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Queuing Analysis

Operations and Quality Management
Analysis of Waiting Lines
Professor Carter

Response time
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Why does response time even matter..
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to businesses you are familiar with? to you as a consumer?

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Why can’t firms just deliver products and provide services when you want them? What are the obstacles? How can firms overcome these obstacles? What does it take, how much does it cost and what are the benefits?

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Why response time matters
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What causes waiting
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Needs are transitory
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Emergency medical treatment Repair service (burst pipe, power outage, broken laptop) Sending a gift, payment or application to meet a deadline

Dice experiment simulates a laundry’s operations
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Time value of consumption
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A new winter coat in Feb. instead of late March Big -screen TV before vs. after the world cup

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Timely supply of goods and services can reduce costs for a firm
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A laundry wants to provide next day service Demand is random with loads per day between 1 and 6 Time required to process a load is random, with number processed per day between 1 and 6 What is the response time performance?

Reduced need for inventory Better matching of supply to demand Opportunity cost of lost sales

Simulation results See Dice simulation.xls
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Performance over 300 days
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t 0 1 2 3 4 5 6 7 8 9 10

Dt 3 4 2 6 2 4 6 1 1 6 1

Ct 3 2 1 4 2 1 6 2 6 1 4

Nt 0 2 3 5 5 8 8 7 2 7 4

35 30

#Unfinished Loads

Avg. demand = 3.5 loads/day Avg. capacity = 3.5 loads/day

6 days of work (21 loads)
25 20 15 10 5 0 1 26 51 76 101 126 151 Days 176 201 226 251 276 301

4 days of work (14 loads)

We have significant delays! Why?

2 days of work (7 loads)

Why queuing models?
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The queuing system
Servers Customer Arrivals Waiting Line Exit

Due to short-term, unpredictable (“statistical”) fluctuations in both demand and capacity, firms often need to provide excess capacity (“safety capacity”)...