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					Problem Description:


Travelers come to the airport in every 4 minutes (distributed exponentially). After the

travelers arrived to the airport they need to check-in, that takes between 1 and 2 minutes

(distributed uniformly).

There are 10 agents in the check-in section. The travelers wait in one queue until one of

the agents is available.

The probability of carrying weapon is 0.1%. Any metal material may activate the metal

detector at the check-in point, than with probability of 0.4 something triggers the alarm.

If the alarm sounds, the travelers walk through the metal detector once more. With

probability 0.1 the alarm sounds again (i.e. if the traveler is not carrying a weapon). If the

traveler is indeed carrying a weapon, the alarm will sound on both occasions with

probability of 1.

After this second inspection if the alarm sounds, the traveler is detected by another means

that takes 1 and 2 minutes (uniformly distributed).

The time take to walk through the metal detector takes 2 seconds.

We model this system, using ARENA. We run the model for a time period of 4 days, 8

replicates.

We need to collect statistics on the following parameters:

1. Flow time of a customer

2. 2. Queue length

3. Number of times alarm sounded and it was false in the period of 4 days

4. Number of times alarm sounded and it was true in the period of 4 days

5. Utilization of the individual agents
    6.   Do you think we should do away with the metal detector based on the frequency of

         the alarms?




    Problem Logic:

                                                 Chance
Arrive   Delay           Chance
 rri
A ve 1    N
         UIF( 1, 2)                              Wit h 0.4
                                                  ls
                                                 Ee
                      Wit h 0.001
                      Ee
                       ls                                    Assign              ?                                                                                                                0
                                                             alarm


                                                             Assign         Inspect                                                                                         Tally          Depart
                                                             alarm                                    Choose                                                                    _ti
                                                                                                                                                                            flow me          epart
                                                                                                                                                                                            D 1
                                                                            metal_detector
                                                                                                                  Count
                                                             Assign                          If carry_w
                                                                                             Ee
                                                                                              ls
                                                                                                       eapon==1    it eapon_alarm
                                                                                                                  wh_w
                                                             alarm
                                                             carry_weapon
                                                                                                                  Count                                 Server
                                                                                                                  it
                                                                                                                  whout_weapon_alarm                     Server 1
                                                                                                                                              Choose
                                                                                                                                                                Assign
                                                                                                                                       If go_again<1           go_again
                                                                                                                                        ls
                                                                                                                                       Ee




                                Simulate
                                ir     ssi
                               A port A gnment
                               60*24*4                                                                                                                                      Choose
                                                                                                                                                       If carry_weapon==1
                                                                                                                                                        ls
                                                                                                                                                       Ee




                                                                                                                                                                                         Chance

                                                                                                                                                                                      Wit h 0.1
                                                                                                                                                                                       ls
                                                                                                                                                                                      Ee


                                                                                                                                                                                                      Assign
                                                                                                                                                                                                      alarm




    Problem modeling:
    1. Arrive 1- assign the following attribute
   go_again = 0 ; Initialize the attribute to 0. This attribute is to classify the

    passenger who went throw the metal detector

   arrival_time = tnow; to store the arrival time of each passenger

   alarm = 0    ; Initialize the attribute to 0. for probability of alarm (faliur), when

    passenger go through the metal detector

   carry_weapon = 0; Initialize the attribute to 0. This attribute is to classify the

    passengers that carry weapons.

2 Delay

   expression=UNIF(1,2):Assign the time to reach check-in point from the enterence

    door as expression that is uniformly distributed between 1 and 2 minutes.

3 Chance

   with 0.1=carry_weapon :

   else=not carry_weapon: assign 2 branches as with probability 0.1% that people

    carry weapon and else that people does not carry weapon.

4 Assign

   carry_weapon=1

    alarm=1 : assign attributes carry_weapon and alarm to 1 because this assignment

    comes from the branch that entity carries weapon and alarm sounds.

5   Chance

   with = 0.4: assign the entity does not carry weapon with probability 0.4, shortly

    after this initialize the attribute to 1. Because this is the probability of people does

    not carry weapon and alarm sounds.

   else : assign entity does not carry weapon and the alarm does not sound. And
           initialize the attribute alarm to 0.

   6       Inspect

          station called




Replications                 Flow                   Queue
                             Time                   Length
                     Min     Max        Mean      Min   Max   Mean False   True      Agent
                                                                   Alarm   Alarm   utilization

       1          1.0344    3.9678     1.6201     0     0      0    618      6      0.01131
       2          1.0338    3.9098     1.6134     0     0      0    631      6      0.01180
       3          1.0338    3.7440     1.5871     0     0      0    585      4      0.01135
       4          1.0336    2.0000     0.0113     0     0      0    595      0      0.11340
       5          1.0346    3.8626     1.6038     0     0      0    601      4      0.11380
       6          1.0347    3.9402     1.6003     0     0      0    613      8      0.11570
       7          4.1707    1.0335     1.6220     0     0      0    658      4      0.01174
       8          1.0333    3.8494     1.6147     0     0      0    618      6      0.11310
  Average         1.4261    3.2884     1.4091     0     0      0    615    4.75     0.06278
Simulation Verification:



I will verify the number of false alarm. We know that with probability of 0.4 the alarm

will ring, and from this probability the alarm will sound again with probability of 0.1.

