1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables). Management are interested in simulating the arrival process in order to decide whether to employ a new customers services representative.

(a) Use the internet or a text book to find an example of a congruential unit random number generator that is different to the one given in the lecture notes and lab exercises.

(b) Use your random number generator to explain why random numbers generated on a computer are called 'pseudo random numbers'.

(c) Use your random number generator to generate 3 unit random numbers. State what 'seed' is used and explain how this can be used to repeat simulation experiments.

(d) Assuming the memory less property and a starting time of 1pm, use your simulated unit random numbers above to generate the arrival times of the next 3 calls arriving at the centre.