{"text_format":"1","workbook":"xlsx","n_sheets":6,"sheets":["template","green time prediction ex 21","green time prediction ex calc27","green time prediction ex calc28","problem 69","problem 70"],"not_rendered":{"charts":15,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"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":"1900"}

{"sheet":"template","index":0,"n_rows":40,"n_cols":4,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
["Input variables","Phase 2","Phase 4"]
["Arrival rate, v",null,null,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen"]
["Headway of bunched vehicles, Δ",null,null,"veh/sec"]
["Bunching factor, b"]
["Lost time, l1",null,null,"sec"]
["Passage time, PT",null,null,"sec"]
["Detection zone length, Lds",null,null,"feet"]
["Vehicle length, Lv",null,null,"feet"]
["Speed, Sa",null,null,"mi/hr"]
["Maximum green, Gmax",null,null,"sec"]
["Minimum green, Gmin",null,null,"sec"]
["Yellow time, Y",null,null,"sec"]
["Red clearance, Rc",null,null,"sec"]
["Saturation flow rate, s",null,null,"veh/hr/green"]
[]
["Calculated variables","Phase 2","Phase 4"]
["Arrival rate, q",null,null,"veh/sec"]
["Arrival rate during red, qr",null,null,"veh/sec"]
["Arrival rate during green, qg",null,null,"veh/sec"]
["Proportion of free vehicles, ϕ"]
["Flow rate parameter, λ",null,null,"veh/sec"]
["Queue at end of red, QueueRed",null,null,"veh"]
["Queue service time, gs",null,null,"sec"]
["Number of extension before max out, n"]
["ProbSubjectPhaseCalled, pv"]
["Maximum allowable headway, MAH",null,null,"sec"]
["ProbGreenExtension, pge"]
["Green extension, ge",null,null,"sec"]
["Effective change interval, Y + Rc",null,null,"sec"]
["Average green interval duration, Green",null,null,"sec"]
["Phase duration, Dp",null,null,"sec"]
[]
["Final values","Phase 2","Phase 4"]
["Cycle length,  C",null,null,"sec"]
["Effective green, g",null,null,"sec"]
["Effective red, r",null,null,"sec"]
["Displayed green, G",null,null,"sec"]
["Displayed red, R",null,null,"sec"]
["Displayed yellow, Y",null,null,"sec"]

{"sheet":"green time prediction ex 21","index":1,"n_rows":61,"n_cols":21,"rows_kept":61,"cut":false,"hidden":false,"merged":[[2,6,2,7],[2,8,2,9]]}
["Input variables","Phase 2","Phase 4",null,null,"Queue Accumulation Polygon (QAP)"]
["Arrival rate, v",700,700,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen",0.75,0.75,null,null,null,"Phase 2",null,"Phase 4"]
["Headway of bunched vehicles, Δ",1.5,1.5,"veh/sec",null,"Points on QAP","Queue","Time","Queue","Time"]
["Bunching factor, b",0.6,0.6,null,null,"Origin",0,0,0,{"$f":"B37","v":34.339472879542335}]
["Lost time, l1",2,2,"sec",null,"Maximum queue",{"$f":"B23","v":2.8543704882449328},{"$f":"B37","v":34.339472879542335},{"$f":"C23","v":2.8543704882449328},{"$f":"J5+C37","v":68.678945759084669}]
["Passage time, PT",2.5,2.5,"sec",null,"Queue at end of green",{"$f":"G27","v":8.8817841970012523E-16},{"$f":"H6+B24+B29","v":56.678945759084669},{"$f":"I27","v":8.8817841970012523E-16},{"$f":"J6+C24+C29","v":91.018418638627011}]
["Detection zone length, Lds",22,22,"feet"]
["Vehicle length, Lv",20,20,"feet",null,"Display indications","Queue","Time","Queue","Time"]
["Speed, Sa",30,30,"mi/hr",null,"Red start",0.2,0,0.2,{"$f":"J5","v":34.339472879542335}]
["Maximum green, Gmax",50,50,"sec",null,"Red end",0.2,{"$f":"B39-B14","v":29.339740649443975},0.2,{"$f":"J10+C39","v":65.67921352898631}]
["Minimum green, Gmin",5,5,"sec",null,"Green start",0.2,{"$f":"H11","v":29.339740649443975},0.2,{"$f":"J11","v":65.67921352898631}]
["Yellow time, Y",3,3,"sec",null,"Green end",0.2,{"$f":"H12+B38","v":53.678945759084669},0.2,{"$f":"J12+C38","v":90.018418638626997}]
["Red clearance, Rc",2,2,"sec",null,"Yellow start",0.2,{"$f":"H13","v":53.678945759084669}]
["Saturation flow rate, s",1900,1900,"veh/hr/green",null,"Yellow end",0.2,{"$f":"H14+B13","v":56.678945759084669}]
[null,null,null,null,null,"Red clear start",0.2,{"$f":"H15","v":56.678945759084669}]
["Calculated variables","Phase 2","Phase 4",null,null,"Red clear end",0.2,{"$f":"H16+B14","v":58.678945759084669},null,null,null,null,null,null,null,null,null,null,1,null,0]
["Arrival rate, q",0.19444444444444445,0.19444444444444445,"veh/sec"]
["Arrival rate during red, qr",8.3074321369169646E-2,8.3074321369169646E-2,"veh/sec"]
["Arrival rate during green, qg",0.35153443654709221,0.35153443654709221,"veh/sec",null,"Capacity calculation"]
["Proportion of free vehicles, ϕ",0.83945702076920736,0.83945702076920736,null,null,"Effective green, g",{"$f":"B36","v":24.339472879542335},null,{"$f":"C36","v":24.339472879542335}]
