a. 5 inithitet b. 20 minutes c. 87 minutes d. 10 minutes For Scenario.1. wlat in the wverage time (minates) opent in the syotesm, \& W. W/ (Hist: an a. 8.7 minutes b. 10 minutes c. 5 minutes d. 20 minutes What is the prabublity alistritiution of L (the bunaber of castomers in the system) for Sce: nario 17 a. Geometric (0.63) b. Geomtetric (05) c. Geometric (0.37) d. Geometric (0.25) mrrieple in fhe fliom P(Z>1), her Scenarie 1 cormst arrivil rate detsilied in the srood bulict poist aloove) a. 10 minutes b. 7,4 minutes c. 37 minutes d. 5 minutes The erectit undon is now considering adding s thind trller (in the fosen of aer M/M/3) =ith then boal of aolving the folbomint arkument. aremint515ans+5118t+1 Recall the terme "ars maid" of "argument of the aniaimas" gives the solution s wuch that the function f()=$15y+$11ELe attains it ruininum valoo. Before solving this problem. what is the utiliastiot for o m 37. (Hint, nementher that A and were given in the opening. mbenatio.) a. 0.4 b. 0.33 c. 0.5 d. 0.67 a. 0.07 customers b. 203 customers for =3=3 a. 35622 b. 545.77 c. 567,33 a. 554,36 What is the optimal number of tellers to staff, s ? (Hint: you lesom the total cant ot s=3 from the above problem; to calenlate s=2 you can simply use the corsespobilins BLv | for Scenario 2 prowented in the table.) a. s=2 tellers b. s=3 tellers Considering s, what is the average number of customers in the system, E [L] a. 2.51 customers b. 1.07 customers C. 1.37 customers d. 3.01 customers 1 Staffing with the M/M/ s Queue MeNese is determining the stafing level for their crodit imion loctited within the university, and has recently hired two teilers (servers). The beginning of the fall semester is their busiest time with incouing frestimen and tranger atudents opening cecounts, On average, it takios a telles E(T)=10 minutes to macesifrilly open an accoint (equivalent to a if =6 per hour) and the average arrival rate has been A=6 per hour. As lilways, we use the exponential distribution an a feasonable approximation for boch the interanival and service times. After metimg with MeNeosefs upperadministration, the mampege of the credit unon is considering two poesalde icenarion for the nervice lavioit: - Scenario 1 : tho M/AM/1 (dedicatul) 4owue that each serve A/2 urivals - Seenario 2 u che M/Ar/2 (pooted) queue that merve all A arrivath For Scenario 1, what is the sverage time (minutes) spent in the system, E[W] ? (Hint: as alwyss, remernber to first derive the mean rumber in the system E[L]. 8.1minuts 312. minnates What is the probability distribution of L (the number of customens in the system) for Scemario 1 ? Gimimatirkgiost Wervices), in the form P(L>1), for Scenorio 1 a. 5 inithitet b. 20 minutes c. 87 minutes d. 10 minutes For Scenario.1. wlat in the wverage time (minates) opent in the syotesm, \& W. W/ (Hist: an a. 8.7 minutes b. 10 minutes c. 5 minutes d. 20 minutes What is the prabublity alistritiution of L (the bunaber of castomers in the system) for Sce: nario 17 a. Geometric (0.63) b. Geomtetric (05) c. Geometric (0.37) d. Geometric (0.25) mrrieple in fhe fliom P(Z>1), her Scenarie 1 cormst arrivil rate detsilied in the srood bulict poist aloove) a. 10 minutes b. 7,4 minutes c. 37 minutes d. 5 minutes The erectit undon is now considering adding s thind trller (in the fosen of aer M/M/3) =ith then boal of aolving the folbomint arkument. aremint515ans+5118t+1 Recall the terme "ars maid" of "argument of the aniaimas" gives the solution s wuch that the function f()=$15y+$11ELe attains it ruininum valoo. Before solving this problem. what is the utiliastiot for o m 37. (Hint, nementher that A and were given in the opening. mbenatio.) a. 0.4 b. 0.33 c. 0.5 d. 0.67 a. 0.07 customers b. 203 customers for =3=3 a. 35622 b. 545.77 c. 567,33 a. 554,36 What is the optimal number of tellers to staff, s ? (Hint: you lesom the total cant ot s=3 from the above problem; to calenlate s=2 you can simply use the corsespobilins BLv | for Scenario 2 prowented in the table.) a. s=2 tellers b. s=3 tellers Considering s, what is the average number of customers in the system, E [L] a. 2.51 customers b. 1.07 customers C. 1.37 customers d. 3.01 customers 1 Staffing with the M/M/ s Queue MeNese is determining the stafing level for their crodit imion loctited within the university, and has recently hired two teilers (servers). The beginning of the fall semester is their busiest time with incouing frestimen and tranger atudents opening cecounts, On average, it takios a telles E(T)=10 minutes to macesifrilly open an accoint (equivalent to a if =6 per hour) and the average arrival rate has been A=6 per hour. As lilways, we use the exponential distribution an a feasonable approximation for boch the interanival and service times. After metimg with MeNeosefs upperadministration, the mampege of the credit unon is considering two poesalde icenarion for the nervice lavioit: - Scenario 1 : tho M/AM/1 (dedicatul) 4owue that each serve A/2 urivals - Seenario 2 u che M/Ar/2 (pooted) queue that merve all A arrivath For Scenario 1, what is the sverage time (minutes) spent in the system, E[W] ? (Hint: as alwyss, remernber to first derive the mean rumber in the system E[L]. 8.1minuts 312. minnates What is the probability distribution of L (the number of customens in the system) for Scemario 1 ? Gimimatirkgiost Wervices), in the form P(L>1), for Scenorio 1
