Question

The arrival rate of a customer at a service window of a cinema hall follows a probability distribution with a mean rate of 45 per hour. The service rate of the clerk follow a poison distribution with a mean of 60 per hour

1. Queue length
2. Queue
3. Traffic
4. Total time spent in the
5. Total time spent in the system
6. Find the probability of having 0 in the
7. Find the probability of having 4 in the system
8. The proportion of time the service facility is idle (in %age)

Answer 1

Data			Results
Arrival rate (l)	45		Average server utilization(r)	0.75
Service rate (m)	60		Average number of customers in the queue(Lq)	2.25
Number of servers	1		Average number of customers in the system(L)	3
			Average waiting time in the queue(Wq)	0.05
			Average time in the system(W)	0.066667
			Probability (% of time) system is empty (P0)	0.25
Probabilities
Number	Probability	Cumulative Probability
0	0.250000	0.250000
1	0.187500	0.437500
2	0.140625	0.578125
3	0.105469	0.683594
4	0.079102	0.762695
5	0.059326	0.822021
6	0.044495	0.866516
7	0.033371	0.899887
8	0.025028	0.924915
9	0.018771	0.943686
10	0.014078	0.957765
11	0.010559	0.968324
12	0.007919	0.976243
13	0.005939	0.982182
14	0.004454	0.986637
15	0.003341	0.989977
16	0.002506	0.992483
17	0.001879	0.994362
18	0.001409	0.995772
19	0.001057	0.996829
20	0.000793	0.997622