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Lunchtime Webinar Series: Introduction to Queuing Analysis
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Queuing Analysis
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An Airline Check-in Queuing System
Multiple channel,
Single phase
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A Simple Queuing System
Queuing systems are evaluated using 4 tendencies:
• The time in the queue
• The time in the system
• The queue length
• The number of “jobs” in the system
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Useful Distributions for Queuing Analysis
Poisson Distribution Customer Arrivals per Unit time
Exponential Distribution Customer Service Times
Time
0 1 2 3 4 5 6 7 8 9 10 11 12
Customers per Time Unit
0
0.05
0.1
0.15
0.2
0.25
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A Simple Queuing System
Queuing systems are evaluated using 4 tendencies:
• The time in the queue
• The time in the system
• The queue length
• The number of “jobs” in the system
The critical system measurements:
• The Mean Arrival Rate
• The Mean Service Rate
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Queuing Analysis - Terms
Arrival Rate (Ri)
Processing Rate (Rp)
Average Number in Queue (Ii)
Average Wait in Queue (Ti)
Average Time in System (T) Average Number in System (I)
Number of resource units
C(2)
C(k)
C(1)
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Process Capacity Rp
Rp = Processing Rate = Process Capacity = (c*a*L)/Tp
• c = number of resource units • a = proportion of availability 0 ≤ a ≤ 1 • L = number of "units" per service event (batch load) • Tp = Average service time per event
For a single server, Rp = c/Tp since:
a = 1 L = 1
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Example
At a small domestic airline economy class check-in area, there are 7 individuals checking passengers in:
• The customer call mean arrival rate (Ri) is 87 passengers/hour • The average time to check a passenger (Tp) in is 4 minutes.
1. Describe the current situation in terms of the Queue Lengths and
Queue Times.
Let the Customer Loss Ratio: Mean time spent by a customer waiting for service
Mean time spent by a customer being served R =
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Example Results
Metric Formulae Current State
Arrival Rate ( / Hr) Ri 87
Service Time per event (min) Tp 4
Service Rate (events / Hr) 15
# Servers c 7
Process Rate per server / Hr Rp = c/Tp 105
Average Utilization = Ri / Rp 0.829
Queue Length* Ii 2.8
Time in Queue (min) Ti = Ii / Rp 1.6
Total in System I = Ii + c 8.5
Time in System (min) T = Ti + Tp 5.6
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Example
At a small domestic airline economy class check-in area, there are 7 individuals checking passengers in.
• The customer call mean arrival rate (Ri) is 87 passengers/hour • The average time to check a passenger in is 4 minutes.
1. What would be the impact of adding one more person (server) to
the check-in counter?
Let the Customer Loss Ratio, R =
Mean time spent by a customer waiting for service
Mean time spent by a customer being served
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Example Results
Metric Formulae Current State Future State
Arrival Rate ( / Hr) Ri 87 87
Service Time per event (min) Tp 4 4
Service Rate (events / Hr) 15 15
# Servers c 7 8
Process Rate per server / Hr Rp = c/Tp 105 120
Average Utilization = Ri / Rp 0.829 0.725
Queue Length* Ii 2.8 0.9
Time in Queue (min) Ti = Ii / Rp 1.6 0.5
Total in System I = Ii + c 8.5 6.7
Time in System (min) T = Ti + Tp 5.6 4.5
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• Queues are not nice – if not managed properly, they give rise to an unsatisfactory customer experience
• There are measures available to determine performance characteristics to assist us with queuing analysis to improve performance
Summary & Conclusion
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• There are several queuing systems, but the most common is the “One Queue, Multiple Servers” queuing system
• There are formulae available to analyse the performance of the queuing systems.
Summary & Conclusion
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• More complex systems can be broken down into multiples of the base system
• The complex queuing system performance is the lowest base system’s performance
Summary & Conclusion (Cont.)
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• Complex queuing systems may require customised modelling and simulation
• There are other ways we can evaluate queuing system performance such as using Excel based analytics or the modelling and simulation functionality within iGrafx
Summary & Conclusion (Cont.)
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