Queueing Theory - Application To Telephony

Application To Telephony

The public switched telephone network (PSTN) is designed to accommodate the offered traffic intensity with only a small loss. The performance of loss systems is quantified by their grade of service, driven by the assumption that if sufficient capacity is not available, the call is refused and lost. Alternatively, overflow systems make use of alternative routes to divert calls via different paths — even these systems have a finite traffic carrying capacity.

However, the use of queueing in PSTNs allows the systems to queue their customers' requests until free resources become available. This means that if traffic intensity levels exceed available capacity, customer's calls are not lost; customers instead wait until they can be served. This method is used in queueing customers for the next available operator.

A queueing discipline determines the manner in which the exchange handles calls from customers. It defines the way they will be served, the order in which they are served, and the way in which resources are divided among the customers. Here are details of four queueing 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.

Last in first out

This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first. Also known as a stack.

Processor sharing

Customers are served equally. Network capacity is shared between customers and they all effectively experience the same delay.

Priority

Customers with high priority are served first.

Queueing is handled by control processes within exchanges, which can be modelled using state equations. Queueing systems use a particular form of state equations known as a Markov chain that models the system in each state. Incoming traffic to these systems is modelled via a Poisson distribution and is subject to Erlang’s queueing theory assumptions viz.

• Pure-chance traffic – Call arrivals and departures are random and independent events.
• Statistical equilibrium – Probabilities within the system do not change.
• Full availability – All incoming traffic can be routed to any other customer within the network.
• Congestion is cleared as soon as servers are free.

Classic queueing theory involves complex calculations to determine waiting time, service time, server utilization and other metrics that are used to measure queueing performance.