• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  • Level: GCSE
  • Subject: Maths
  • Word count: 2957

Decision and Discrete.

Extracts from this document...

Introduction

Name: Minesh Mepa                Centre Number: - 20780

        Decision and Discrete 1 Coursework: - Queuing Problem

DECISION AND DISCRETE 1 COURSEWORKBY MINESH MEPA

What is simulation?

I am running a simulation by generating random numbers on my calculator and by doing this I can work out the solution to my problem.

The problem

For this piece of coursework, we had to go into a place (possibly a store), which had a queuing problem in there. This was so that we could then simulate the times in, which a customer entered the shop, and simulate the time in which, the person gets served.

        For my piece of coursework, I decided to go into Greggs; I decided to go at lunchtime. This is because the shop would mostly get crowded then, so it would be a good idea to do it at lunchtime and simulate the problem.

        When I went in the shop to collect the data, there wasn’t much of a queue, but then it gradually began to grow, and it grew to upto the entrance.

        There were only three servers in the shop, but only one server was open at the time, although there was a lot of staff serving behind the one server.

I noted the arrival and serving times of 50 people.

...read more.

Middle

0.01

1.54.58

1.55.12

0.14

After I had collected the above data, I had to put the data into groups so that it would be easier for simulation. Before I could put the data into groups, I tallied the different seconds up into a table. This was so that I could know the size to put the groups at. For example, if there were a lot of values between 0 and 10, I would size the groups like 0-2, 2-5, and 5-10, but if there weren’t any values for a certain length such as from 20 to 40, I would size the groups into bigger numbers such as 20-30 and 31-40, etc.

        The following are the tables for the IATs and the serving times. The first table is for the IATs and the second table is for the serving times: -

IAT (SECS)

FREQUENCY

1

5

2

10

3

1

4

1

5

3

6

0

7

1

8

0

9

0

10

1

11

3

12

2

13

0

14

1

15

1

16

0

17

0

18

0

19

0

20

1

21

0

22

1

23

0

24

0

25

2

26

1

27

1

28

0

29

0

30

0

31

0

32

1

33

1

34

0

35

0

36

1

37

2

38

1

39

0

40

0

41

0

42

0

43

0

44

0

45

0

46

1

47

1

48

1

49

0

50

1

51

1

52

1

SERVING TIMES

FREQUENCY

1

0

2

0

3

0

4

0

5

0

6

0

7

1

8

0

9

3

10

2

11

5

12

5

13

3

14

2

15

3

16

4

17

2

18

3

19

3

20

0

21

4

22

3

23

0

24

2

25

1

26

2

27

0

28

0

29

0

30

0

31

0

32

0

33

0

34

0

35

0

36

0

37

0

38

0

39

0

40

1

From the above tables, I can make the groups and extend my coursework. I am now going to group the IATs and the service times, so that I can work the percentage and the cumulative percentage as well.

IATs

FREQUENCY

Percentage

RN #

MID POINT

1-3

16

32

00 - 31

2

4-6

5

10

32 - 41

5

7-10

2

4

42 - 45

9

11-13

5

10

46 - 54

12

14-19

3

6

55 - 60

17

20-24

2

4

61 - 64

22

25-30

5

10

65 - 74

28

31-38

6

12

75 - 86

35

39-52

6

12

87 - 100

46

...read more.

Conclusion

There was a major change to the length of the queue when the second sever was introduced. However, there was a lot of idle time.

        To see what the effect would be on the serving time, idle time, and the q length, I decided to introduce a third server.

By introducing the third server, I got the following results: -

  • Average Q Time
  • Idle server time 1
  • Idle server time 2
  • Idle server time 3
  • Average Service Time

Average Q Time      =

   Total Q Time

         =

23

0.46

Total Number of customers

50

Average Idle            =

   Total Idle Server Time 1

         =

552

11.04

Server Time 1

Total Number of customers

50

Average Idle            =

   Total Idle Server Time 2

         =

568

11.36

Server Time 2

Total Number of customers

50

Average Idle            =

   Total Idle Server Time 3

         =

559

11.18

Server Time 3

Total Number of customers

50

Average                   =

   Total Service Time

         =

821

16.42

Service Time

Total Number of customers

50

As you can see by introducing the third sever into the shop, there hardly is a queue or the waiting time. You can also identify that the average service time has also been decreased as well.

Solution

However, introducing a third server into the shop would cause some servers such as server 2 and 3 to have a lot of idle time. Because of this, I have changed the actual rule, the new rule for the solution is: -

Have two servers open, if both are free go to server 1, if not, go the server, which has the least queue. If the queue lengthens up to the entrance of the shop, then introduce the third server.

The reason why I have changed the rule so that they only open the third server when it gets busy is so that it will reduce the actual idle time, which is given.

Candidate Number: - 2273                Page  of

...read more.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE T-Total essays

  1. Urban Settlements have much greater accessibility than rural settlements. Is this so?

    Towards Dartford... Cars: Vans: Buses: Motorbikes: Pushbikes: |||||||| Total: 8 Total: 0 Total: 0 Total: 0 Total: 0 Overall South Darenth has a relatively low traffic density. Sketch Maps to Show Count Locations (Traffic and Pedestrian): Bexley: 1. 2. 3.

  2. T-Shapes Coursework

    30 150 50 200 50 250 70 320 70 350 90 440 90 450 110 560 110 550 130 680 b) Here are the results of the 5 calculations for a 7x1 "T" on Width 20 Grid: Middle Number Sum of Wing Sum of Tail Total Sum (Wing + Tail)

  1. T-Shapes Coursework

    36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 2nd T-Shape: T-Total 10

  2. Maths Coursework T-Totals

    This will also work in reverse, as we can find any T-Number's value at any time by using v-g. Translations Vertical Again, we shall use our standard gird size and position to establish our basic starting point; 1 2 3 4 5 6 7 8 9 10 11 12 13

  1. T-Total Coursework

    88 89 90 91 92 93 94 95 96 97 98 99 We will start again with the T-Shape with the lowest T-Number, which will be 24. The T-Total would be 1 + 2 + 3 + 13 + 24 = 43 We can again use the longer formula as

  2. Maths coursework

    at the base of the t-shape N- 8: this is the number above N and in each case, to get back to N you have to minus 8 N- 17: this is the number left of N - 16 and in each case, to get back to N you have

  1. I am going to investigate how changing the number of tiles at the centre ...

    This tells you the formula is based on N�. The second difference is 4 and you divide this by 2, to get 2. This is the multiplier of N�, so you should now have 2N�. You will then need to find the second part of the equation, this will be

  2. ICT Coursework: Data Management Systems

    The software I require is Microsoft Excel, a spreadsheet package. I am going to use this as it can be used to do many calculations automatically, and I am familiar with the package. The sources of input data for this product are as follows: * The price the customer buys

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work