customer service center in an international airlines flier program gets telephone calls from customers in three tiers
Question:
customer service center in an international airline’s flier program gets telephone calls from customers in three tiers of their program. Tier 1 customers call
according to a Poisson process having a rate of 1.1 per minute. Tier 2 customers call
according to a Poisson process having a rate of 2.2 per minute. Tier 3 customers call
according to a Poisson process having a rate of 4.4 per minute. Knowing that the three Poisson
processes are independent.
(1) What is the probability that a total of 13 calls are received during a 90-second
interval?
(2) Given that a total of 20 calls are received during a certain time interval, what is the probability that 7 of them were from tier 2 customers?
(3) What is the expected value of the number of tier 3 calls received during a 20- minute interval, given that 47 tier 2 calls were received during that same interval?
(4) Given that 4 tier 1 customers called during a 2-minute interval, what is the expected value of the total number of calls during a 6-minute interval that completely contains that 2-minute interval?
Suppose we begin monitoring calls at some point in time.
(5) What is the probability that the first Tier 1 call occurs before the first Tier 2 call?
(6) What is the probability that the 5th Tier 1 call occurs before the 6th Tier 2 call?
(7) What is the probability that the first four calls are all from Tier 3?
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman