DATA604_Home_Work_4

# Deterministic Distribution D has a constant value d, this can be represented as mean and standard # deviation

# mu = d
# sigma = 0

# Value of rho

# rho = lambda/mu 
# rho = lambda/d

# Formula for M/G/1 system (in this case general dist G will be deterministic dist D)

# Wq = lambda*(sigma^2 + 1/mu)/2(1-lambda/mu)

# Put the value of sigma = 0
# Wq = lambda/(2*d-2*lambda)


# Using Littles Law rest can be calculated.

# Lq = lambda*Wq = lambda*(lambda/2(d-lambda))

# W = Wq + E(S)

# L = lambda * W 
# L = lambda^2/2*(d-lambda) + lambda/d

# 1. From the above formulas we can conclude that constant service rate must greater than or equal to interarrival rate (d >= lambda)

# 2. For equal mean and Some variation of sigma i.e sigma > 0, the Wq would increase.

lambda = 1
d = 1/0.9

rho = lambda/d

Wq = lambda/(2*d-2*lambda)

Lq = lambda^2 / (2*d-2*lambda)

W = (lambda/(2*d-2*lambda)) + 1/d

L = (lambda^2/(2*d-2*lambda)) + lambda/d

# Final Result.
df= data.frame(Wq , Lq, W, rho, L)
df