The call center for souq.com has five workers answering incoming phone calls for orders. If the five phone lines are busy, a potential customer gets a busy signal and this represents a lost sales opportunity. The calls occur randomly (i.e., according to a Poisson process) at a mean rate of 15 per hour. The length of a telephone conversation follows an exponential distribution with a mean of 4 minutes. What is the average waiting time on phone and the percentage of lost sales?

We have 5 workers so we have 5*6o minutess available = 300 minutes.
As each call takes 4 mins and we can answer 75 calls per hour

µ (Mue) = Service rate = 75 calls /hour

λ (Lambda) = Arrival rate = 15

Expected Waiting time in system (Ws ) = 1/ (µ – λ) hrs = 1/(75-15) hrs= 1/60 hrs= 1min

Expected Waiting time in queue Wq = λ/ µ * (µ – λ) = 15/75(75-15) = 15/4500 = 1/300 = .2 Mins

Expected number of customers = λ2/ µ * (µ – λ) = 225/4500 = 1/20 = 0.5

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