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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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Contact BMGI at: infosa@bmgi.com info.eu@bmgi.com

Thank you!

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