Question Consider the main gate of a campus university where the security officers perform two types of security checks: ID Check (IDC) and Automobile Trunk Check (ATC). Suppose that the system works as follows. The security checks are performed consecutively, i.e. incoming cars must pass the IDC before an ATC is performed. There are two types of cars arriving to the university: regular cars (RC) and suspicious cars (SC). Both regular and suspicious cars must pass the IDC before entering the university. On the other hand, ATC is only performed on suspicious cars. Thus, the regular cars are allowed to enter the university after IDC, whereas the suspicious cars are directed to the parking area where another security officer performs the ATC. Once both security checks are completed, the suspicious cars are also allowed to enter the university. For simplicity, assume that there are two security officers in this system. The first officer (501) handles IDC at the main gate and the second officer (SO2) handles ATC at the parking area. Basically, they cannot help each other. Both types of cars are served according to FIFO rule for both security checks. The system is empty and the resources are idle at time 0. The following tables show the arrival times (Not interarrival times! Arrival times are given directly) and the service times of the cars. All time units are given in minutes. Arrival Times Suspicious cars (SC) Regular cars (RC) 1 1.00 2.00 8.50 8.00 N 3 10.00 15.00 4 16.00 18.00 Service Times ID Check (IDC) Automobile Trunk Check (ATC) Suspicious cars (SC) Regular cars (RC) Suspicious cars (SC) 1 2.00 6.00 3.00 2 2 3.50 0.50 5.00 3 3 2.50 3.50 1.50 4 1.50 9.00 3.00 The primary events of the simulation and the abbreviations used to represent those events are given as follows: Arrival of regular cars (RC Arr) Arrival of a suspicious cars (SC_Arr) End of Automobile Trunk Check (End_ATC) End of ID Check (End_IDC) a) Fill in the simulation table given in the Excel document Hand Simulation Sheet" (available on Moodle). Run the simulation for 15 minutes. Please keep only the required statistics (see parts b and c). The meaning of each column header in the Excel file is given below and also in the file itself. B_SO2(t) a variable denoting whether the second officer is busy or not (In Queue)IDC shows the entity (with type and arrival time) in the IDC queue (In Queue)ATC shows the entity in the ATC queue In IDC shows the entity at IDC In ATC shows the entity at ATC N(IDC) number of entities that passed the queue of IDC EWQ (IDC) total waiting time in the queue of IDC [B_SO2 area under B(t) curve which is used to calculate the utilization of the second officer b) What is the average waiting time for the first officer? Show all your work. c) Calculate the utilization of the second officer. Show all your work. x] 5 = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER f! Calibri 11 AR A Metni kaydr Genel LP Yaptr c Birlestir ve Otala Ekle 78 Sil % Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Otomatik Toplam Doldur - Srala ve Filtre Bul ve Temizle - Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler A AE74 fic V F H 1 P R R S T A B D 1 Just-Finished Event 2 2 Entity Entity Type Time (t) Event Type E state Variable B_302t) Attributes (in Queue}ATC L statistical Accumulatora NIDC) WQ (IDC) B_302 M N O Event Calendar Entity No. Entity Type Time In Queue DC In IDC In ATC Event Type 45 15,00 End 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 b) c) Primary Events: Arrival of regular cars(RC_Aer) Arrival of a suspicious cars (SC_Aer) End of Automobile Trunk Check (End_ATC) End of ID Check (End_IDC) Average waiting time for the first officer utilization of the second officer 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 B 902/0) a variable denoting whether the second officer is busy or not (In Queue IDC shows the entity with type and arrival time in the IDC queue (in Queue ATC shows the entity in the ATC queue In DC shows the entity at