DATA604_Discussion_Week_2

Dilip Ganesan

M/M/1 Problem

  1. M/M/1 queue with arrival rate lambda = 1 per minute and service rate mu = 1/0.9 per minute.
# Step 1 : Calculate p

# Formula for p=lambda/c*sigma

# lambda=arrival rate(reciprocal of interarrival time)
lambda=1

# sigma=the service rate
mu=1/0.9

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

# 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/mu

# 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 8.1 8.1 9 0.9 9