Reference no: EM131251802

(Poisson processes and queues) Consider a situation involving a server, e.g., a cashier at a fastfoodrestaurant, an automatic bank teller machine, a telephone exchange, etc. Units typically arrivefor service in a random fashion and form a queue when the server is busy. It is often the case that thenumber of arrivals at the server, for some specific unit of time ? ,can be modeled by a Poisson ????distribution and is such that the number of arrivals in nonoverlapping periods are independent. It willbe showen that ?? is the average number of arrivals during a time period of length t, and so ? is therate of arrivals per unit of time.Suppose telephone calls arrive at a help line at the rate of two per minute. A Poisson process providesa good model.(a) What is the probability that five calls arrive in the next 2 minutes?(b) What is the probability that five calls arrive in the next 2 minutes and then five more calls arrivein the following 2 minutes?(c) What is the probability that no calls will arrive during a 10-minute period?