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Q&A and M/D/1 Queues
CMSC 12100 / CAPP 30121 - Computer Science with Applications I
Q&A and M/D/1 Queues CMSC 12100 / CAPP 30121 - Computer Science - - PowerPoint PPT Presentation
Q&A and M/D/1 Queues CMSC 12100 / CAPP 30121 - Computer Science - - PowerPoint PPT Presentation
Q&A and M/D/1 Queues CMSC 12100 / CAPP 30121 - Computer Science with Applications I Q&A M/D/1 Queues Stack data type A stack is a sequence of items which are added (pushed) to the top of the stack and removed PUSH POP (popped)
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M/D/1 Queues
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Stack data type
BOTTOM TOP BOTTOM TOP PUSH POP
A stack is a sequence of items which are added (pushed) to the top of the stack and removed (popped) from the top.
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Queue data type
A queue is a sequence of items which are added (enqueued) to the back of the queue and removed (dequeued) from the front.
BACK FRONT BACK FRONT DEQUEUE ENQUEUE
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Queue data type
We can use queues to model many real-world processes, such as waiting in line to check in at the airport or waiting to vote at a polling station. These processes often differ in the following aspects:
BACK FRONT
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Queue data type
We can use queues to model many real-world processes, such as waiting in line to check in at the airport or waiting to vote at a polling station. These processes often differ in the following aspects:
- The number of servers
BACK FRONT
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Queue data type
We can use queues to model many real-world processes, such as waiting in line to check in at the airport or waiting to vote at a polling station. These processes often differ in the following aspects:
- The number of servers
- The service time
BACK FRONT
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Queue data type
We can use queues to model many real-world processes, such as waiting in line to check in at the airport or waiting to vote at a polling station. These processes often differ in the following aspects:
- The number of servers
- The service time
- The rate of arrival
BACK FRONT
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M/D/1 queue
In this lecture, we’re going to simulate the movement of customers through an M/D/1 queue.
- Customer arrivals follow a Markov process (M) with parameter 𝜇. We will
draw customer interarrival times from an exponential distribution with parameter 𝜇.
- The service time of each customer is deterministic (D) with parameter 𝜈.
Service will take time 1/𝜈 for every customer.
- There is only one (1) server.
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Example
Let’s say our probability distribution generates the interarrival times 2, 2, and 6. These are the time since last arrival, so we have three customers arriving at times 2, 4, and 10. Let’s also say that service time is exactly 3.
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Example
Time
M/D/1 queue
BACK
3 2 1
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Example
Time 1
M/D/1 queue
BACK
3 2 1
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Example
Time 1 2 Customer 1 arrives, starts service
M/D/1 queue
BACK
1 3 2
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Example
Time 1 2 Customer 1 arrives, starts service 3
M/D/1 queue
BACK
1 3 2
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Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives
M/D/1 queue
BACK
1 2 3
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Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service
M/D/1 queue 1
BACK
2 3
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Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service 6
M/D/1 queue 1
BACK
2 3
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Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service 6 7
M/D/1 queue 1
BACK
2 3
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2
Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service 6 7 8 Customer 2 departs
M/D/1 queue
BACK
1 3
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2
Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service 6 7 8 Customer 2 departs 9
M/D/1 queue
BACK
1 3
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Example
Time 1 2 Customer 1 arrives, starts service 3 4 Customer 2 arrives 5 Customer 1 departs, Customer 2 starts service 6 7 8 Customer 2 departs 9 10 Customer 3 arrives, starts service
M/D/1 queue
BACK
3 21