Solutions. Note, because landing and take-off arrivals are not staggered, all taking-off aeroplanes wait for 2 minutes before entering the runway.
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1 Chapter 2 Solutions E2.1 Time aeroplane arrival Taking-off aeroplane arrival On runway (L - landed, T - taken-off) (L) (T) (L) (T) (L) (T) (L) (T) Total 5 5 L - 4, T - 4 Note, because landing and take-off arrivals are not staggered, all taking-off aeroplanes wait for 2 minutes before entering the runway. E2.2a Airport Runway Simulation: B-Events Event Type Change in state B1 Arrival aeroplane arrives and enters landing B2 Arrival Taking-off aeroplane arrives and enters takeoff B3 Finish activity Aeroplane clears runway and outputs to world (increment take-off/landing count by 1) Future events to schedule B1 B2 1
2 Airport Runway Simulation: C-Events Event Type Condition Change in state C1 Start activity Aeroplane in landing Aeroplane landing, and runway is idle runway in use C2 Start activity Aeroplane in take-off Aeroplane taking-off, and runway is idle runway in use Future events to schedule B3 B3 Note: priority of landing over take-off is implied by ordering of C-events. E2.2b Airport Runway Simulation: Clock = 0 (Initialise Simulation) Runway Empty Empty Idle B1 4 B2 4 Taken-off 0 Airport Runway Simulation: Clock = 4 Runway B L1 T1 Idle C Empty T1 L1 B3 6 B1 8 B2 8 Taken-off 0 Airport Runway Simulation: Clock = 6 Runway B Empty T1 Idle C Empty Empty T1 B1 8 B2 8 B3 8 2
3 Landed 1 Taken-off 0 Airport Runway Simulation: Clock = 8 Runway B L2 T2 Idle C Empty T2 L2 B3 10 B1 12 B2 12 Landed 1 Airport Runway Simulation: Clock = 10 Runway B Empty T2 Idle C Empty Empty T2 B1 12 B2 12 B3 12 Landed 2 Airport Runway Simulation: Clock = 12 Runway B L3 T3 Idle C Empty T3 L3 B3 14 B1 16 B2 16 Landed 2 Taken-off 2 Airport Runway Simulation: Clock = 14 3
4 Runway B Empty T3 Idle C Empty Empty T3 B1 16 B2 16 B3 16 Landed 3 Taken-off 2 Airport Runway Simulation: Clock = 16 Runway B L4 T4 Idle C Empty T4 L4 B3 18 B1 20 B2 20 Landed 3 Taken-off 3 Airport Runway Simulation: Clock = 18 Runway B Empty T4 Idle C Empty Empty T4 B1 20 B2 20 B3 20 Landed 4 Taken-off 3 Airport Runway Simulation: Clock = 20 Runway B L5 T5 Idle C Empty T5 L5 Event Time B3 22 B1 24 4
5 B2 24 Landed 4 Taken-off 4 E2.3a Airport Runway Simulation: B-Events Event Type Change in state B1 Arrival aeroplane arrives and enters landing. Sample aeroplane type: small (S) or large (L). B2 Arrival Taking-off aeroplane arrives and enters takeoff. Sample aeroplane type: small (S) or large (L). B3 Finish activity Aeroplane clears runway and outputs to world (increment take-off/landing count by 1) Future events to schedule B1 B2 Airport Runway Simulation: C-Events Event Type Condition Change in state C1 Start activity Aeroplane in landing Aeroplane landing, and runway is idle runway in use C2 Start activity Aeroplane in take-off Aeroplane taking-off, and runway is idle runway in use Future events to schedule B3 B3 E2.3b Sampling Inter-Arrival Times for Sample range (minutes) Random numbers Sample RN/ RN/ RN/ RN/100 Sample first random number to obtain range and then a second random number (RN) to determine actual inter-arrival time within the range. Sampled Inter-Arrival Times: Random numbers taken from first line of Table 2.14 (Chapter 2). First random number Inter-arrival time range Second random number Inter-arrival time 5
6 Sampled Inter-Arrival Times: Taking-Off Random numbers taken from sixth line of Table 2.14 (Chapter 2). First random number Inter-arrival time Second random range number Inter-arrival time Sampling Aeroplane Type Random numbers Aeroplane type Large Small Sampled Aeroplane Types Random numbers taken from eleventh and sixteenth line of Table 2.14 (Chapter 2). Random number aeroplanes Random number Taking-off aeroplanes 27 Large 43 Small 24 Large 28 Large 31 Small 43 Small 05 Large 18 Large 15 Large 66 Small Note: separate streams (lines) of random numbers are used for landing and taking-off aeroplanes (see section 8.3.2). E2.3c 6
7 Simulation run for minutes with random arrivals and runway times. Airport Runway Simulation: Clock = 0 (Initialise Simulation) Runway Empty Empty Idle B B Taken-off 0 Airport Runway Simulation: Clock = 3.44 Runway B Empty T1 (S) Idle C Empty Empty T1 (S) B = 4.94 B B = 7.34 Taken-off 0 Airport Runway Simulation: Clock = 4.94 Runway B Empty T1 (S) Idle C Empty Empty Idle B B Airport Runway Simulation: Clock = 5.43 Runway B L1 (L) Empty Idle C Empty Empty L1 (L) 7
8 B B = 7.64 B = 7.93 Airport Runway Simulation: Clock = 7.34 Runway B Empty T2 (L) L1 (L) C Empty T2 (L) L1 (L) B B B = Airport Runway Simulation: Clock = 7.64 Runway B L2 (L) T2 (L) L1 (L) C L2 (L) T2 (L) L1 (L) B B = B Airport Runway Simulation: Clock = 7.93 Runway B L2 (L) T2 (L) Empty C Empty T2 (L) L2 (L) Event Time B =
9 B B Landed 1 Airport Runway Simulation: Clock = Runway B Empty T2 (L) Empty C Empty Empty T2 (L) B B B = Landed 2 Airport Runway Simulation: Clock = Runway B L3 (S) Empty T2 (L) C L3 (S) Empty T2 (L) B B B = Landed 2 Airport Runway Simulation: Clock = Runway B L3 (S) T3 (S) T2 (L) C L3 (S) T3 (S) T2 (L) B B = B
10 Landed 2 10
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