Question

At a one-man barber shop, the customers arrive following Poisson process at an average rate of 5 per hour and they are served according to exponential distribution with an average service rate of 10 minutes. Assuming that only 5 seats are available for waiting customers, find the average time a customers, find the average time a customer spends in the system.​

Answer 1

Answer:

Which type of queuing system is likely to form in front of two counters in a small

railway ticketing centre (one for enquiry and the other for ticket booking) with

Poisson arrival and Exponential Service?

i. One M/M/2

ii. Two M/M/2

iii. One M/M/1

iv. Two M/M/1

2. Under M/D/1 model, average number of customers in the system is given by

i.

ii.

iii.

iv.

3. In a small barber shop, only one customer can get hair cut while another

customer can wait in a chair. Any other arriving customer has to wait outside as

there is only one chair available. The customers arrive randomly at 6 per hour.

The service is exponential and takes 6 minutes on the average. Find the

probability that an arriving customer will have to wait outside.

i. 36 %

ii. 40 %

iii. 60 %

iv. 64 %

4. An overhead crane of ABC Ltd. moves jobs from one machine to another and

must be used every time a machine requires loading or unloading. The demand

for service is random. Data taken by recording the elapsed time between service

calls followed an exponential distribution having a mean of a call every 24

minutes. In a similar manner, the actual service time of loading or unloading took

an average of 8 minutes. If the machine time is valued at Rs. 8.50 per hour, how

much does the downtime cost per day? [Assume 8 hour work per day]

Step-by-step explanation:

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