["Flow rate parameter, λ",0.23043918217193932,0.23043918217193932,"veh/sec",null,"Cycle length,  C",{"$f":"B35","v":58.678945759084669},null,{"$f":"C35","v":58.678945759084669}]
["Queue at end of red, QueueRed",2.8543704882449328,2.8543704882449328,"veh",null,"Saturation flow rate, s",{"$f":"B15","v":1900},null,{"$f":"C15","v":1900}]
["Queue service time, gs",16.195621737043872,16.195621737043872,"sec",null,"Capacity, c",{"$f":"(G21/G22)*G23","v":788.10206749446911},null,{"$f":"(I21/I22)*I23","v":788.10206749446911}]
["Number of extension before max out, n",11.18033419239887,11.18033419239887,null,null,"Arrival rate, v",{"$f":"B2","v":700},null,{"$f":"C2","v":700}]
["ProbSubjectPhaseCalled, pv",0.99998899853324819,0.99998899853324819,null,null,"Degree of saturation",{"$f":"G25/G24","v":0.88820982569610196},null,{"$f":"I25/I24","v":0.88820982569610196}]
["Maximum allowable headway, MAH",3.4523809523809526,3.4523809523809526,"sec",null,"Queue at end of green",{"$f":"QueueAtEndOfGreen(B23,B15,B20,B11,B24,B29,B6)","v":8.8817841970012523E-16},null,{"$f":"QueueAtEndOfGreen(C23,C15,C20,C11,C24,C29,C6)","v":8.8817841970012523E-16}]
["ProbGreenExtension, pge",0.46468775667748619,0.46468775667748619,null,null,"Uniform delay, sec/veh",{"$f":"UniformDelay(B2,B37,B24,B23,G27,B29,G22)","v":7.0896413982920885},null,{"$f":"UniformDelay(C2,C37,C24,C23,I27,C29,I22)","v":7.0896413982920885}]
["Green extension, ge",6.1438511424984634,6.1438511424984634,"sec"]
["Effective change interval, Y + Rc",5,5,"sec",null,"Time calculations","Y-axis","X-axis","Y-axis","X-axis"]
["Average green interval duration, Green",24.339205109640695,24.339205109640695,"sec",null,"Red and Phase Duration"]
["Phase duration, Dp",29.339472879542335,29.339472879542335,"sec",null,"Red display",3,0,3]
[null,null,null,null,null,null,3,{"$f":"H32+B39-B14","v":29.339740649443975},3]
["Final values","Phase 2","Phase 4",null,null,"Green display",3,{"$f":"H33","v":29.339740649443975},3]
["Cycle length,  C",58.678945759084669,58.678945759084669,"sec",null,null,3,{"$f":"H34+B38","v":53.678945759084669},3]
["Effective green, g",24.339472879542335,24.339472879542335,"sec",null,"Yellow display",3,{"$f":"H35","v":53.678945759084669}]
["Effective red, r",34.339472879542335,34.339472879542335,"sec",null,null,3,{"$f":"H36+B13","v":56.678945759084669}]
["Displayed green, G",24.339205109640695,24.339205109640695,"sec",null,"Red clearance display",3,{"$f":"H37","v":56.678945759084669}]
["Displayed red, R",31.339740649443975,31.339740649443975,"sec",null,null,3,{"$f":"H38+B14","v":58.678945759084669}]
["Displayed yellow, Y",3,3,"sec",null,"Cycle length",4,0]
[null,null,null,null,null,null,4,{"$f":"B35","v":58.678945759084669}]
[null,null,null,null,null,"Phase duration",3.2,{"$f":"H34","v":29.339740649443975}]
["Intermediate values/iteration number","Green2","Green4","Cycle",null,null,3.2,{"$f":"H39","v":58.678945759084669}]
[1,29.529131401975448,29.529131401975448,69.058263016111994]
[2,26.228667697601626,26.228667697601626,62.457412681496805,null,"Effective times"]
[3,25.01114783633269,25.01114783633269,60.022561670397991,null,"Effective red1",2,0]
[4,24.571617738487976,24.571617738487976,59.143655036179261,null,null,2,{"$f":"H46+B37","v":34.339472879542335}]
[5,24.414722497951793,24.414722497951793,58.829939571024589,null,"Effective green",2,{"$f":"H47","v":34.339472879542335}]
[6,24.358977065894237,24.358977065894237,58.718478615324329,null,null,2,{"$f":"H48+B36","v":58.678945759084669}]
[7,24.339205109640695,24.339205109640695,58.678945759084669,null,"Effective red2",2,{"$f":"H49","v":58.678945759084669}]
[null,null,null,null,null,null,2,{"$f":"H50+B13+B14-2","v":61.678945759084669}]
[]
[null,null,null,null,null,"Phase duration components"]
[null,null,null,null,null,"Lost time, l1",1,{"$f":"B39","v":31.339740649443975}]
[null,null,null,null,5,null,1,{"$f":"H54+B6","v":33.339740649443975}]
[null,null,null,null,null,"Green service time, gs",1,{"$f":"H55","v":33.339740649443975}]
[null,null,null,null,null,null,1,{"$f":"H56+B24","v":49.535362386487847}]
[null,null,null,null,null,"Green extension time, ge",1,{"$f":"H57","v":49.535362386487847}]
[null,null,null,null,null,null,1,{"$f":"H58+B29","v":55.67921352898631}]
[null,null,null,null,null,"Y+Rc",1,{"$f":"H59","v":55.67921352898631}]
[null,null,null,null,null,null,1,{"$f":"H60+B13+B14","v":60.67921352898631}]

{"sheet":"green time prediction ex calc27","index":2,"n_rows":61,"n_cols":21,"rows_kept":61,"cut":false,"hidden":false,"merged":[[2,6,2,7],[2,8,2,9]]}
