EXP-6

14-12-2024

Name : YUGABHARATHI M

REG: 24900675

Series Queues with infinite capacity - Open Jackson Network

Aim :

To find (a) average number of materials in the system (b) average number of materials in the each conveyor of (c) waiting time of each material in the system (d) waiting time of each material in each conveyor, if the arrival of materials follow Poisson process with the mean interval time 12 seconds, service time of lathe machine in series follow exponential distribution with service time 1 second, 1.5 seconds and 1.3 seconds respectively and average service time of robot is 7 seconds.

Software required :

Visual components and Python

Theory

Procedure :

Experiment:

**Developed by: CH.Dinesh Kumar **Register No:24000305

Program

arr_time=float(input("Enter the mean inter arrival time of objects from Feeder (in secs): "))

ser_time1=float(input("Enter the mean inter service time of Lathe Machine 1 (in secs) : "))

ser_time2=float(input("Enter the mean inter service time of Lathe Machine 2 (in secs) : "))

ser_time3=float(input("Enter the mean inter service time of Lathe Machine 3 (in secs) : "))

Robot_time=float(input("Enter the Additional time taken for the Robot (in secs) : "))

lam=1/arr_time

mu1=1/(ser_time1+Robot_time)

mu2=1/(ser_time2+Robot_time)

mu3=1/(ser_time3+Robot_time)

print("-----------------------------------------------------------------------")

print("Series Queues with infinite capacity- Open Jackson Network")

print("-----------------------------------------------------------------------")

if (lam < mu1) and (lam < mu2) and (lam < mu3):

Ls1=lam/(mu1-lam)
Ls2=lam/(mu2-lam)
Ls3=lam/(mu3-lam)
Ls=Ls1+Ls2+Ls3
Lq1=Ls1-lam/mu1
Lq2=Ls2-lam/mu2
Lq3=Ls3-lam/mu3
Wq1=Lq1/lam
Wq2=Lq2/lam
Wq3=Lq3/lam
Ws=Ls/(3*lam)
print("Average number of objects in the system S1 : %0.2f "%Ls1)
print("Average number of objects in the system S2 : %0.2f "%Ls2)
print("Average number of objects in the system S3 : %0.2f "%Ls3)
print("Average number of objects in the overall system    : %0.2f "%Ls)
print("Average number of objects in the conveyor S1  :  %0.2f "%Lq1)
print("Average number of objects in the conveyor S2  :  %0.2f "%Lq2)
print("Average number of objects in the conveyor S3  :  %0.2f "%Lq3)
print("Average waiting time of an object in the conveyor S1 : %0.2f secs"%Wq1)
print("Average waiting time of an object in the conveyor S2 : %0.2f secs"%Wq2)
print("Average waiting time of an object in the conveyor S3 : %0.2f secs"%Wq3)

else:

print("Warning! Objects Over flow will happen in the conveyor")

print("----------------------------------------------------------------------")

Output

Enter the mean inter arrival time of objects from Feeder (in secs): 12

Enter the mean inter service time of Lathe Machine 1 (in secs) : 1

Enter the mean inter service time of Lathe Machine 2 (in secs) : 1.5

Enter the mean inter service time of Lathe Machine 3 (in secs) : 1.3

Enter the Additional time taken for the Robot (in secs) : 7

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Series Queues with infinite capacity- Open Jackson Network

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Average number of objects in the system S1 : 2.00

Average number of objects in the system S2 : 2.43

Average number of objects in the system S3 : 2.24

Average number of objects in the overall system : 6.67

Average number of objects in the conveyor S1 : 1.33

Average number of objects in the conveyor S2 : 1.72

Average number of objects in the conveyor S3 : 1.55

Average waiting time of an object in the conveyor S1 : 16.00 secs

Average waiting time of an object in the conveyor S2 : 20.64 secs

Average waiting time of an object in the conveyor S3 : 18.62 secs

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Result

The average number of material in the system and in the conveyor and waiting time are succesfully found.