Markov Chain Simulation

Markov_Chain.jl

using Compat, Random, Distributions

# to set a markov chain, use a dictionary data structure like this.
example_set = Dict("lambda"=>19.5, "mu"=>1, "k"=>10, "max_na"=>500000)

# Uniform distribution
uniform_d = Uniform()

function Markov_Chain(paratmers)
    global uniform_d
    # initialize paratmers
    # queue size
    Q_size = 0
    # N_a is number of customer arrivals counted so far
    # N_b is number of blocked customers counted so far
    N_a, N_b = 0, 0
    lambda = paratmers["lambda"]
    mu = paratmers["mu"]
    k = paratmers["k"]
    max_na = paratmers["max_na"]
    rand_X = rand(uniform_d, max_na)
    for x in rand_X
        if x < lambda/(lambda+Q_size*mu)
            N_a = N_a + 1
            if Q_size == k
                N_b = N_b + 1
                #println("Blocking happens")
            else
                Q_size = Q_size + 1
            end
        else
            Q_size = Q_size - 1
        end
    end
    return N_b/N_a
end

test_case = Dict("lambda"=>19.5, "mu"=>1, "k"=>10, "max_na"=>100000000)

result_set = []
for i=1:10
    x = Markov_Chain(test_case)
    push!(result_set, x)
end

E_x = mean(result_set)
Var_x = var(result_set)
sigma = sqrt(Var_x)
Ur = 2.23*(sigma/sqrt(11))
lower_bound = E_x-Ur
upper_bound = E_x+Ur
println("Mean blocking probability:$(E_x)")
println("Confidence Interval 95%:($(lower_bound), $(upper_bound))\n")