Projects:2014s2-76 Teletraffic Modelling and Analysis of the New Britannia Roundabout

2015-06-05T00:34:43Z

A1617207: /* aim */

The objective of the project is to use teletraffic theory to construct a teletraffic model for the new Britannia roundabout. The project will also serve as an independent study by evaluating the existing roundabout’s efficacy against its previous design.
== Project Overview ==
=== Aim ===
The objective of the project is to use teletraffic theory to construct a teletraffic model for the new Britannia roundabout. It will attempt to replicate the actual road traffic flow under a set of scenarios for analysis. The project will also serve as an independent study by evaluating the existing roundabout’s efficacy against its previous design.

===Motivation===
The Britannia intersection is identified by the Department of Planning, Transport and Infrastructure (DPTI) in South Australia as an essential route [1]. It forms a part of the inner city route of Adelaide where an estimation of 52,000 vehicles pass through the intersection daily [2]. The previous configuration of the intersection consists of a single dual lane roundabout serving five major roads as shown in Figure.

[[File:Original Configuration of Britannia Intersection.jpg|600px|thumb|left|Original Configuration of Britannia Intersection]]

For years, commuters have complained about the excessive delays they have experienced during the morning and afternoon peak hour traffic [4]. It was also the worst non-signalized intersection within South Australia for collisions as there were a total of 308 recorded crashes between 2008 and 2012 [5].

There were several ideas to improve the intersection which suggestions include replacing the roundabout with traffic lights, underpass, flyovers or creation of roads [6]. However all of them were rejected due to either cost, environmental or political issues.

In 2013, the state government approved a $3.2 million upgrade to the Britannia intersection where it is replaced with an innovative dual roundabout shown in Figure 2. Extensive modelling suggested the new configuration will reduce crashes by up to 29% and a 10% to 15% increase in efficiency during the afternoon peak hours is expected [1].

Figure 2: New configuration of intersection [6]

The results generated from the project will act as further evidence to support or debunk the efficacy of the new Britannia roundabout. It will be of interest to the stakeholders of the Britannia upgrade and traffic engineers or researchers working on intersection solutions.

===Previous Studies===
A final year project group modelled the single roundabout using teletraffic theory for their final year project in 2006 [8]. Their approach regarded the roundabout as a server accepting the queuing cars from each access road, and sending them to their intended exit roads. The group came to a conclusion that the roundabout was more efficient than an intersection with traffic lights under all traffic conditions addressed.
Our group will be reviewing the previous results in 2006 with our results of the dual roundabout for comparison of the two roundabouts.

==Background==
Queuing theory is the mathematical method of analyzing congestion and delays of waiting lines [9]. Models are constructed in queuing theory to predict queue lengths and waiting times. It has been applied to the design of call centers, routing of the traffic on the internet, shipping orders efficiently from warehouse, improving road traffic flow etc. Its roots originated in 1909 when the Danish engineer Agner Krarup Erlang created queuing models to describe the Copenhagen Telephone Exchange that he was working for [10]. The queuing system has a basic model of a process shown in Figure 3 whereby the customers arrive and wait in line for their turn to be serviced. They will leave the system after they have been serviced. It is a very useful model and serves as a basis to analyse complex queueing networks such as the new dual roundabout at the Britannia intersection.
[[File:Basic Queuing System.jpg|600px|Basic Queuing System]]

==Analysis Methods==
===Queuing Theory===
*Characteristics of Queuing System
A queuing system can be defined by six characteristics:

#Arrival process.
#Service process.
#Number of servers in parallel.
#System capacity.
#Population constraints.
#Queuing discipline.

The Kendall’s Notation is the standard used to describe a queuing system and the format is (A/S/N/Sc/Pc/Qd) where the abbreviations represent the six traits listed earlier.

The first characteristic describes the type of arrival process and the common standard abbreviations:
#M = Interarrival times are independent, identically distributed (IID) and exponentially distributed. (Memoryless/Poisson/Markovian).
#D = Interarrival times are IID and deterministic (fixed or constant).
#G = Interarrival times are IID and controlled by a generic distribution.

The second characteristic describes the type ofthe service times. They share the same abbreviations as the arrival process:

#M = Service times are IID and exponentially distributed.
#D = Service times are IID and deterministic.
#G = Service times are IID and controlled by a generic distribution.

The third characteristic is the quantity of parallel servers in the system. Servers are considered parallel if they provide the same type of service and a customer only has to go through one of them to complete their service.
The fourth characteristic is the maximum capacity that the system can hold; this includes the customers in the queue and the customers in the server.
The fifth characteristic provides the size of the population where the customers are drawn from.

The sixth characteristic is the type of queue discipline. The common ones are:
#FCFS = First come, first served; the first customer waiting in line will get served first.
#LCFS = Last come, first served; the last customer waiting in line will get serverd first.
#SIRO = Service in random order; a customer is randomly drawn from the queue to enter service.

