Simulation For Queuing Problems Using Random Numbers

1. Simulation of Queuing problems using Random numbers -- Renuka Narang

12. Solution Calculation of Basis of random allocation Inter arrival time Probability Cumulative Probability Basis of random allocation 3 0.1 0.1 0.0 -- 0.09 4 0.2 0.3 0.1 -- 0.29 5 0.5 0.8 0.3 -- 0.79 6 0.1 0.9 0.9 -- 0.89 7 0.1 1 0.9 -- 0.99 Service time Probability Cumulative Probability Basis of random allocation 3 0.3 0.3 0.0 -- 0.29 4 0.5 0.8 0.3 -- 0.79 5 0.1 0.9 0.8 -- 0.89 6 0.1 1 0.9 -- 0.99

13. Solution Customer Random Number Inter arrival time Random number Service time Time of arrival Service starts at Service ends at Waiting customer Idle time Inter arrival time 3 4 5 6 7 Service time 3 4 5 6 Basis of random allocation 0.0 -- 0.09 0.1 -- 0.29 0.3 -- 0.79 0.9 -- 0.89 0.9 -- 0.99 Basis of random allocation 0.0 -- 0.29 0.3 -- 0.79 0.8 -- 0.89 0.9 -- 0.99 1 25 4 92 6 9.04 9.04 9.10 -- 4 2 19 4 41 4 9.08 9.10 9.14 2 -- 3 64 5 66 4 9.13 9.14 9.18 1 -- 4 82 6 07 3 9.19 9.19 9.22 -- 1 5 62 5 44 4 9.24 9.24 9.28 -- 2 9.29 9.29 9.32 -- 1 9.33 9.33 9.37 -- 1 9.40 9.40 9.44 -- 3 9.44 9.44 9.49 -- -- 9.48 9.49 9.53 1 -- Total time 53 mins Total waiting time 4 mins Total idle time 12 mins 6 74 5 29 3 7 29 4 52 4 8 92 7 43 4 9 24 4 87 5 10 23 4 55 4