["Input variables","Phase 2","Phase 4",null,null,"Queue Accumulation Polygon (QAP)"]
["Arrival rate, v",800,100,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen",0.5,0.5,null,null,null,"Phase 2",null,"Phase 4"]
["Headway of bunched vehicles, Δ",1.5,1.5,"veh/sec",null,"Points on QAP","Queue","Time","Queue","Time"]
["Bunching factor, b",0.6,0.6,null,null,"Origin",0,0,0,{"$f":"B37","v":21.087081208456524}]
["Lost time, l1",2,2,"sec",null,"Maximum queue",{"$f":"B23","v":4.4552274100190141},{"$f":"B37","v":21.087081208456524},{"$f":"C23","v":0.55690342625237677},{"$f":"J5+C37","v":50.292905515274185}]
["Passage time, PT",2.5,2.5,"sec",null,"Queue at end of green",{"$f":"G27","v":0},{"$f":"H6+B24+B29","v":38.292905515274192},{"$f":"I27","v":0},{"$f":"J6+C24+C29","v":59.37998672373071}]
["Detection zone length, Lds",22,22,"feet"]
["Vehicle length, Lv",20,20,"feet",null,"Display indications","Queue","Time","Queue","Time"]
["Speed, Sa",30,30,"mi/hr",null,"Red start",0.2,0,0.2,{"$f":"J5","v":21.087081208456524}]
["Maximum green, Gmax",50,50,"sec",null,"Red end",0.2,{"$f":"B39-B14","v":16.089673426874906},0.2,{"$f":"J10+C39","v":50.932869265661381}]
["Minimum green, Gmin",5,5,"sec",null,"Green start",0.2,{"$f":"H11","v":16.089673426874906},0.2,{"$f":"J11","v":50.932869265661381}]
["Yellow time, Y",3,3,"sec",null,"Green end",0.2,{"$f":"H12+B38","v":35.292905515274185},0.2,{"$f":"J12+C38","v":58.37998672373071}]
["Red clearance, Rc",2,2,"sec",null,"Yellow start",0.2,{"$f":"H13","v":35.292905515274185}]
["Saturation flow rate, s",1900,1900,"veh/hr/green",null,"Yellow end",0.2,{"$f":"H14+B13","v":38.292905515274185}]
[null,null,null,null,null,"Red clear start",0.2,{"$f":"H15","v":38.292905515274185}]
["Calculated variables","Phase 2","Phase 4",null,null,"Red clear end",0.2,{"$f":"H16+B14","v":40.292905515274185},null,null,null,null,null,null,null,null,null,null,1,null,0]
["Arrival rate, q",0.22222222222222221,2.7777777777777776E-2,"veh/sec"]
["Arrival rate during red, qr",0.2132616839540678,1.9068017890648447E-2,"veh/sec"]
["Arrival rate during green, qg",0.23196876925978901,5.1134772222237987E-2,"veh/sec",null,"Capacity calculation"]
["Proportion of free vehicles, ϕ",0.81873075307798193,0.97530991202833273,null,null,"Effective green, g",{"$f":"B36","v":19.205824306817661},null,{"$f":"C36","v":11.087081208456526}]
["Flow rate parameter, λ",0.27291025102599392,2.8269852522560365E-2,"veh/sec",null,"Cycle length,  C",{"$f":"B35","v":40.292905515274185},null,{"$f":"C35","v":40.292905515274185}]
["Queue at end of red, QueueRed",4.4552274100190141,0.55690342625237677,"veh",null,"Saturation flow rate, s",{"$f":"B15","v":1900},null,{"$f":"C15","v":1900}]
["Queue service time, gs",15.061162039451826,1.1683868634625014,"sec",null,"Capacity, c",{"$f":"(G21/G22)*G23","v":905.64494459503715},null,{"$f":"(I21/I22)*I23","v":522.80802356340212}]
["Number of extension before max out, n",7.6407817025559783,2.3947238705368132,null,null,"Arrival rate, v",{"$f":"B2","v":800},null,{"$f":"C2","v":100}]
["ProbSubjectPhaseCalled, pv",0.99986502956723078,0.67169323630363009,null,null,"Degree of saturation",{"$f":"G25/G24","v":0.88334838589279963},null,{"$f":"I25/I24","v":0.19127479972172381}]
["Maximum allowable headway, MAH",3.4523809523809526,3.4523809523809526,"sec",null,"Queue at end of green",{"$f":"QueueAtEndOfGreen(B23,B15,B20,B11,B24,B29,B6)","v":0},null,{"$f":"QueueAtEndOfGreen(C23,C15,C20,C11,C24,C29,C6)","v":0}]
["ProbGreenExtension, pge",0.5194503739157188,7.7062279273490852E-2,null,null,"Uniform delay, sec/veh",{"$f":"UniformDelay(B2,B37,B24,B23,G27,B29,G22)","v":8.9931327782355712},null,{"$f":"UniformDelay(C2,C37,C24,C23,I27,C29,I22)","v":7.5566414725922089}]
["Green extension, ge",2.1446622673658351,7.9186943449940248,"sec"]
["Effective change interval, Y + Rc",5,5,"sec",null,"Time calculations","Y-axis","X-axis","Y-axis","X-axis"]
["Average green interval duration, Green",19.203232088399279,7.447117458069326,"sec",null,"Red and Phase Duration"]
["Phase duration, Dp",24.205824306817661,16.087081208456524,"sec",null,"Red display",3,0,3]
[null,null,null,null,null,null,3,{"$f":"H32+B39-B14","v":16.089673426874906},3]
["Final values","Phase 2","Phase 4",null,null,"Green display",3,{"$f":"H33","v":16.089673426874906},3]
["Cycle length,  C",40.292905515274185,40.292905515274185,"sec",null,null,3,{"$f":"H34+B38","v":35.292905515274185},3]
["Effective green, g",19.205824306817661,11.087081208456526,"sec",null,"Yellow display",3,{"$f":"H35","v":35.292905515274185}]
["Effective red, r",21.087081208456524,29.205824306817661,"sec",null,null,3,{"$f":"H36+B13","v":38.292905515274185}]
