DATA604_Discussion_Week_2

Dilip Ganesan

M/M/1 Problem

  1. For an M/M/1 queue with mean interarrival time of 1.25 minutes and mean service team 1 minute, find all five of Wq, W, Lq, L and p. For each, interpret in words. Be sure to state all your units, and the relevant time frame of operation.
# Step 1 : Calculate p

# Formula for p=lambda/c*sigma

# lambda=arrival rate(reciprocal of interarrival time)
lambda=1/1.25

# sigma=the service rate
sigma=1/1

# 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  4 3.2 5 0.8 4