Transportation Engineering
CETRANSPO
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Queuing Theory in Traffic Engineering: Models and Applications, Slides of Transportation Engineering
An overview of queuing theory with a focus on traffic engineering applications. It covers various queuing models, including d/d/1, m/d/1, and m/m/1, explaining their underlying assumptions and performance equations. The document also discusses real-life causes of queue generation in different transportation modes and provides examples of how to compute average queue length, waiting time, and time spent in the system. It is useful for understanding and estimating highway performance measures related to vehicle delay and traffic queue lengths. The document also explores time-dependent deterministic queues and their solutions, offering a comprehensive look at queuing models in traffic scenarios. The document also includes examples of how to compute average queue length, waiting time, and time spent in the system.
Typology: Slides
2023/2024
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Transportation Engineering
CETRANSPO
MODULE 4
Queuing Model
Theory and
Analysis
Introduction
Queuing
Queueing is the study of traffic behavior
near a certain section where demand
exceeds available capacity
Cumulative Input-Output Diagram
(Newell Curve)
Traffic Queue
Importance of Queuing Theory
- Retail
- Telecommunications
- Transportation
- Finance and banking
- Computing
- Logistics
- Project management
Understanding Queuing Theory
- Arrival, which refers to the arrival of customers who
are first in line.
- Capacity, which refers to the system’s limit with
regards to the number of customers in line.
- Service, which refers to service points where
service occurs.
- Departure or output, which refers to customers
leaving the system after receiving service.
Kendall’s Notation
- A for the arrival process.
- S for the mathematical distribution of the service time.
- c for the number of servers.
- K for the capacity of the queue (if not unlimited).
- N for the number of possible customers (if not infinite).
- D for the queuing discipline (first-in, first-out by default).
Queuing models
- Single Channel, Single Phase A single-channel, single-phase business has only one server. As soon as a customer is attended to, they receive full service.
- Single Channel, Multi Phase A single-channel, multi-phase business has one server and a multi-step servicing process.
- Multi Channel, Single Phase A multi-channel, single-phase business has several servers and a one- step servicing process.
- Multi Channel, Multi Phase A multi-channel, multi-phase business has several servers and a multi- step servicing process.