#Forklift problem
lam=54/12  #Incoming Rate
mu=22/3  #Outgoing Rate

#Flow Rate Matrix
F=[[0 for i in range(28)] for j in range(28)]
F[0][0]=-lam
F[0][1]=mu
F[1][0]=lam
F[1][1]=-(lam+mu)
F[1][2]=2*mu
for k in [2..26]:
    F[k][k-1]=lam
    F[k][k]=-(lam+(2*mu))
    F[k][k+1]=2*mu

F[27][26]=lam
F[27][27]=-2*mu
F.append([1 for i in range(28)])

w=[0 for i in range(28)]
w.append(1)

F=Matrix(F)
w=vector(w)

steadystate=F.solve_right(w)
steadystate=[round(x,5) for x in steadystate]

table([[n,steadystate[n]] for n in range(28)],header_row=["State","Probability"])