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Teletraffic Queuing Theory This article is one of a group being considered for deletion in accordance with Wikipedia's deletion policy. Please see the policy discussion page of the votes for deletion list for details. This request is being discussed to form a consensus whether this is, or could be, an article appropriate for Wikipedia. If you feel deletion is not justified by Wikipedia deletion policy you may vote against its deletion. Please do not remove this notice or blank this article while the question is being considered. However, you are welcome to continue editing this article, especially if you can address the concerns of those who believe the article should be deleted. Should you do so, please remark on the policy discussion page regarding its improvement. Public Switched Telephone Networks (PSTNs) are generally designed to accommodate heavy traffic loads. They are designed as either a loss system or an overflow system. The performance of loss systems is primarily determined by their Grade of Service (GoS), and is driven by the assumption that if congestion is encountered in a circuit, the call is dropped 1. Overflow systems make use of alternative routes to divert calls via different paths; however even these systems have a finite or maximum traffic carrying capacity 1. The use of Queuing Theory in PSTNs allows loss systems to queue their users until any congestion has abated. This means that if traffic intensity levels exceed available capacity, subscriber’s calls are no longer dropped; they instead wait until they can be served 2. Queuing Discipline determines the manner in which the exchange handles subscribers 2. It defines the manner in which customers are served, the order in which they are served, and the way in which resources are divided between customers 3. There are three main Queuing Disciplines: - First In First Out – This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first 3.
- Last In First Out – This principle also serves customers one at a time, however it serves the customer with the shortest waiting time first 3.
- Processor Sharing – Customers are served equally. Network capacity is shared between subscribers and they all effectively experience the same delay 3.
Queuing is handled by control processes within exchanges, which can be modelled using State Equations 3. Queuing Systems utilise a particular form of state equations known as Markov Chains which model the system in each state 2. Traffic in these equations is modelled via a Poisson distribution and is subject to Erlang’s Queuing Theory Assumptions 1: - Pure-Chance Traffic – Call arrivals and departures are random and independent events 1.
- Statistical Equilibrium – Probabilities within the system do not change 1.
- Full Availability – All incoming traffic can be routed to any other subscriber within the network 1.
- Congestion is cleared as soon as servers are free 1.
A notation for describing Queues and their characteristics was developed by Kendall and can be viewed at 4. Classic queuing theory involves complex calculations to determine call waiting time, service time, server utilisation and many other calculations which are used to measure queuing performance 3. Classic Queuing Theory suffers from a number of disadvantages. The first and most obvious is that it is too mathematically restrictive for real-life modelling 5. The second reason is that heavily simplified uncertainty assumptions are made 5. These disadvantages require that a different approach be used in a number of queuing applications. The technique described in 5 examines the use of Simulation as an alternative to mathematical analysis of queues. It was found that the advantages of simulation directly counteract the disadvantages of classic queuing theory and that a combination of the two provides the best analytical method with is able to achieve the greatest accuracy. References 1 Flood, J.E. Telecommunications Switching, Traffic and Networks, Chapter 4: Telecommunications Traffic, New York: Prentice-Hall, 1998. 2 Bose S.J., Chapter 1 - An Introduction to Queuing Systems, Kluwer/Plenum Publishers, 2002. 3 Penttinen A., Chapter 8 – Queuing Systems, Lecture Notes: S-38.145 - Introduction to Teletraffic Theory, Helsinki University of Technology, Fall 1999. 4 Penttinen A., Kendall’s Notation for Queuing Models, Lecture Notes: S-38.145 - Introduction to Teletraffic Theory, Helsinki University of Technology, Fall 1999. 5 van Dijk N.M., To pool or not to pool? “the benefits of combining queuing and simulation”, Proceedings of the Winter Simulation Conference, 2002.
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