Wilfrid Laurier University BU 247:BU275: Business Decision Models – Lecture 9 (W5-1)| L9 Simulation I_prelecture | 2026 Update

•BU275: Business Decision
Models – Lecture 9 (W5-1)



Instructor – Xinyuan Felix
Zhang
Winter 2026

,2
Course
• Practice problems: up to queueing; see related slides for M/M/S
systems; formula sheet; more exercises (MyLS folder)

• Assignment 1: email me if need help with group formation;
simulation this week

• Midterm (Feb 13): More exercises, sample midterm, review session

• Early Feedback Form

• Supply chain case challenge

• Sapphire Program (student initiative supporting autistic students, in
other files)

,3
Today’s lecture

Queueing
• Recap: M/M/1 formulae & Cost Analysis

• Examples: Cost Analysis and Utilization

Computer Simulation
• Intro to Simulation

• Monte Carlo: Random Variable to Random Variates

• Examples with Excel

, Recap: Little’s Law & M/M/1 Queuing System
1
• Average Measures: L = L_q + L_s, W = W_q +
m
l l
• Utilization: ρ = 𝒔 m and system is stable if ρ = m < 1
• Little’s Law: L=l W or Lq= lWq

• M/M/1 Queuing System (stable):

• Probability of n customers in the system: l l l
E.g., P_0 =𝟏 − , P_1 = (𝟏 − )
m m m
l
• Average # of customers in the system: L = Prob of more than 1 people in the system
m -l l l l
= 1 – P_0 – P_1 = 1 - 𝟏 − - (𝟏 − )
• Average waiting time in the system: W = 1 /(µ - λ) m m m
or W = L/ λ
• Average # of customers in queue: Lq = λ2 /[µ(µ - λ)] E.g., A help desk gets 2 request/hour,
and the agent can process 5/hour.
or Lq = λWq = L – λ/ µ
2 2 2∗2 4
• Average waiting time in queue: Wq = λ /[µ(µ - λ)] 𝐿=
5−2
=
3
𝐿𝑄 =
5∗3
=
15

or Wq = Lq/ λ = W – (1/ µ) 𝟏 𝟏
𝑊= = hours 𝝀 𝟐
𝝁−𝝀 𝟑 Wq = = hours
𝝁(𝝁−𝝀) 𝟏𝟓