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You are managing a call center where arrivals follow a Poisson process - with rate of 300 calls per hour and the service time is exponential with a mean of 2 minute...

Question

You are managing a call center where arrivals follow a Poisson process - with rate of 300 calls per hour and the service time is exponential with a mean of 2 minutes. (a) What is the approximate number of servers needed s0 that the proba: bility that a customer has a nonzero wait in queue is 592 (6) If the arrival rate doubles, what is the approximate number of servems needed to maintain the same level of service? (c) Suppose that you are given the steady-state probabilities po Pta Give a form

You are managing a call center where arrivals follow a Poisson process - with rate of 300 calls per hour and the service time is exponential with a mean of 2 minutes. (a) What is the approximate number of servers needed s0 that the proba: bility that a customer has a nonzero wait in queue is 592 (6) If the arrival rate doubles, what is the approximate number of servems needed to maintain the same level of service? (c) Suppose that you are given the steady-state probabilities po Pta Give a formula or procedure for computing the expected number o customers in queue and the variance of the number of customers i queue using these values comniter



Answers

At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution.
a. On average, how much time occurs between five consecutive calls?
b. Find the probability that after a call is received, it takes more than three minutes for the next call to occur.
c. Ninety-percent of all calls occur within how many minutes of the previous call?
d. Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute.
e. Find the probability that less than 20 calls occur within an hour.


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