BA341 17th Edition Lecture 17 Outline of Last Lecture I. Service Call Center with uncertaintyII. Waiting-line terminology III. M/M/1 Queue Outline of Current Lecture IV. Performance Metrics for M/M/1V. Waiting-Line with multiple serversVI. Solution via QCalcCurrent LectureManaging 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 mino (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/µ = 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 serversCustomers 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 λ = 1/20m = 3 /hour- What is the clerk’s service rate?o ts = 15 min =1/4 h -> μ = 4 /hour- What is the Clerk’s average utilization?o ρ = λ / μ = 3/4 -> 75%- What is the probability that an arriving customer has to wait?o Same as ρ = 3/4 = 0.75- What is the probability that an arriving customer will be served without waiting?o 1- ρ = 1- λ / μ = 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 / λ= 3 customers / 3 customers/h= 1 hour- How long does customers spend waiting?o Wq = Ws - ts = 1 hour – 15 min = 45 minHere is the solution via
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