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Introduction
An M/M/1 queue consists of a first-in-first-out (FIFO) buffer with packets arriving randomly according to a Poisson process. It also includes a processor, also known as server, used for the packets’ retrieval from the buffer at a specified service rate. Therefore, the model statistics’ collection requires node and project as the two major components. These two constituents also contribute in the running of simulating statistics results. In general, the M/M/1 queue requires packet arrival rate, packet size, and service capacity.
Objective
The objective of this lab experiment is to explore the node editor and to assess how it can be used for the creation of the M/M/1queue. It is also aimed at using the project editor for the collection and displaying of different types of stats. The simulation process will help in learning the ways to apply filters to the collected data. Furthermore, it will also demonstrate how the node and project editors work to build the M/M/1 queue and run a simulation. Later, the results will also be analyzed.
Packet Size
Service Capacity
Packet Arrival Rate
If the combined effect of the average packet arrival rate and the average packet size exceeds the service capacity, the queue size will grow to an indefinite extent.
Methods
Queuing in a system may occur in a number of cases. For instance, when customers in a restaurant want to buy meals and eat at the very place, they have to be in queues even in drive thru lanes or take-away lines. Another example in this regard is that of a bank wherein customers come for different purposes. However, due to the limited number of staff, every customer is required to wait for his turn.
In this case, however, we are concerned with the queuing in networks. Therefore, it is necessary for a designer to possess a clear understanding of the network while designing it. Here, the M/M/1 queue is described through a Poisson process controlling the arrival of packets into an infinite buffer. Hence, when a packet reaches the head of the buffer, the server processed it and sent it to its destination Fig1.1 shows the M/M/1 queue system.
When Node Editor is used in the process, its main job is to build a queue model using source, queue and sink and to link them together using packet stream (Fig 1.2). Thus, each of these components has different jobs as follows:
Source: Its job is to generate packets and determine its service rate given as packet per second.
Queue: It is known as the server or buffer.
Sink: It is used for the destruction of the generated packets by the source.
Packet Streams: They are used to facilitate the movement of packets between modules.
Result and Discussion
Once the process simulation of M/M/1 is completed, an issue may occur i.e. mean queue delay. In order to resolve this issue, an average filter can be selected. The effectiveness of the simulation is mandatory for accuracy and stability. Fig1.3 shows average queuing delay, whereas Fig1.4 shows time average of queue size. It is clear from the graph that the queue settles within 5 hours during simulation. Fig1.5 portrays time averaged queue size. This graph denotes that the time average does not exceed the acceptable limitation of 20 seconds.
Traffic intensity or queuing in a system (p) is defined as the arrival rate (λ) over the average service rate (µ)
p = λ/µ
In this M/M/1 queuing lab experiment, six measurements were carried out for calculating the traffic intensity or the queuing in a system (p). Later, the findings were plotted on a graph. Fig1.6 shows the delay time in queue and a range of queue utilization (0.4 - 0.9):
At arrival rate 9000 and average service rate 9600 = 9000/9600 = 0.9 at 15s of delay.
At arrival rate 9000 and service rate x and traffic intensity 0.8 at 4.00s of delay to achieve service rate x = 9000/0.8 = 11250.
At arrival rate 9000 and service rate x and traffic intensity 0.7 at 2.40s of delay to achieve service rate x = 9000/0.7 = 12857.
At arrival rate 9000 and service rate x and traffic intensity 0.6 at 1.50s of delay to achieve service rate x = 9000/0.6 = 15000.
At arrival rate 9000 and service rate x and traffic intensity 0.5 at 1.00s of delay to achieve service rate x = 9000/0.5 = 18000.
At arrival rate 9000 and service rate x and traffic intensity 0.4 at 0.65s of delay to achieve service rate x = 9000/0.4= 22500.
Conclusion
During the M/M/1 queuing system lab experiment performed according to Poisson process, the M/M/1 queuing system packets randomly arrive to the first-in-first-out (FIFO) buffer. In addition, the processor known as server restores packets form the buffer at a specific service data. Moreover, it is important to consider the Node and Project Editors when creating the queuing system model because of their major roles. They are used for the collection of statistics of the model and to run the simulating statistics result.