["Displayed green, G",19.203232088399279,7.447117458069326,"sec",null,"Red clearance display",3,{"$f":"H37","v":38.292905515274185}]
["Displayed red, R",18.089673426874906,29.845788057204857,"sec",null,null,3,{"$f":"H38+B14","v":40.292905515274185}]
["Displayed yellow, Y",3,3,"sec",null,"Cycle length",4,0]
[null,null,null,null,null,null,4,{"$f":"B35","v":40.292905515274185}]
[null,null,null,null,null,"Phase duration",3.2,{"$f":"H34","v":16.089673426874906}]
["Intermediate values/iteration number","Green2","Green4","Cycle",null,null,3.2,{"$f":"H39","v":40.292905515274185}]
[1,40.238869201910539,14.294326289334467,65.480891462932078]
[2,25.64121844493501,9.278859169281116,46.716522926683105,null,"Effective times"]
[3,20.396457168837731,7.7277839185859039,41.029183931221624,null,"Effective red1",2,0]
[4,19.204044601586908,7.4067328498962359,40.097046690171126,null,null,2,{"$f":"H46+B37","v":21.087081208456524}]
[5,19.203232088399279,7.447117458069326,40.292905515274185,null,"Effective green",2,{"$f":"H47","v":21.087081208456524}]
[null,null,null,null,null,null,2,{"$f":"H48+B36","v":40.292905515274185}]
[null,null,null,null,null,"Effective red2",2,{"$f":"H49","v":40.292905515274185}]
[null,null,null,null,null,null,2,{"$f":"H50+B13+B14-2","v":43.292905515274185}]
[]
[null,null,null,null,null,"Phase duration components"]
[null,null,null,null,null,"Lost time, l1",1,{"$f":"B39","v":18.089673426874906}]
[null,null,null,null,5,null,1,{"$f":"H54+B6","v":20.089673426874906}]
[null,null,null,null,null,"Green service time, gs",1,{"$f":"H55","v":20.089673426874906}]
[null,null,null,null,null,null,1,{"$f":"H56+B24","v":35.150835466326733}]
[null,null,null,null,null,"Green extension time, ge",1,{"$f":"H57","v":35.150835466326733}]
[null,null,null,null,null,null,1,{"$f":"H58+B29","v":37.295497733692571}]
[null,null,null,null,null,"Y+Rc",1,{"$f":"H59","v":37.295497733692571}]
[null,null,null,null,null,null,1,{"$f":"H60+B13+B14","v":42.295497733692571}]

{"sheet":"green time prediction ex calc28","index":3,"n_rows":61,"n_cols":21,"rows_kept":61,"cut":false,"hidden":false,"merged":[[2,6,2,7],[2,8,2,9]]}
["Input variables","Phase 2","Phase 4",null,null,"Queue Accumulation Polygon (QAP)"]
["Arrival rate, v",1050,400,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen",0.5,0.5,null,null,null,"Phase 2",null,"Phase 4"]
["Headway of bunched vehicles, Δ",1.5,1.5,"veh/sec",null,"Points on QAP","Queue","Time","Queue","Time"]
["Bunching factor, b",0.6,0.6,null,null,"Origin",0,0,0,{"$f":"B37","v":25.392770554113959}]
["Lost time, l1",2,2,"sec",null,"Maximum queue",{"$f":"B23","v":8.9596373943164682},{"$f":"B37","v":25.392770554113959},{"$f":"C23","v":3.4131951978348445},{"$f":"J5+C37","v":71.377850888769018}]
["Passage time, PT",2.5,2.5,"sec",null,"Queue at end of green",{"$f":"G27","v":0},{"$f":"H6+B24+B29","v":59.377850888769032},{"$f":"I27","v":0},{"$f":"J6+C24+C29","v":84.770621442882984}]
["Detection zone length, Lds",22,22,"feet"]
["Vehicle length, Lv",20,20,"feet",null,"Display indications","Queue","Time","Queue","Time"]
["Speed, Sa",30,30,"mi/hr",null,"Red start",0.2,0,0.2,{"$f":"J5","v":25.392770554113959}]
["Maximum green, Gmax",50,50,"sec",null,"Red end",0.2,{"$f":"B39-B14","v":20.39277114824236},0.2,{"$f":"J10+C39","v":68.394548452726468}]
["Minimum green, Gmin",5,5,"sec",null,"Green start",0.2,{"$f":"H11","v":20.39277114824236},0.2,{"$f":"J11","v":68.394548452726468}]
["Yellow time, Y",3,3,"sec",null,"Green end",0.2,{"$f":"H12+B38","v":56.377850888769032},0.2,{"$f":"J12+C38","v":83.770621442882998}]
["Red clearance, Rc",2,2,"sec",null,"Yellow start",0.2,{"$f":"H13","v":56.377850888769032}]
["Saturation flow rate, s",1900,1900,"veh/hr/green",null,"Yellow end",0.2,{"$f":"H14+B13","v":59.377850888769032}]
[null,null,null,null,null,"Red clear start",0.2,{"$f":"H15","v":59.377850888769032}]
["Calculated variables","Phase 2","Phase 4",null,null,"Red clear end",0.2,{"$f":"H16+B14","v":61.377850888769032},null,null,null,null,null,null,null,null,null,null,1,null,0]
["Arrival rate, q",0.29166666666666669,0.1111111111111111,"veh/sec"]
["Arrival rate during red, qr",0.35258068652371288,7.415811045213995E-2,"veh/sec"]
["Arrival rate during green, qg",0.24869975838269029,0.22146931150168717,"veh/sec",null,"Capacity calculation"]
["Proportion of free vehicles, ϕ",0.76912636436857051,0.90483741803595963,null,null,"Effective green, g",{"$f":"B36","v":35.985080334655073},null,{"$f":"C36","v":15.392770554113962}]
