{"text_format":"1","workbook":"xlsx","n_sheets":4,"sheets":["M-M-c","facto","M-M-m-inf","M-M-m-b"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[{"sheet":"facto","index":1,"reason":"part_missing"},{"sheet":"M-M-m-inf","index":2,"reason":"part_missing"},{"sheet":"M-M-m-b","index":3,"reason":"part_missing"}],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1904"}

{"sheet":"M-M-c","index":0,"n_rows":32,"n_cols":32,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Model 4 (M/M/s Queue):"]
[null,"Multiple servers,  Infinite population, Poisson arrival, FCFS, Exponential service time, Unlimited waiting room"]
[null,"Yellow cells need user inputed values"]
["Inputs"]
[null,"Units of time","hour",null,null,"Ta & Tp /min"]
[null,"Arrival rate - R",{"$f":"60/F6","v":10},"customers per",{"$f":"C5","v":"hour"},6]
[null,"Service rate - Rp",{"$f":"60/F7","v":20},"customers per",{"$f":"C5","v":"hour"},3]
[null,"Number of identical servers - c",1,"servers"]
[]
["Outputs"]
[null,"Direct outputs from inputs"]
[null,"Mean time between arrivals- Ta",{"$f":"1/C6","v":0.1},{"$f":"C5","v":"hour"}]
[null,"Mean time per service - Tp",{"$f":"1/C7","v":0.05},{"$f":"C5","v":"hour"}]
[null,"Traffic intensity - U",{"$f":"C6/C7/C8","v":0.5}]
[]
["Summary measures",null,null,null,null,null,"c®",null,1,{"$f":"I16+1","v":2},{"$f":"J16+1","v":3},4,5,6,7,8,9,{"$f":"Q16+1","v":10},null,null,null,6,11,{"$f":"W16+0.1","v":11.1},{"$f":"X16+0.1","v":11.2},11.299999999999999,11.399999999999999,11.499999999999998,11.599999999999998,11.699999999999998,11.799999999999997,11.899999999999997]
[null,"Average utilization rate of server - U",{"$f":"C6/C7/C8","v":0.5},null,null,null,null,{"$f":"C17","v":0.5},0.5,0.25,0.16666666666666666,0.125,0.1,8.3333333333333329E-2,7.1428571428571425E-2,6.25E-2,5.5555555555555552E-2,0.05,null,null,{"$f":"C17","v":0.5},0.3,0.55000000000000004,0.55499999999999994,0.55999999999999994,0.56499999999999995,0.56999999999999995,0.57499999999999996,0.57999999999999985,0.58499999999999985,0.58999999999999986,0.59499999999999986]
[null,"Average number of customers waiting in line Ii",{"$f":"(C6/C7)^(C8+1)/C8/FACT(C8)/(1-C6/C7/C8)^2 *C22","v":0.5},null,null,null,null,{"$f":"C18","v":0.5},0.5,3.3333333333333333E-2,3.0303030303030299E-3,2.5786487880350697E-4,1.9500019500019502E-5,1.30537737154434E-6,7.7884956131298456E-8,4.1785897501951307E-9,2.033267072290679E-10,9.0430006756522639E-12,null,null,{"$f":"C18","v":0.5},0.12857142857142856,0.6722222222222225,0.69219101123595483,0.71272727272727254,0.73385057471264337,0.75558139534883706,0.77794117647058803,0.80095238095238019,0.82463855421686694,0.84902439024390175,0.87413580246913491]
[null,"Average number of customers in system I",{"$f":"C18+C6/C7","v":1},null,null,null,"Metrics®",1,1,0.53333333333333333,0.50303030303030305,0.50025786487880353,0.50001950001950002,0.50000130537737153,0.50000007788495615,0.5000000041785897,0.50000000020332669,0.50000000000904299,null,null,1,0.42857142857142855,1.2222222222222225,1.2471910112359548,1.2727272727272725,1.2988505747126433,1.3255813953488369,1.3529411764705879,1.38095238095238,1.4096385542168668,1.4390243902439015,1.4691358024691348]
