you have stack installed, you can execute it by running
git clone [email protected]:jhrcek/bank-simulation.git
cd bank-simulation
stack run$ stack run
Yellow customers only: what are the average and maximum customer waiting times?
sample size = 10, average waiting time = 1.48 s, maximum waiting time = 9.83 s
sample size = 100, average waiting time = 0.59 s, maximum waiting time = 12.34 s
sample size = 1000, average waiting time = 0.49 s, maximum waiting time = 22.54 s
sample size = 10000, average waiting time = 0.43 s, maximum waiting time = 29.66 s
Red customers only: what are the average and maximum queue lengths in-front of the teller?
sample size = 10, average queue length = 1.48, maximum queue length = 5
sample size = 100, average queue length = 0.51, maximum queue length = 5
sample size = 1000, average queue length = 0.46, maximum queue length = 5
sample size = 10000, average queue length = 0.44, maximum queue length = 7
Which type of customer gives the gives the closest value between the average and maximum customer waiting times?
sample size = 10, The difference was minimal for Yellow customers: 8.35 s
sample size = 100, The difference was minimal for Yellow customers: 11.74 s
sample size = 1000, The difference was minimal for Yellow customers: 22.05 s
sample size = 10000, The difference was minimal for Yellow customers: 29.23 s
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The following image represents my understanding of the situation we're simulating.
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The function from the assignment modelling customer arrival is Cummulative distribution function, so we can use Inverse transform sampling to generate random arrival times. That is, starting from the function modelling arrival time of customers, we can invert it to get a function from interval [0,1] to arrival times. Applying that inverse function to a number sampled uniformly from interval [0,1] we get a random arrival time (as time delta from previous arrival in seconds). This is represented by
arrivalDeltain the code. -
I'm using monad MonadRandom to generate simulation entities (Customers). This allows for random data to be generated purely using evalRand, so particular simulations could potentially be reproduced by providing the same random generator seed
StdGen. -
The average queue lenght is calculated as weighted average, using "Time the queue had length X" as weight.
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