["Flow rate parameter, λ",0.39880626300592548,0.12064498907146128,"veh/sec",null,"Cycle length,  C",{"$f":"B35","v":61.377850888769032},null,{"$f":"C35","v":61.377850888769032}]
["Queue at end of red, QueueRed",8.9596373943164682,3.4131951978348445,"veh",null,"Saturation flow rate, s",{"$f":"B15","v":1900},null,{"$f":"C15","v":1900}]
["Queue service time, gs",32.104418018075492,11.142999863276282,"sec",null,"Capacity, c",{"$f":"(G21/G22)*G23","v":1113.9466704324661},null,{"$f":"(I21/I22)*I23","v":476.49540720833602}]
["Number of extension before max out, n",3.9532273982568702,8.1626944442977916,null,null,"Arrival rate, v",{"$f":"B2","v":1050},null,{"$f":"C2","v":400}]
["ProbSubjectPhaseCalled, pv",0.99999998348959074,0.9989152333623933,null,null,"Degree of saturation",{"$f":"G25/G24","v":0.94259449565243536},null,{"$f":"I25/I24","v":0.83946244591001851}]
["Maximum allowable headway, MAH",3.4523809523809526,3.4523809523809526,"sec",null,"Queue at end of green",{"$f":"QueueAtEndOfGreen(B23,B15,B20,B11,B24,B29,B6)","v":0},null,{"$f":"QueueAtEndOfGreen(C23,C15,C20,C11,C24,C29,C6)","v":0}]
["ProbGreenExtension, pge",0.64694158409263702,0.2850516514325343,null,null,"Uniform delay, sec/veh",{"$f":"UniformDelay(B2,B37,B24,B23,G27,B29,G22)","v":14.388269756408189},null,{"$f":"UniformDelay(C2,C37,C24,C23,I27,C29,I22)","v":14.295902964395273}]
["Green extension, ge",1.8806623165795839,2.2497706908376807,"sec"]
["Effective change interval, Y + Rc",5,5,"sec",null,"Time calculations","Y-axis","X-axis","Y-axis","X-axis"]
["Average green interval duration, Green",35.985079740526672,15.376072990156525,"sec",null,"Red and Phase Duration"]
["Phase duration, Dp",40.985080334655073,20.392770554113962,"sec",null,"Red display",3,0,3]
[null,null,null,null,null,null,3,{"$f":"H32+B39-B14","v":20.39277114824236},3]
["Final values","Phase 2","Phase 4",null,null,"Green display",3,{"$f":"H33","v":20.39277114824236},3]
["Cycle length,  C",61.377850888769032,61.377850888769032,"sec",null,null,3,{"$f":"H34+B38","v":56.377850888769032},3]
["Effective green, g",35.985080334655073,15.392770554113962,"sec",null,"Yellow display",3,{"$f":"H35","v":56.377850888769032}]
["Effective red, r",25.392770554113959,45.985080334655066,"sec",null,null,3,{"$f":"H36+B13","v":59.377850888769032}]
["Displayed green, G",35.985079740526672,15.376072990156525,"sec",null,"Red clearance display",3,{"$f":"H37","v":59.377850888769032}]
["Displayed red, R",22.39277114824236,43.001777898612509,"sec",null,null,3,{"$f":"H38+B14","v":61.377850888769032}]
["Displayed yellow, Y",3,3,"sec",null,"Cycle length",4,0]
[null,null,null,null,null,null,4,{"$f":"B35","v":61.377850888769032}]
[null,null,null,null,null,"Phase duration",3.2,{"$f":"H34","v":20.39277114824236}]
["Intermediate values/iteration number","Green2","Green4","Cycle",null,null,3.2,{"$f":"H39","v":61.377850888769032}]
[1,49.999999999989235,19.521375474698747,79.521667232624111]
[2,42.831925307064729,18.849177921147124,71.683845071833574,null,"Effective times"]
[3,40.585243542965884,16.929323626267749,67.520451447538662,null,"Effective red1",2,0]
[4,38.377546722757394,16.4863830619223,64.87303257919055,null,null,2,{"$f":"H46+B37","v":25.392770554113959}]
[5,37.490372264672892,15.920021768601311,63.422192601449538,null,"Effective green",2,{"$f":"H47","v":25.392770554113959}]
[6,36.779640578311195,15.730034348631699,62.523373781363148,null,null,2,{"$f":"H48+B36","v":61.377850888769032}]
[7,36.453838530882834,15.55190680783585,62.020712944290594,null,"Effective red2",2,{"$f":"H49","v":61.377850888769032}]
[8,36.220044822987902,15.479250192592158,61.715049335734648,null,null,2,{"$f":"H50+B13+B14-2","v":64.377850888769032}]
[9,36.103824203396194,15.421583402585142,61.541646055496365]
[10,36.025918597909211,15.39506871966268,61.43751356102721,null,"Phase duration components"]
[11,35.985079740526672,15.376072990156525,61.377850888769032,null,"Lost time, l1",1,{"$f":"B39","v":22.39277114824236}]
[null,null,null,null,5,null,1,{"$f":"H54+B6","v":24.39277114824236}]
[null,null,null,null,null,"Green service time, gs",1,{"$f":"H55","v":24.39277114824236}]
[null,null,null,null,null,null,1,{"$f":"H56+B24","v":56.497189166317852}]
[null,null,null,null,null,"Green extension time, ge",1,{"$f":"H57","v":56.497189166317852}]
[null,null,null,null,null,null,1,{"$f":"H58+B29","v":58.377851482897434}]
[null,null,null,null,null,"Y+Rc",1,{"$f":"H59","v":58.377851482897434}]
[null,null,null,null,null,null,1,{"$f":"H60+B13+B14","v":63.377851482897434}]

{"sheet":"problem 69","index":4,"n_rows":61,"n_cols":21,"rows_kept":61,"cut":false,"hidden":false,"merged":[[2,6,2,7],[2,8,2,9]]}
