Apowersoft PARTA Quest in this site of the paper. Question A1 (25 marks) A dental hospital has two dental nurses and one dentist. The dentist has specialist knowledge and skills for dealing with patients who require specialist treatments (e.g. fillings, root canals). If the dentist is busy and a patient requires a specialist treatment they must wait until the dentist becomes free. Patients with general dental problems can see any of the staff, but the dentist will only attend to a general patient if both dental nurses are busy. Customers wait in the waiting room if they cannot be seen immediately. The hospital opens at 9am and closes at 5pm each day. The time between general patients arriving at the dental hospital follows a negative exponential distribution with mean of 0.2 hours, and the time between special treatment patients arriving at the dental hospital follows a negative exponential distribution with mean of 0.5 hours. The service time of a general patient is described by a uniform distribution between 0.5 and 1 hours, and the service time of a specialist treatment patient can be described by a uniform distribution between 1 and 2 hours. a) How can random numbers can be used to model the variability in this situation? Specify the formulae you would use. (25% of marks) b) Using discrete event simulation, simulate the system up to the time of departure of the 1st patient requiring general treatment. How long does each customer wait to be seen by one of the dental staff? Do all your calculations to 3 decimal places. Use 4-digit random numbers from the formulae sheet. For each process, use the following number stream: General patient inter-arrival times (5th row): 6524 3011 7654 4608 8595 5921 2692 8923 2024 2108... Special Treatment patient inter-arrival times (7th row): 7493 5070 3768 5243 5010 3662 3924 6180 0823 9804 General patient service times (1st row): 1869 8478 8578 4023 9576 2595 5664 6042 0073 3181 Special Treatment patient service times (3rd row): 1139 9393 4279 6670 6454 5597 4593 5746 5139 0827 (40% of marks) c) The staff at the dental hospital are interested in improving patient experience. On the outcome of a survey, long waiting times appear to be the largest cause of poor customer experiences. Firstly, explain how simulation can be used to investigate the waiting time of customers in the current system. Secondly, suggest a simple change that could be made to the system to improve waiting times, and how simulation could be used to investigate the impact of this change. (25% of marks) d) Would it be appropriate to use a warm up period for this system? Justify your answer. (10% of marks) turn quer for Dart B Apowersoft Screen Capture Pro Random Number Table 18 69 84 78 85 90 42 07 45 05 11 39 93 93 42 04 02 90 28 57 65 24 30 11 76 88 63 38 47 22 74 93 50 70 37 59 92 61 13 70 95 66 35 30 81 58 06 82 95 26 90 56 88 94 82 50 92 45 85 29 20 35 55 39 34 16 68 04 81 03 70 85 24 45 64 36 30 41 26 27 11 95 80 73 74 76 24 89 95 31 18 51 46 37 70 39 17 80 58 79 62 20 18 35 83 32 79 82 90 36 17 90 70 55 04 41 72 55 75 33 99 09 48 09 27 78 40 23 95 76 09 10 69 83 27 79 66 70 64 54 73 45 00 38 10 54 46 08 85 95 37 45 12 47 25 68 52 43 50 10 70 79 38 76 86 02 03 39 76 82 00 91 28 99 34 19 68 54 54 98 60 06 35 25 38 20 96 86 55 69 26 88 36 81 77 03 96 99 32 33 32 90 51 74 28 39 94 06 80 61 71 81 97 34 73 29 79 68 10 70 57 36 78 29 29 22 82 81 06 52 87 53 33 10 99 39 65 20 06 36 63 42 62 06 73 86 56 90 23 89 25 95 56 64 60 70 64 00 92 80 55 97 45 93 57 08 36 56 79 91 59 21 26 92 89 45 53 05 79 92 36 62 39 24 61 82 30 60 12 34 26 91 97 90 90 75 52 06 56 10 00 71 90 39 38 93 57 56 68 37 41 42 41 54 52 16 19 06 50 93 14 81 41 83 41 70 73 67 08 14 79 09 79 20 20 04 99 15 94 06 04 57 74 48 89 54 92 20 18 75 00 27 64 37 42 80 52 18 36 66 48 15 67 66 25 51 84 09 33 02 77 72 78 94 95 42 00 73 31 81 27 65 93 61 90 46 51 39 08 27 92 64 23 92 21 23 20 24 21 08 85 46 48 38 26 80 08 23 98 04 76 19 15 88 10 28 78 51 47 95 00 78 27 19 79 62 92 18 35 37 80 61 81 40 99. 17 55 95 12 49 81 30 91 40 08 05 94 10 63 13 48 31 32 52 84 67 50 82 79 87 23 04 16 34 38 84 53 50 25 95 47 98 33 96 34 64 89 01 73 58 78 59 55 69 58 62 09 92 71 29 55 64 72 35 89 33 23 23 54 43