to calculate the number of false alarms we need to find out the total number of traveler

that went through the system. This number can be taken from the our report(the counter

in the depart block) after we run the program. Therefore the formula to find the number

of false alarm is:

# of false alarms = # of passengers checking in  [0.4+ (0.4  0.1)]

The average # of traveler = total travelers / # of replications = 11407/8 = 1425.875

1425.875  [0.4+ (0.4  0.1)] = 627.385

We can see that our verification results are matching with the results from the simulation

report, 627.385  615 (average false alarms from the table).
.
                              ARENA Simulation Results
                              T-230 - License #9400000

                         Summary for Replication 1 of 8

Project:   Airport Assignme                     Run execution date :   4/ 2/2000
Analyst:   talaysun                             Model revision date:   4/ 2/2000

Replication ended at time       : 5760.0
                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000      1954
flow_time                1.6201      .02274       1.0344      3.9687      1392
Server 1_R_Q Queue Tim   .00000      (Insuf)      .00000      .00000        62

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01131      7.8857E-04   .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)      .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01662      (Insuf)      .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm           618     Infinite
                    travelers                     1392     Infinite
                    with_weapon_alarm                6     Infinite

Beginning replication 2 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 2 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000      3993
flow_time                1.6165      .01538       1.0338      3.9687      2858
Server 1_R_Q Queue Tim   .00000      (Insuf)      .00000      .00000       126

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01155      3.6133E-04   .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)      .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01678      (Insuf)      .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm          1249     Infinite
                    travelers                     2858     Infinite
                    with_weapon_alarm               12     Infinite
Beginning replication 3 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 3 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000      5954
flow_time                1.6067      .01292       1.0338      3.9687      4277
Server 1_R_Q Queue Tim   .00000      (Insuf)      .00000      .00000       173

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01149      3.7198E-04   .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)      .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01537      .00284       .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm          1834     Infinite
                    travelers                     4277     Infinite
                    with_weapon_alarm               16     Infinite

Beginning replication 4 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 4 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000      7914
flow_time                1.6060      .01082       1.0336      3.9687      5705
Server 1_R_Q Queue Tim   .00000      (Insuf)      .00000      .00000       236

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01145      2.6722E-04 .00000        2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)    .00000        .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01567      .00208       .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm          2429     Infinite
                    travelers                     5705     Infinite
                    with_weapon_alarm               16     Infinite

Beginning replication 5 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 5 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000      9880
flow_time                1.6055      .01072       1.0336      3.9687      7125
Server 1_R_Q Queue Tim   .00000      (Insuf)      .00000      .00000       295

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01144      2.2985E-04   .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)      .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01553      .00179       .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm          3030     Infinite
                    travelers                     7125     Infinite
                    with_weapon_alarm               20     Infinite

Beginning replication 6 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 6 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier               Average    Half Width    Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000      .00000      .00000     11880
flow_time                1.6046      .00896      1.0336      3.9687      8564
Server 1_R_Q Queue Tim   .00000      .00000      .00000      .00000       355

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01146      (Corr)      .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)     .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)     10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)     10.000      10.000     10.000
Server 1_R Busy          .01551      .00157      .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)     .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm         3643     Infinite
                    travelers                    8564     Infinite
                    with_weapon_alarm              28     Infinite

Beginning replication 7 of 8

                               ARENA Simulation Results
                               T-230 - License #9400000

                         Summary for Replication 7 of 8

Project:   Airport Assignme                      Run execution date :    4/ 2/2000
Analyst:   talaysun                              Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000      .00000      .00000     13909
flow_time                1.6070      .00893      1.0335      3.9687     10006
Server 1_R_Q Queue Tim   .00000      .00000      .00000      .00000       430

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01150      (Corr)      .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)     .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)     10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)     10.000      10.000     10.000
Server 1_R Busy          .01610      .00157      .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)     .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm          4301    Infinite
                    travelers                    10006    Infinite
                    with_weapon_alarm               32    Infinite

Beginning replication 8 of 8
                              ARENA Simulation Results
                              T-230 - License #9400000

                         Summary for Replication 8 of 8

Project:   Airport Assignme                       Run execution date :    4/ 2/2000
Analyst:   talaysun                               Model revision date:    4/ 2/2000

Replication ended at time         : 5760.0

                                    TALLY VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Observations
_______________________________________________________________________________

metal_detector_R_Q Que   .00000      .00000       .00000      .00000     15864
flow_time                1.6078      .00932       1.0333      3.9687     11407
Server 1_R_Q Queue Tim   .00000      .00000       .00000      .00000       500

                              DISCRETE-CHANGE VARIABLES

Identifier              Average   Half Width Minimum     Maximum   Final Value
_______________________________________________________________________________

metal_detector_R Busy    .01148      2.0260E-04   .00000      2.0000     .00000
# in Server 1_R_Q        .00000      (Insuf)      .00000      .00000     .00000
metal_detector_R Avail   10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Available     10.000      (Insuf)      10.000      10.000     10.000
Server 1_R Busy          .01644      .00159       .00000      2.0000     .00000
# in metal_detector_R_   .00000      (Insuf)      .00000      .00000     .00000

                                      COUNTERS

                    Identifier                Count   Limit
                    _________________________________________

                    without_weapon_alarm           4919    Infinite
                    travelers                     11407    Infinite
                    with_weapon_alarm                38    Infinite


Simulation run time: 0.27 minutes.
Simulation run complete.

				
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