[null,"Average time waiting in line Ti",{"$f":"C18/C6","v":0.05},{"$f":" \"in \" &$C$5","v":"in hour"},{"$f":"60*C20","v":3},null,null,0.05,0.05,3.3333333333333331E-3,3.0303030303030298E-4,2.5786487880350696E-5,1.9500019500019503E-6,1.3053773715443401E-7,7.7884956131298453E-9,4.1785897501951306E-10,2.0332670722906789E-11,9.0430006756522637E-13,null,null,0.05,2.1428571428571425E-2,6.1111111111111137E-2,6.2359550561797733E-2,6.363636363636363E-2,6.4942528735632166E-2,6.6279069767441856E-2,6.7647058823529407E-2,6.9047619047618997E-2,7.0481927710843342E-2,7.1951219512195075E-2,7.3456790123456739E-2]
[null,"Average time in system - T",{"$f":"C19/C6","v":0.1},{"$f":" \"in \" &$C$5","v":"in hour"},null,null,null,0.1,0.1,5.333333333333333E-2,5.0303030303030308E-2,5.002578648788035E-2,5.0001950001949999E-2,5.000013053773715E-2,5.0000007788495615E-2,5.0000000417858972E-2,5.0000000020332669E-2,5.00000000009043E-2,null,null,0.1,7.1428571428571425E-2,0.11111111111111115,0.11235955056179774,0.11363636363636362,0.11494252873563217,0.11627906976744184,0.1176470588235294,0.11904761904761899,0.12048192771084335,0.12195121951219508,0.12345679012345674]
[null,"Probability of no customers in system (P0)",{"$f":"P0inf(C8,C6/C7)","v":0.5},"(this is the probability of empty system)",null,null,null,0.5,0.5,0.6,0.60606060606060608,0.60649819494584845,0.60652860652860652,0.60653054191436206,0.6065306535716094,0.60653065942032358,0.60653065969985764,0.60653065971211795,null,null,0.5,0.7,0.44999999999999996,0.44500000000000006,0.44000000000000006,0.43500000000000005,0.43000000000000005,0.42500000000000004,0.42000000000000015,0.4150000000000002,0.41000000000000014,0.40500000000000008]
[null,"Probability that all servers are busy",{"$f":"(C8*C14)^C8/factorial(C8)/(1-C14)*C22","v":0.5},"(this is also the \"percentage who wait in queue\")",null,null,null,0.5,0.5,9.9999999999999992E-2,1.515151515151515E-2,1.8050541516245488E-3,1.7550017550017549E-4,1.435915108698774E-5,1.01250442970688E-6,6.2678846252926962E-8,3.4565540228941541E-9,1.71817012837393E-10,null,null,0.5,0.3,0.55000000000000004,0.55499999999999994,0.55999999999999994,0.56499999999999995,0.56999999999999995,0.57499999999999996,0.57999999999999985,0.58499999999999996,0.58999999999999986,0.59499999999999975]
[null,"Probability that at least one server is idle",{"$f":"1-C23","v":0.5},"(this is also the \"percentage who don't wait in queue\")",null,null,null,0.5,0.5,0.9,0.98484848484848486,0.99819494584837543,0.99982449982449983,0.99998564084891306,0.99999898749557026,0.99999993732115378,0.99999999654344596,0.99999999982818299,null,null,0.5,0.7,0.44999999999999996,0.44500000000000006,0.44000000000000006,0.43500000000000005,0.43000000000000005,0.42500000000000004,0.42000000000000015,0.41500000000000004,0.41000000000000014,0.40500000000000025]
[null,null,null,null,null,null,null,0,0,0,0,0,0,0,0,0,0,0]
[null,"Distribution of number of customers in system"]
[null,"n (customers)","P(n in system)"]
[null,0,{"$f":"IF(B28=0,C22,IF(B28<C8+1,(C8*C14)^B28/factorial(B28)*C22, (C8*C14)^B28/factorial(C8)/C8^(B28-C8)*C22))","v":0.5}]
[]
[null,"Distribution of time in queue"]
[null,"t (time in queue)","P(wait > t)"]
[null,0,{"$f":"C23*EXP(-C8*C7*(1-C14)*B32)","v":0.5}]