A cinema has a single ticket counter that is manned by acashier. The cashier is capable to handle 280 customers in an hour.Customers arrive at the counter at the rate of four customers perminute. Daniel, the owner who studied queuing models feels that allthe seven assumptions for a single-channel model are met. Byassuming Exponential service times and Poisson arrival rate, answerthe following questions.
a) State three assumptions mentioned above.
b) Determine the average number of customers waiting to buyticket.
c) Determine the percentage of time the cashier is free.
d) Calculate the average time spent by each customer in thesystem.
e) Calculate the average time each customer needs to spendwaiting to buy ticket.
f) The management of the theatre is planning to increase thenumber of counters if the probability of the system is busy ishigher than 0.5. Is it necessary to increase the number ofcounters?