["Input variables","Phase 2","Phase 4",null,null,"Queue Accumulation Polygon (QAP)"]
["Arrival rate, v",875,650,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen",0.5,0.5,null,null,null,"Phase 2",null,"Phase 4"]
["Headway of bunched vehicles, Δ",1.5,1.5,"veh/sec",null,"Points on QAP","Queue","Time","Queue","Time"]
["Bunching factor, b",0.6,0.6,null,null,"Origin",0,0,0,{"$f":"B37","v":36.949664446303117}]
["Lost time, l1",2,2,"sec",null,"Maximum queue",{"$f":"B23","v":8.794054406931453},{"$f":"B37","v":36.949664446303117},{"$f":"C23","v":6.5327261308633648},{"$f":"J5+C37","v":82.28689516890617}]
["Passage time, PT",2.5,2.5,"sec",null,"Queue at end of green",{"$f":"G27","v":0},{"$f":"H6+B24+B29","v":70.28689516890617},{"$f":"I27","v":0},{"$f":"J6+C24+C29","v":107.23655961520929}]
["Detection zone length, Lds",22,22,"feet"]
["Vehicle length, Lv",20,20,"feet",null,"Display indications","Queue","Time","Queue","Time"]
["Speed, Sa",30,30,"mi/hr",null,"Red start",0.2,0,0.2,{"$f":"J5","v":36.949664446303117}]
["Maximum green, Gmax",50,50,"sec",null,"Red end",0.2,{"$f":"B39-B14","v":31.949665258785409},0.2,{"$f":"J10+C39","v":79.286952224672291}]
["Minimum green, Gmin",5,5,"sec",null,"Green start",0.2,{"$f":"H11","v":31.949665258785409},0.2,{"$f":"J11","v":79.286952224672291}]
["Yellow time, Y",3,3,"sec",null,"Green end",0.2,{"$f":"H12+B38","v":67.286895168906156},0.2,{"$f":"J12+C38","v":106.23655961520927}]
["Red clearance, Rc",2,2,"sec",null,"Yellow start",0.2,{"$f":"H13","v":67.286895168906156}]
["Saturation flow rate, s",1900,1900,"veh/hr/green",null,"Yellow end",0.2,{"$f":"H14+B13","v":70.286895168906156}]
[null,null,null,null,null,"Red clear start",0.2,{"$f":"H15","v":70.286895168906156}]
["Calculated variables","Phase 2","Phase 4",null,null,"Red clear end",0.2,{"$f":"H16+B14","v":72.286895168906156},null,null,null,null,null,null,null,null,null,null,1,null,0]
["Arrival rate, q",0.24305555555555555,0.18055555555555555,"veh/sec"]
["Arrival rate during red, qr",0.23825396711861219,0.14372776088036246,"veh/sec"]
["Arrival rate during green, qg",0.24805465966270104,0.24275822187542453,"veh/sec",null,"Capacity calculation"]
["Proportion of free vehicles, ϕ",0.80352257368906077,0.85001609022539815,null,null,"Effective green, g",{"$f":"B36","v":35.337230722603039},null,{"$f":"C36","v":26.94966444630311}]
["Flow rate parameter, λ",0.30735836152040569,0.21048017472247951,"veh/sec",null,"Cycle length,  C",{"$f":"B35","v":72.286895168906156},null,{"$f":"C35","v":72.286895168906156}]
["Queue at end of red, QueueRed",8.794054406931453,6.5327261308633648,"veh",null,"Saturation flow rate, s",{"$f":"B15","v":1900},null,{"$f":"C15","v":1900}]
["Queue service time, gs",31.438425490858503,22.920273348195991,"sec",null,"Capacity, c",{"$f":"(G21/G22)*G23","v":928.80927056092492},null,{"$f":"(I21/I22)*I23","v":708.34917350276805}]
["Number of extension before max out, n",4.108175728343558,6.0883098471136359,null,null,"Arrival rate, v",{"$f":"B2","v":875},null,{"$f":"C2","v":650}]
["ProbSubjectPhaseCalled, pv",0.99999997700775412,0.99999788287656666,null,null,"Degree of saturation",{"$f":"G25/G24","v":0.94206639375118584},null,{"$f":"I25/I24","v":0.91762653831551333}]
["Maximum allowable headway, MAH",3.4523809523809526,3.4523809523809526,"sec",null,"Queue at end of green",{"$f":"QueueAtEndOfGreen(B23,B15,B20,B11,B24,B29,B6)","v":0},null,{"$f":"QueueAtEndOfGreen(C23,C15,C20,C11,C24,C29,C6)","v":0}]
["ProbGreenExtension, pge",0.55905300812396697,0.43641520855453342,null,null,"Uniform delay, sec/veh",{"$f":"UniformDelay(B2,B37,B24,B23,G27,B29,G22)","v":17.114905395766627},null,{"$f":"UniformDelay(C2,C37,C24,C23,I27,C29,I22)","v":17.082224782068046}]
["Green extension, ge",1.8988052317445394,2.0293910981071197,"sec"]
["Effective change interval, Y + Rc",5,5,"sec",null,"Time calculations","Y-axis","X-axis","Y-axis","X-axis"]
["Average green interval duration, Green",35.337229910120747,26.94960739053699,"sec",null,"Red and Phase Duration"]
["Phase duration, Dp",40.337230722603046,31.94966444630311,"sec",null,"Red display",3,0,3]
[null,null,null,null,null,null,3,{"$f":"H32+B39-B14","v":31.949665258785409},3]
["Final values","Phase 2","Phase 4",null,null,"Green display",3,{"$f":"H33","v":31.949665258785409},3]
["Cycle length,  C",72.286895168906156,72.286895168906156,"sec",null,null,3,{"$f":"H34+B38","v":67.286895168906156},3]
["Effective green, g",35.337230722603039,26.94966444630311,"sec",null,"Yellow display",3,{"$f":"H35","v":67.286895168906156}]
