Queueing Theory & Computer Networking
The Internet was first established in the late 1960s by a group of academics whose work was underwritten by the US Department of Defense . Their work would not have been possible without queueing theory, which helped them to determine the optimum number of servers and the size of the data packets required to make the systems work for everyday use.
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History
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Queueing theory was invented in the 1940s by A.K. Erlang to study data over telephone networks. It was applied to the theory of computer networking in the Leonard Kleinrock in the 1950s, building on the work of by James Jackson, who studied queuing theory in reference to multiple nodes.
Significance
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Queuing theory is important to computer networking because it can precisely predict the length of time a computer will need to wait for the data it requests. This goes beyond simply measuring the amount of time for a data transfer, but takes into account the statistical variability of the requests of all computers over the network: sometimes lots of people want to transfer data, and sometime no one does. When the requests pile up, there is a queue (or a line), and engineers must predict the exact length of the queue.
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Function
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Queuing theory only requires three pieces of information to predict the length of the queue: the variability of the requests, the time it takes to process these requests, and the number of queues. In the case of networking, that means the variability of which computers request information, the amount of time the servers take to process the request, and the number of servers.
Considerations
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As the number of users on the Internet increases, the variability decreases. This allows engineers to use servers more efficiently to handle the data. Also, Kleinrock discovered that queues would decrease if the length of the requests decreased, leading scientists to break data into packets. Packets actually increase the time to transfer large files, but overall it helps the Internet because of the many small messages that travel over it.
Other Uses
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Queuing theory is used in retail situations to predict how long customers will wait in line and is useful in determining the optimal number of cashiers, parking lot attendants, or call center employees, as well as how to engineer the line itself. Psychologists have embellished this field by investigating how people perceive time differently, depending on whether they wait in groups, wait after initially being processed, wait if the wait is perceived as unfair, etc.
Queueing theory is also used in manufacturing to determine how long it will take to create products when the availability of materials is variable.
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