Generally only the first three characteristics are defined for majority of the queuing systems. By default, it is assumed that a system has unlimited capacity, unlimited population size and possesses a FCFS service discipline unless otherwise stated.

*Burke’s Theorem
Burke’s Theorem states that for any M/M/1, M/M/m or M/M/∞ queue under steady state conditions that possess Poisson arrival rates, then the departure process is also a Poisson process [12]. It also explains the number of customers in the queue at a specific time is independent of the departure process prior to the specific time.

*Queuing Network
The queuing system shown in section 2 (Figure 3) relates to a single server or parallel server system where a customer’s entire service time is spent with a single server. In reality there are many cases where the customer’s service is not completed until the customer has been served by more than one server.
Queuing network models can be classified into three groups: open queuing networks, closed queuing networks and mixed queuing networks [13]. They function in the same manner as a single server/parallel server system. The difference is at the completion of one service, the customer has the option to proceed to another queue to be served by another server. This project will cover the open queuing network portion.
In open queuing networks, the customer who has finished a service can either move to another queue to be serviced or depart from the system.
[[File:Basic Open Queuing Network System.jpg|600px|Basic Open Queuing Network System]]
Using the Burke’s Theorem in section 3.1.2, the splitting and combining of Poisson processes in an open queuing network simple means that the arrival process will follow the Poisson distribution to each queue.

*Jackson Network
A Jackson network is essentially an arbitrary open network of M/M/m queues that makes use of the Jackson theorem to have a product-form solution [13].
The Jackson theorem states that as long as the arrival rate at each queue allows for equilibrium, it is possible to obtain the joint state distribution of the queuing network.
The internal arrival rate can be found by assuming the system is at steady state conditions:
[[File:internal arrival rate.jpg]]
where j = 1,..., K and Λj is the external Poisson arrival rate. For example there are three queues feeding to internal queue 1. The first queue is an external queue with an arrival rate of 0.1 that only goes to internal queue 1. The second queue is an external queue with an arrival rate of 0.08 that has a 50% chance of going to internal queue 1. The third queue is an external queue with an arrival rate of 0.15 that has a 10% chance of going to internal queue 1. The internal arrival rate of this queue is 0.155.
The implications of Jackson Theorem are:
*Once the possible destinations have been worked out, all queues in the system can assessed individually.
*The connections joining the internal queues will behave like a Poisson process, even if there is a feedback in the system.

===Analysis of Roads Leading to Britannia Intersection===
*Naming conventions for lanes and Britannia Layout
*Queues with Potential Destinations
*Queue Destination Probabilities
*Maximum Queue Length
*Queues Considered as Poisson Process
===Analysis of Roundabouts===
*Characteristics of Roundabouts
*Segmentation of roundabout
*Entry and Exit Rules
==Implementation==
===MATLAB===
*Queuing process
*Roundabout
*Output Files for Results and Simulation
===Demonstration Models===
*Design of demonstration models
*Input source files
===Simulation and Performance of Software===
*Quadstone Paramics
*Netbeans IDE
*MATLAB
==Results==
===Waiting Times===
===Queue Lengths===
===Throughput===
===Comparison with DPTI Reported Results===
===Other Performance Improvements===
==Conclusion==
With a good project management and team strategy, the team is able to achieve the main objectives of constructing a teletraffic model of the new Britannia intersection and evaluate its efficacy against the previous model. The design of the queuing network model is able to produce most of the characteristics of queue formation and fair service. The software also allows for new modules to be integrated to the system in future. The results of the simulations has shown that the new upgrade to the Britannia intersection generally has enhanced the performance in terms of reduced waiting time, shorter queue lengths and increase in throughput.
==Further work==
In order to model the queuing system as accurately as possible, the addition of another queuing process can be considered in the form of public buses. Their arrival are based on their bus schedule, hence their arrivals are not random. There are many complications in handling this as heavier vehicles require a longer stopping distance and this can affect the entry rules in the roundabout. It should be noted that in the movement survey, commercial vehicles only account for 1.5% to 4% of the traffic on each leg. Therefore the results may not differ much.
Another consideration will be to research on how to handle choked roundabouts. The group went for a site survey and noticed the cars in the internal queues often exceed the allowed queue length and spill over to the roundabout. The current system assumes the roundabout servers are always stepping with no stops. The spill over was mitigated by preventing the job heading to a particular internal queue from entering the roundabout if the quantity of cars in that internal queue and the cars in the roundabout of the same destination exceed the maximum queue length.
Another scenario will be to find out if it is feasible to handle the queues and the servers when an accident occurs inside the roundabout.
Research could be done to investigate the possibility of cars travelling at different speeds in the roundabouts instead of one fixed speed. In the real life the cars are travelling above the assumed speed of 18 km/h and they do not have uniform speed across all cars.
==Team Management==
===Tasks and Interim Roles Allocation===

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Projects:2014s2-76 Teletraffic Modelling and Analysis of the New Britannia Roundabout