["Effective red, r",36.949664446303117,45.337230722603046,"sec",null,null,3,{"$f":"H36+B13","v":70.286895168906156}]
["Displayed green, G",35.337229910120747,26.94960739053699,"sec",null,"Red clearance display",3,{"$f":"H37","v":70.286895168906156}]
["Displayed red, R",33.949665258785409,42.337287778369166,"sec",null,null,3,{"$f":"H38+B14","v":72.286895168906156}]
["Displayed yellow, Y",3,3,"sec",null,"Cycle length",4,0]
[null,null,null,null,null,null,4,{"$f":"B35","v":72.286895168906156}]
[null,null,null,null,null,"Phase duration",3.2,{"$f":"H34","v":31.949665258785409}]
["Intermediate values/iteration number","Green2","Green4","Cycle",null,null,3.2,{"$f":"H39","v":72.286895168906156}]
[1,45.900164831134362,30.592788678610656,86.492953951770176]
[2,39.07936603988815,32.545382638441716,81.624754080173602,null,"Effective times"]
[3,39.932924857129834,28.605717526282042,78.538653853889855,null,"Effective red1",2,0]
[4,36.969755392999097,29.306350351417255,76.27612627662603,null,null,2,{"$f":"H46+B37","v":36.949664446303117}]
[5,37.294335811788827,27.605513001074968,74.899877975009247,null,"Effective green",2,{"$f":"H47","v":36.949664446303117}]
[6,35.993636121615516,27.914354657110703,73.908028602688375,null,null,2,{"$f":"H48+B36","v":72.286895168906156}]
[7,36.152922778572297,27.16513520793,73.318102065281082,null,"Effective red2",2,{"$f":"H49","v":72.286895168906156}]
[8,35.576864043629413,27.316816415860412,72.893729776062315,null,null,2,{"$f":"H50+B13+B14-2","v":75.286895168906156}]
[9,35.662462459924363,26.983008373531788,72.645523455816516]
[10,35.405797704835422,27.060088578855119,72.465941479302529,null,"Phase duration components"]
[11,35.452082301998814,26.910365818760944,72.362504834178807,null,"Lost time, l1",1,{"$f":"B39","v":33.949665258785409}]
[12,35.337229910120747,26.94960739053699,72.286895168906156,5,null,1,{"$f":"H54+B6","v":35.949665258785409}]
[null,null,null,null,null,"Green service time, gs",1,{"$f":"H55","v":35.949665258785409}]
[null,null,null,null,null,null,1,{"$f":"H56+B24","v":67.388090749643908}]
[null,null,null,null,null,"Green extension time, ge",1,{"$f":"H57","v":67.388090749643908}]
[null,null,null,null,null,null,1,{"$f":"H58+B29","v":69.286895981388454}]
[null,null,null,null,null,"Y+Rc",1,{"$f":"H59","v":69.286895981388454}]
[null,null,null,null,null,null,1,{"$f":"H60+B13+B14","v":74.286895981388454}]

{"sheet":"problem 70","index":5,"n_rows":61,"n_cols":21,"rows_kept":61,"cut":false,"hidden":false,"merged":[[2,6,2,7],[2,8,2,9]]}
["Input variables","Phase 2","Phase 4",null,null,"Queue Accumulation Polygon (QAP)"]
["Arrival rate, v",200,350,"veh/hr"]
["Proportion vehicles arriving on green, Pgreen",0.5,0.5,null,null,null,"Phase 2",null,"Phase 4"]
["Headway of bunched vehicles, Δ",1.5,1.5,"veh/sec",null,"Points on QAP","Queue","Time","Queue","Time"]
["Bunching factor, b",0.6,0.6,null,null,"Origin",0,0,0,{"$f":"B37","v":18.892286040116716}]
["Lost time, l1",2,2,"sec",null,"Maximum queue",{"$f":"B23","v":0.78407834331609272},{"$f":"B37","v":18.892286040116716},{"$f":"C23","v":1.3721371008031624},{"$f":"J5+C37","v":38.192614792853568}]
["Passage time, PT",2.5,2.5,"sec",null,"Queue at end of green",{"$f":"G27","v":0},{"$f":"H6+B24+B29","v":26.192614792853565},{"$f":"I27","v":0},{"$f":"J6+C24+C29","v":45.084900832970277}]
["Detection zone length, Lds",22,22,"feet"]
["Vehicle length, Lv",20,20,"feet",null,"Display indications","Queue","Time","Queue","Time"]
["Speed, Sa",30,30,"mi/hr",null,"Red start",0.2,0,0.2,{"$f":"J5","v":18.892286040116716}]
["Maximum green, Gmax",50,50,"sec",null,"Red end",0.2,{"$f":"B39-B14","v":15.830744526672714},0.2,{"$f":"J10+C39","v":35.764343871938564}]
["Minimum green, Gmin",5,5,"sec",null,"Green start",0.2,{"$f":"H11","v":15.830744526672714},0.2,{"$f":"J11","v":35.764343871938564}]
["Yellow time, Y",3,3,"sec",null,"Green end",0.2,{"$f":"H12+B38","v":23.192614792853561},0.2,{"$f":"J12+C38","v":44.084900832970277}]
["Red clearance, Rc",2,2,"sec",null,"Yellow start",0.2,{"$f":"H13","v":23.192614792853561}]
["Saturation flow rate, s",1900,1900,"veh/hr/green",null,"Yellow end",0.2,{"$f":"H14+B13","v":26.192614792853561}]
[null,null,null,null,null,"Red clear start",0.2,{"$f":"H15","v":26.192614792853561}]
["Calculated variables","Phase 2","Phase 4",null,null,"Red clear end",0.2,{"$f":"H16+B14","v":28.192614792853561},null,null,null,null,null,null,null,null,null,null,1,null,0]
["Arrival rate, q",5.5555555555555552E-2,9.7222222222222224E-2,"veh/sec"]
["Arrival rate during red, qr",4.1424913862966942E-2,7.1098427145783516E-2,"veh/sec"]
