ISyE 3232Stochastic Manufacturing and Service SystemsFall 2011H. AyhanHomework 6September 23, 2011(Due: September 28, Wednesday)1. The arrival rate of customers to an ATM machine is 30 per hour with exponentially distirbuted in-terarrival times. The transaction times of two customers are independent and identically distributed.Each transaction time (in minutes) is distributed according to the following p.d.f.:f(s) =‰4λ2se-2λsfors≥00otherwisewhereλ= 2/3.(a) What is the average waiting for each customer?(b) What is the average number of customers waiting in line?(c) What is the average number of customers at the site?2. A store stocks a particular item.The demand for the product each day is 1 item with probability1/6th, 2 items with probability 3/6th, and 3 items with probability 2/6th.Assume that the dailydemands are independent and identically distributed. Each evening if the remaining stock is less than3 items, the store orders enough to bring the total stock up to 6 items. These items reach the storebefore the beginning of the following day. Assume that any demand is lost when the item is out of
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Probability theory, English-language films, Markov chain, Stochastic Manufacturing