BA341 17th Edition Lecture 17 Outline of Last Lecture I Service Call Center with uncertainty II Waiting line terminology III M M 1 Queue Outline of Current Lecture IV Performance Metrics for M M 1 V Waiting Line with multiple servers VI Solution via QCalc Current Lecture Managing Process Variability Determining More Performance Metrics M M 1 15 h 20 h The average number of customers in system is o Ls 1 0 75 1 0 75 3 cust o Or Ls 15 20 15 3 cust The average time in system flow time is o Ws Ls 3 jobs 15 cust per hour 0 2 hours 12 min o Or Ws 1 1 20 15 0 2 hours The average of customers in the waiting line is o Lq 2 15 2 20 20 15 2 25 cust The average of customers receiving service is o Ls Lq 3 cust 2 25 cust 0 75 cust o Ls Lq The average time in queue waiting time where ts is service time is o Wq Ws ts Ws 1 0 2 hrs 1 20 hr 0 15 hrs or 9 minutes These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Waiting Lines with multiple servers Customers arrive at a store at an average rate of one every 20 minutes Their requests for service require on average 15 minutes to be processed by the clerk on duty What is the arrival rate of customers o 1 20m 3 hour What is the clerk s service rate o ts 15 min 1 4 h 4 hour What is the Clerk s average utilization o 3 4 75 What is the probability that an arriving customer has to wait o Same as 3 4 0 75 What is the probability that an arriving customer will be served without waiting o 1 1 1 3 4 0 25 How many customers are on average at the store o Ls 1 0 75 1 0 75 3 customers On average how many customers are waiting o Lq Ls 3 0 75 3 25 customers How long does a customer spend at the store o Ws Ls 3 customers 3 customers h 1 hour How long does customers spend waiting o Wq Ws ts 1 hour 15 min 45 min Here is the solution via QCalc
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