IDC In ATC shows the entity at ATC N(IDC) number of entities that passed the queue of IDC WQ (IDC) total waiting time in the queue of IDC B_S02 area under B[t) curve which is used to calculate the utilization of the second officer Hand Simulation HAZIR HH EL 1 + %62 ORI XV wlos () TUR TUR 16:52 x] HS = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER f! Otomatik Toplam Calibri 11 AR A Metni kaydr Genel LP Doldur - Yaptr Birlestir ve Otala 0 Ekle 68 Sil % Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Temizle - Srala ve Filtre Bul ve Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler AE74 fic F H 1 P R S T E state Variable B_302t) 0 G Attributes (In Queue ATC L Statistical Accumulators NIDC) TWQ (DC) B_S02 0,00 0,00 M N Event Calendar Entity No. Entity Type | Time (In Queue DC In IDC In ATC Event Type Arrival Time IDC Se 1.00 SC Cars 1 2 3 4 8,50 10,00 16,00 IDC Se RC Cars 1 1 2 Arrival Time 2.00 8,00 15,00 18,00 4 A B D 1 Just-Finished Event 2 2 Entity Entity Type Time to Event Type 3 0.00 Initialization 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 Hand Simulation HAZIR EL 1 + %62 ORI xlwl 02 . () TUR 16:52 x] HS = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER It Otomatik Toplarm Calibri 11 AR A Metni kaydr Genel H Doldur Yaptr K TA Sil Ekle Birlestir ve Otala D% 78 Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Temizle - Srala ve Filtre Bul ve Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler AE74 X fir M N P R S T U V w X Y z AA AB AC AD AE AF AG AH Al Event Calendar Time Entity No. Entity Type Event Type SC Cars 1 2 3 4 Arrival Time 1.00 8.50 10,00 16.00 IDC Service Time 2.00 3,50 2,50 1.50 ATC Service Time 3,00 5,00 1,50 3,00 RC Cars 1 2 3 4 Arrival Time 2.00 3.00 15,00 18.00 IDC Service Time 6.00 0,50 3,50 9.00 K L 1 stical Accumulators 2 ( WQ (IDC) B_SO2 0.00 0,00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ww 39 40 41 Hand Simulation HAZIR I + %62 gi xlwl 02 0 () TUR 16:52 Question Consider the main gate of a campus university where the security officers perform two types of security checks: ID Check (IDC) and Automobile Trunk Check (ATC). Suppose that the system works as follows. The security checks are performed consecutively, i.e. incoming cars must pass the IDC before an ATC is performed. There are two types of cars arriving to the university: regular cars (RC) and suspicious cars (SC). Both regular and suspicious cars must pass the IDC before entering the university. On the other hand, ATC is only performed on suspicious cars. Thus, the regular cars are allowed to enter the university after IDC, whereas the suspicious cars are directed to the parking area where another security officer performs the ATC. Once both security checks are completed, the suspicious cars are also allowed to enter the university. For simplicity, assume that there are two security officers in this system. The first officer (501) handles IDC at the main gate and the second officer (SO2) handles ATC at the parking area. Basically, they cannot help each other. Both types of cars are served according to FIFO rule for both security checks. The system is empty and the resources are idle at time 0. The following tables show the arrival times (Not interarrival times! Arrival times are given directly) and the service times of the cars. All time units are given in minutes. Arrival Times Suspicious cars (SC) Regular cars (RC) 1 1.00 2.00 8.50 8.00 N 3 10.00 15.00 4 16.00 18.00 Service Times ID Check (IDC) Automobile Trunk Check (ATC) Suspicious cars (SC) Regular cars (RC) Suspicious cars (SC) 1 2.00 6.00 3.00 2 2 3.50 0.50 5.00 3 3 2.50 3.50 1.50 4 1.50 9.00 3.00 The primary events of the simulation and the abbreviations used to represent those events are given as follows: Arrival of regular cars (RC Arr) Arrival of a suspicious cars (SC_Arr) End of Automobile Trunk Check (End_ATC) End of ID Check (End_IDC) a) Fill in the simulation table given in the Excel document Hand Simulation Sheet" (available on Moodle). Run