["Arrival rate during green, qg",8.4317474711627885E-2,0.15369435536370671,"veh/sec",null,"Capacity calculation"]
["Proportion of free vehicles, ϕ",0.95122942450071402,0.91621887165087768,null,null,"Effective green, g",{"$f":"B36","v":9.3003287527368474},null,{"$f":"C36","v":8.8922860401167103}]
["Flow rate parameter, λ",5.7650268151558423E-2,0.10428507482205113,"veh/sec",null,"Cycle length,  C",{"$f":"B35","v":28.192614792853561},null,{"$f":"C35","v":28.192614792853561}]
["Queue at end of red, QueueRed",0.78407834331609272,1.3721371008031624,"veh",null,"Saturation flow rate, s",{"$f":"B15","v":1900},null,{"$f":"C15","v":1900}]
["Queue service time, gs",1.7680913892288881,3.6679976138700705,"sec",null,"Capacity, c",{"$f":"(G21/G22)*G23","v":626.78204061722113},null,{"$f":"(I21/I22)*I23","v":599.28259937437542}]
["Number of extension before max out, n",3.8981577851589848,6.8135785287185469,null,null,"Arrival rate, v",{"$f":"B2","v":200},null,{"$f":"C2","v":350}]
["ProbSubjectPhaseCalled, pv",0.79157097151156497,0.93570505081531397,null,null,"Degree of saturation",{"$f":"G25/G24","v":0.31909018931533328},null,{"$f":"I25/I24","v":0.58403164110785888}]
["Maximum allowable headway, MAH",3.4523809523809526,3.4523809523809526,"sec",null,"Queue at end of green",{"$f":"QueueAtEndOfGreen(B23,B15,B20,B11,B24,B29,B6)","v":0},null,{"$f":"QueueAtEndOfGreen(C23,C15,C20,C11,C24,C29,C6)","v":0}]
["ProbGreenExtension, pge",0.15003090198809588,0.25256220434885901,null,null,"Uniform delay, sec/veh",{"$f":"UniformDelay(B2,B37,B24,B23,G27,B29,G22)","v":5.1713610686701994},null,{"$f":"UniformDelay(C2,C37,C24,C23,I27,C29,I22)","v":5.7490483506885512}]
["Green extension, ge",5.5322373635079591,3.2242884262466402,"sec"]
["Effective change interval, Y + Rc",5,5,"sec",null,"Time calculations","Y-axis","X-axis","Y-axis","X-axis"]
["Average green interval duration, Green",7.3618702661808477,8.3205569610317145,"sec",null,"Red and Phase Duration"]
["Phase duration, Dp",14.300328752736847,13.892286040116712,"sec",null,"Red display",3,0,3]
[null,null,null,null,null,null,3,{"$f":"H32+B39-B14","v":15.830744526672714},3]
["Final values","Phase 2","Phase 4",null,null,"Green display",3,{"$f":"H33","v":15.830744526672714},3]
["Cycle length,  C",28.192614792853561,28.192614792853561,"sec",null,null,3,{"$f":"H34+B38","v":23.192614792853561},3]
["Effective green, g",9.3003287527368474,8.8922860401167103,"sec",null,"Yellow display",3,{"$f":"H35","v":23.192614792853561}]
["Effective red, r",18.892286040116716,19.300328752736853,"sec",null,null,3,{"$f":"H36+B13","v":26.192614792853561}]
["Displayed green, G",7.3618702661808477,8.3205569610317145,"sec",null,"Red clearance display",3,{"$f":"H37","v":26.192614792853561}]
["Displayed red, R",17.830744526672714,16.872057831821849,"sec",null,null,3,{"$f":"H38+B14","v":28.192614792853561}]
["Displayed yellow, Y",3,3,"sec",null,"Cycle length",4,0]
[null,null,null,null,null,null,4,{"$f":"B35","v":28.192614792853561}]
[null,null,null,null,null,"Phase duration",3.2,{"$f":"H34","v":15.830744526672714}]
["Intermediate values/iteration number","Green2","Green4","Cycle",null,null,3.2,{"$f":"H39","v":28.192614792853561}]
[1,15.046205745819156,17.998760168625356,43.104437937832998]
[2,9.5011106055908243,11.083747583468879,31.70866127129948,null,"Effective times"]
[3,7.8819200606965838,9.1017767783077694,29.055557074576086,null,"Effective red1",2,0]
[4,7.4705462089709114,8.5232239761721242,28.387794382695045,null,null,2,{"$f":"H46+B37","v":18.892286040116716}]
[5,7.3781698228708663,8.3626074176240923,28.226820359379339,null,"Effective green",2,{"$f":"H47","v":18.892286040116716}]
[6,7.3618702661808477,8.3205569610317145,28.192614792853561,null,null,2,{"$f":"H48+B36","v":28.192614792853561}]
[null,null,null,null,null,"Effective red2",2,{"$f":"H49","v":28.192614792853561}]
[null,null,null,null,null,null,2,{"$f":"H50+B13+B14-2","v":31.192614792853561}]
[]
[null,null,null,null,null,"Phase duration components"]
[null,null,null,null,null,"Lost time, l1",1,{"$f":"B39","v":17.830744526672714}]
[null,null,null,null,5,null,1,{"$f":"H54+B6","v":19.830744526672714}]
[null,null,null,null,null,"Green service time, gs",1,{"$f":"H55","v":19.830744526672714}]
[null,null,null,null,null,null,1,{"$f":"H56+B24","v":21.598835915901603}]
[null,null,null,null,null,"Green extension time, ge",1,{"$f":"H57","v":21.598835915901603}]
[null,null,null,null,null,null,1,{"$f":"H58+B29","v":27.131073279409563}]
[null,null,null,null,null,"Y+Rc",1,{"$f":"H59","v":27.131073279409563}]
[null,null,null,null,null,null,1,{"$f":"H60+B13+B14","v":32.131073279409563}]