A company has a call center for the purpose of responding to telephone inquiries

Question

A company has a call center for the purpose of responding to telephone inquiries from its customers. A telephone call received from this center is one of either two types: call from an existing customer or call from a new customer. For each hour, the number of calls received from this call center has a Poisson distribution with mean 10 and the percentage of calls from existing customers is 40%. (a) (5 points) Calculate the probability that on a given hour, there are more than 3 calls from a new customer. (b) (8 points) Calculate the conditional probability that if there is exactly one call made on a given hour, then it is a call made from an existing customer. (c) Suppose that this same company has 100 call centers all over the world. Each call center are independently run and receives calls from either existing or new customers in exactly the same fashion as described above. (i) (2 points) Describe the distribution of N, the total number of calls received from all 100 call centers on any given hour. (ii) (5 points) Use a suitable approximation to estimate the probability that on a given hour, there are at most 1,100 calls received from all call centers.

Explanation / Answer

Interactive voice response (IVR) is a technology that allows a computer to interact with humans through the use of voice and DTMF tones input via keypad. In telecommunications, IVR allows customers to interact with a company’s host system via a telephone keypad or by speech recognition, after which they can service their own inquiries by following the IVR dialogue. IVR systems can respond with prerecorded or dynamically generated audio to further direct users on how to proceed. IVR applications can be used to control almost any function where the interface can be broken down into a series of simple interactions. IVR systems deployed in the network are sized to handle large call volumes. IVR technology is also being introduced into automobile systems for hands-free operation. Current deployment in automobiles revolves around satellite navigation, audio and mobile phone systems. It's common in industries that have recently entered the telecommunications industry to refer to an automated attendant as an IVR. The terms, however, are distinct and mean different things to traditional telecommunications professionals, whereas emerging telephony and VoIP professionals often use the term IVR as a catch-all to signify any kind of telephony menu, even a basic automated attendant.[citation needed] The term voice response unit (VRU), is sometimes used as well.

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