the simulation for 15 minutes. Please keep only the required statistics (see parts b and c). The meaning of each column header in the Excel file is given below and also in the file itself. B_SO2(t) a variable denoting whether the second officer is busy or not (In Queue)IDC shows the entity (with type and arrival time) in the IDC queue (In Queue)ATC shows the entity in the ATC queue In IDC shows the entity at IDC In ATC shows the entity at ATC N(IDC) number of entities that passed the queue of IDC EWQ (IDC) total waiting time in the queue of IDC [B_SO2 area under B(t) curve which is used to calculate the utilization of the second officer b) What is the average waiting time for the first officer? Show all your work. c) Calculate the utilization of the second officer. Show all your work. x] 5 = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER f! Calibri 11 AR A Metni kaydr Genel LP Yaptr c Birlestir ve Otala Ekle 78 Sil % Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Otomatik Toplam Doldur - Srala ve Filtre Bul ve Temizle - Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler A AE74 fic V F H 1 P R R S T A B D 1 Just-Finished Event 2 2 Entity Entity Type Time (t) Event Type E state Variable B_302t) Attributes (in Queue}ATC L statistical Accumulatora NIDC) WQ (IDC) B_302 M N O Event Calendar Entity No. Entity Type Time In Queue DC In IDC In ATC Event Type 45 15,00 End 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 b) c) Primary Events: Arrival of regular cars(RC_Aer) Arrival of a suspicious cars (SC_Aer) End of Automobile Trunk Check (End_ATC) End of ID Check (End_IDC) Average waiting time for the first officer utilization of the second officer 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 B 902/0) a variable denoting whether the second officer is busy or not (In Queue IDC shows the entity with type and arrival time in the IDC queue (in Queue ATC shows the entity in the ATC queue In DC shows the entity at IDC In ATC shows the entity at ATC N(IDC) number of entities that passed the queue of IDC WQ (IDC) total waiting time in the queue of IDC B_S02 area under B[t) curve which is used to calculate the utilization of the second officer Hand Simulation HAZIR HH EL 1 + %62 ORI XV wlos () TUR TUR 16:52 x] HS = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER f! Otomatik Toplam Calibri 11 AR A Metni kaydr Genel LP Doldur - Yaptr Birlestir ve Otala 0 Ekle 68 Sil % Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Temizle - Srala ve Filtre Bul ve Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler AE74 fic F H 1 P R S T E state Variable B_302t) 0 G Attributes (In Queue ATC L Statistical Accumulators NIDC) TWQ (DC) B_S02 0,00 0,00 M N Event Calendar Entity No. Entity Type | Time (In Queue DC In IDC In ATC Event Type Arrival Time IDC Se 1.00 SC Cars 1 2 3 4 8,50 10,00 16,00 IDC Se RC Cars 1 1 2 Arrival Time 2.00 8,00 15,00 18,00 4 A B D 1 Just-Finished Event 2 2 Entity Entity Type Time to Event Type 3 0.00 Initialization 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 Hand Simulation HAZIR EL 1 + %62 ORI xlwl 02 . () TUR 16:52 x] HS = ? . X Hand Simulation Sheet (2).xls [Uyumluluk Modu] - Excel GRNM DOSYA GR EKLE SAYFA DZEN FORMLLER VERI GZDEN GER It Otomatik Toplarm Calibri 11 AR A Metni kaydr Genel H Doldur Yaptr K TA Sil Ekle Birlestir ve Otala D% 78 Biim Koullu Tablo Olarak Hcre Biimlendirme Biimlendir - Stilleri Stiller Temizle - Srala ve Filtre Bul ve Uygula Se Dzenleme Pano Yaz Tipi Hizalama Sayi Hcreler AE74 X fir M N P R S T U V w X Y z AA AB AC AD AE AF AG AH Al Event Calendar Time Entity No. Entity Type Event Type SC Cars 1 2 3 4 Arrival Time 1.00 8.50 10,00 16.00 IDC Service Time 2.00 3,50 2,50 1.50 ATC Service Time 3,00 5,00 1,50 3,00 RC Cars 1 2 3 4 Arrival Time 2.00 3.00 15,00 18.00 IDC Service Time 6.00 0,50 3,50 9.00 K L 1 stical Accumulators 2 ( WQ (IDC) B_SO2 0.00 0,00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ww 39 40 41 Hand Simulation HAZIR I + %62 gi xlwl 02 0 () TUR 16:52
