You have been asked to continue a single server queueing theory analysis started by a temporary employee who is no longer with the company that employs you. Only one piece of paper with no explanation written by this employee has been given to you. It states that the probability of having to wait for service is 0.60 and that the average time in the system is 0.25 minutes.

Copy the following table into your answer book and fill in the corresponding numeric values. These values should be computed by making use of an algebraic approach (so without enumerating different values). Clearly explain the steps you take in arriving at your answer.

                                                                                                              (7 marks)

Factor	Value (4dp)
Traffic intensity
Average number of customers in the queue
Probability that there are three customers in the system

      (b)        For the single server simulation given below what is the average queue length? Show your working and give your answer to 4dp.

                                                                                                                                 (4 marks)

Interarrival time	Service time	Customer	Arrival time	Start of service	End of service
4	8	1	4	4	12
9	6	2	13	13	19
2	5	3	15	19	24
1	3	4	16	24	27
8	10	5	24	27	37
9	7	6	33	37	44
9	1	7	42	44	45
7	2	8	49	49	51

      (c)        The payoff table below shows for a company the final year end profits expected (£’000) from four possible choices (A, B, C and D) with respect to three possible scenarios (S1 to S3 respectively) for the forthcoming year.

	A	B	C	D
S1	17	3	-8	15
S2	-8	11	13	-3
S3	-6	-2	14	6

Here, for example, if the company makes choice B (and it can only choose one of A, B, C or D) and the scenario for the forthcoming year turns out to be S1 then it makes a profit of £3000. The company estimates that the probabilities associated with scenarios S1, S2 and S3 occurring are 0.40, 0.20 and 0.40 respectively.

Copy the following table into your answer book and fill in the choice that should be made under each criterion and the associated value.

Criteria	Choice	Associated value £’000 (2dp)
Optimistic
Conservative
Regret
Equally likely
EMV

Based on your analysis which choice from A, B, C or D would you recommend the company makes? Clearly state the single major reason for the choice that you are recommending