e calculated [10]. Calculation of the queuing (pictured)6 probability and average waiting times are outside the scope of this book, and generally complex to calculate. On-line tools (e.g. http://www.math.vu.nl/~koole/ccmath/ErlangC/index.php) can be used to calculate the desired performance parameters of a packet-switched system. Example 8.2 A router in a packet-switched system receives 360 000 packets every hour. Each packet takes on average 10 ms to be processed. The router has two servers to process the received packets. What is the probability that a packet has to wait? What percentage of packets wait more than 10 ms? Answer The probability that a packet has to wait is 33.3%. The percentage of packets that wait more than 10 ms is 12.3%. It should be noted that the Erlang-C formula assumes the behaviour of incoming packet traffic and processing time to be modelled by exponential probability distribution. In practice this is not a realistic assumption and more complex behaviour models have been developed to 6Alasdair McLellan (own work) [CC BY-SA 3.0 (https://commons.wikimedia.org/wiki/File%3AVolcano_causes queue_at_Bergen_Station.jpg)]. Packetised Data Communications characterise packet traffic and processing. These do not lend themselves easily to closed-form formulas, and therefore the performances of complex networks are evaluated using computer simulations, for example OPNET [11]. Call Centre Application The Erlang-C formula has found an application in calculating the number of operators at call centres. The principle behind the calculation of the number of operators is the same: how long it takes to serve one customer, how many customers call every hour, and how many operators there must be to provide a certain quality of service. Example 8.3 Assume 200 customers call the Origin Energy help line every hour, and that each call lasts 5 min. How many operators are required to ensure no-one waits more than 1 min? How many operators are required SO only 10% of customers wait more than 1 min? Answer The number 