WAITING LINES Problems and Solutions

# WAITING LINES Problems and Solutions - WAITING LINES...

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WAITING LINES Problem one Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every 6 minutes. The service rate of each service desk is 4 minutes per customer. A. How often (what percentage of time) is each service desk idle? B. What is the probability that both service clerks are busy? C. What is the probability that both service clerks are idle? D. How many customers, on average, are waiting in line in front of each service desk? E. How much time does a customer spend at the desk (waiting a plus the service time)? SOLUTION: Use model 1. 10/hour 15/hour a. 1- = 15 10 1 = .3333 or 33.33% b. P(both clerks busy) = P(one clerk busy) * P(one clerk busy)

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= 2 = 2 15 10 = .4444 or 44.44 c. P(both clerks idle) = P(one clerk idle) * P(one clerk idle) = (.3333)(.3333) = .1111 or 11.11% d. ) 10 15 ( 15 10 ) ( 2 2 q L = 1.33 customers e. 2 10 15 10 s L 2 . 10 2 s s L W or 12 minutes
Problem two Sharp Discounts Wholesale Club is considering consolidating its two service desks (see problem one above) into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of 4 minutes per customer. A. What is the probability of waiting in line? B. How many customers, on average, are waiting in line? C. How much time does a customer spend at the service desk (waiting plus service time)? D. Do you think the sharp discounts wholesale club should consolidate the service desks? SOLUTION: Use model 3 20/hour 15/hour a. 0.533 b. 1.0667 c. 0.12 hours or 7.2 minutes d. Yes, fewer customers in line and shorter time in system.

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Problem three Burrito King (a new fast food franchise opening up Nationwide) has successfully automated burrito production for its drive up fast food establishments. The Burro Master 9000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive up window according to a Poisson distribution at an average of one every 50 seconds.

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