Reference no: EM132998647

Consider a call center. Customers call in according to a Poisson process with an average rate of 19 customers per hour. Each customer has a 50% probability of requiring an English-speaking server or requiring a Spanish-speaking server, so the arrival process for each type of service is Poisson with an average rate of 9.5 customers per hour.

HINT: In a Poisson arrival process, the interarrival times (times elapsed between successive customer arrivals) are independent, exponentially-distributed random variables, which have a coefficient of variation of

1. (a) Suppose that the call center has one English-speaking server and one Spanish-speaking server, and each of them provides exponentially-distributed service times with a mean of 6 minutes. On average, how long must a customer wait on the line before being served?

(b) How many customers you expect to be waiting in each line before being served?

(c) Now suppose we replace the two servers by two bilingual servers, both of whom provide exponentially-distributed service times with a mean of 6 minutes. On average, how long must a customer wait on the line before being served?

(d) How many customers you expect to be waiting in line before being served?