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hmwk611 - ISyE 3232 H Ayhan Stochastic Manufacturing and...

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ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2011 H. Ayhan Homework 6 September 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 ) = 4 λ 2 se - 2 λs for s 0 0 otherwise where λ = 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 probability 1/6th, 2 items with probability 3/6th, and 3 items with probability 2/6th. Assume that the daily demands are independent and identically distributed. Each evening if the remaining stock is less than 3 items, the store orders enough to bring the total stock up to 6 items. These items reach the store before the beginning of the following day. Assume that any demand is lost when the item is out of
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