question archive Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2
Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2
Subject:Operations ManagementPrice:2.87 Bought7
Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.
A. The probability that the operator is busy = (round your response to two decimal places).
B. The average time that a caller must wait before reaching the operator = minutes (round your response to two decimal places).
C. The average number of calls waling to be answered = calls (round your response to two decimal places).
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
This system of queuing is M/M/1 model.
Given that, Arrival rate, λ = 2 calls per minute
Service rate, μ = 60/15 = 4 calls per minute
a) Probability that the operator is busy = λ/μ = 2/4 = 50%
b) Average waiting time = λ/μ/(μ-λ) = 2/4/(4-2) = 0.25 minute
c) Average number of calls waiting to be answer = λ2/μ/(μ-λ) = 0.5
