DATA604_Home_Work_5

Dilip Ganesan

M/M/1 Problem 4.10.2 Steady State

  1. M/M/1 queue with arrival rate lambda = 120 per hour and service rate mu = 190 per hour and c=1.
# Step 1 : Calculate p

# Formula for p=lambda/c*sigma

# lambda=arrival rate(reciprocal of interarrival time)
lambda=120

# sigma=the service rate
sigma=190

# Since the value of c=1 excluding in the formula.
p=lambda/sigma

# Using Little's Law we can calculate rest of values.

# L=p/(1-p)

L=p/(1-p)

# W = L/lambda

W= L/lambda

# W = Wq + E(s)

Es = 1/sigma

# W = Wq + Es

Wq = W - Es

# Lq = lambda * Wq

Lq = lambda * Wq

# Final Result.
df= data.frame(Wq , Lq, W, p, L)
df
##            Wq       Lq          W         p        L
## 1 0.009022556 1.082707 0.01428571 0.6315789 1.714286